## CryptoDB

### Recently updated IACR publications

CryptoDB is periodically updated by manual and automatic processes. Whenever a paper is added or modified it will appear in this list, e.g., when a video appears.

A separate history of changes tracks schema and process changes. There is further information about CryptoDB in the documentation.

Year
Venue
Title
2018
ASIACRYPT
Secure Computation with Low Communication from Cross-Checking
We construct new four-party protocols for secure computation that are secure against a single malicious corruption. Our protocols can perform computations over a binary ring, and require sending just 1.5 ring elements per party, per gate. In the special case of Boolean circuits, this amounts to sending 1.5 bits per party, per gate. One of our protocols is robust, yet requires almost no additional communication. Our key technique can be viewed as a variant of the “dual execution” approach, but, because we rely on four parties instead of two, we can avoid any leakage, achieving the standard notion of security.
2018
ASIACRYPT
2018
ASIACRYPT
Concretely Efficient Large-Scale MPC with Active Security (or, TinyKeys for TinyOT)
In this work we develop a new theory for concretely efficient, large-scale MPC with active security. Current practical techniques are mostly in the strong setting of all-but-one corruptions, which leads to protocols that scale badly with the number of parties. To work around this issue, we consider a large-scale scenario where a small minority out of many parties is honest and design scalable, more efficient MPC protocols for this setting. Our results are achieved by introducing new techniques for information-theoretic MACs with short keys and extending the work of Hazay et al. (CRYPTO 2018), which developed new passively secure MPC protocols in the same context. We further demonstrate the usefulness of this theory in practice by analyzing the concrete communication overhead of our protocols, which improve upon the most efficient previous works.
2018
ASIACRYPT
2018
ASIACRYPT
Non-interactive Secure Computation from One-Way Functions
The notion of non-interactive secure computation (NISC) first introduced in the work of Ishai et al. [EUROCRYPT 2011] studies the following problem: Suppose a receiver R wishes to publish an encryption of her secret input y so that any sender S with input x can then send a message m that reveals f(x, y) to R (for some function f). Here, m can be viewed as an encryption of f(x, y) that can be decrypted by R. NISC requires security against both malicious senders and receivers, and also requires the receiver’s message to be reusable across multiple computations (w.r.t. a fixed input of the receiver).All previous solutions to this problem necessarily rely upon OT (or specific number-theoretic assumptions) even in the common reference string model or the random oracle model or to achieve weaker notions of security such as super-polynomial-time simulation.In this work, we construct a NISC protocol based on the minimal assumption of one way functions, in the stateless hardware token model. Our construction achieves UC security and requires a single token sent by the receiver to the sender.
2018
ASIACRYPT
Simple and Efficient Two-Server ORAM
We show a protocol for two-server oblivious RAM (ORAM) that is simpler and more efficient than the best prior work. Our construction combines any tree-based ORAM with an extension of a two-server private information retrieval scheme by Boyle et al., and is able to avoid recursion and thus use only one round of interaction. In addition, our scheme has a very cheap initialization phase, making it well suited for RAM-based secure computation. Although our scheme requires the servers to perform a linear scan over the entire data, the cryptographic computation involved consists only of block-cipher evaluations.A practical instantiation of our protocol has excellent concrete parameters: for storing an N-element array of arbitrary size data blocks with statistical security parameter $\lambda$, the servers each store 4N encrypted blocks, the client stores $\lambda +2\log N$ blocks, and the total communication per logical access is roughly $10 \log N$ encrypted blocks.
2018
ASIACRYPT
More is Less: Perfectly Secure Oblivious Algorithms in the Multi-server Setting
The problem of Oblivious RAM (ORAM) has traditionally been studied in the single-server setting, but more recently the multi-server setting has also been considered. Yet it is still unclear whether the multi-server setting has any inherent advantages, e.g., whether the multi-server setting can be used to achieve stronger security goals or provably better efficiency than is possible in the single-server case.In this work, we construct a perfectly secure 3-server ORAM scheme that outperforms the best known single-server scheme by a logarithmic factor. In the process we also show, for the first time, that there exist specific algorithms for which multiple servers can overcome known lower bounds in the single-server setting.
2018
ASIACRYPT
A Universally Composable Framework for the Privacy of Email Ecosystems
Email communication is amongst the most prominent online activities, and as such, can put sensitive information at risk. It is thus of high importance that internet email applications are designed in a privacy-aware manner and analyzed under a rigorous threat model. The Snowden revelations (2013) suggest that such a model should feature a global adversary, in light of the observational tools available. Furthermore, the fact that protecting metadata can be of equal importance as protecting the communication context implies that end-to-end encryption may be necessary, but it is not sufficient.With this in mind, we utilize the Universal Composability framework [Canetti, 2001] to introduce an expressive cryptographic model for email “ecosystems” that can formally and precisely capture various well-known privacy notions (unobservability, anonymity, unlinkability, etc.), by parameterizing the amount of leakage an ideal-world adversary (simulator) obtains from the email functionality.Equipped with our framework, we present and analyze the security of two email constructions that follow different directions in terms of the efficiency vs. privacy tradeoff. The first one achieves optimal security (only the online/offline mode of the users is leaked), but it is mainly of theoretical interest; the second one is based on parallel mixing [Golle and Juels, 2004] and is more practical, while it achieves anonymity with respect to users that have similar amount of sending and receiving activity.
2018
ASIACRYPT
State Separation for Code-Based Game-Playing Proofs
The security analysis of real-world protocols involves reduction steps that are conceptually simple but still have to account for many protocol complications found in standards and implementations. Taking inspiration from universal composability, abstract cryptography, process algebras, and type-based verification frameworks, we propose a method to simplify large reductions, avoid mistakes in carrying them out, and obtain concise security statements.Our method decomposes monolithic games into collections of stateful packages representing collections of oracles that call one another using well-defined interfaces. Every component scheme yields a pair of a real and an ideal package. In security proofs, we then successively replace each real package with its ideal counterpart, treating the other packages as the reduction. We build this reduction by applying a number of algebraic operations on packages justified by their state separation. Our method handles reductions that emulate the game perfectly, and leaves more complex arguments to existing game-based proof techniques such as the code-based analysis suggested by Bellare and Rogaway. It also facilitates computer-aided proofs, inasmuch as the perfect reductions steps can be automatically discharged by proof assistants.We illustrate our method on two generic composition proofs: a proof of self-composition using a hybrid argument; and the composition of keying and keyed components. For concreteness, we apply them to the KEM-DEM proof of hybrid-encryption by Cramer and Shoup and to the composition of forward-secure game-based key exchange protocols with symmetric-key protocols.
2018
ASIACRYPT
Security of the Blockchain Against Long Delay Attack
The consensus protocol underlying Bitcoin (the blockchain) works remarkably well in practice. However proving its security in a formal setting has been an elusive goal. A recent analytical result by Pass, Seeman and shelat indicates that an idealized blockchain is indeed secure against attacks in an asynchronous network where messages are maliciously delayed by at most $\varDelta \ll 1/np$, with n being the number of miners and p the mining hardness. This paper improves upon the result by showing that if appropriate inconsistency tolerance is allowed the blockchain can withstand even more powerful external attacks in the honest miner setting. Specifically we prove that the blockchain is secure against long delay attacks with $\varDelta \ge 1/np$ in an asynchronous network.
2018
ASIACRYPT
Homomorphic Secret Sharing for Low Degree Polynomials
Homomorphic secret sharing (HSS) allows n clients to secret-share data to m servers, who can then homomorphically evaluate public functions over the shares. A natural application is outsourced computation over private data. In this work, we present the first plain-model homomorphic secret sharing scheme that supports the evaluation of polynomials with degree higher than 2. Our construction relies on any degree-k (multi-key) homomorphic encryption scheme and can evaluate degree-$\left( (k+1)m -1 \right)$ polynomials, for any polynomial number of inputs n and any sub-logarithmic (in the security parameter) number of servers m. At the heart of our work is a series of combinatorial arguments on how a polynomial can be split into several low-degree polynomials over the shares of the inputs, which we believe is of independent interest.
2018
ASIACRYPT
Constructing Ideal Secret Sharing Schemes Based on Chinese Remainder Theorem
Since (t, n)-threshold secret sharing (SS) was initially proposed by Shamir and Blakley separately in 1979, it has been widely used in many aspects. Later on, Asmuth and Bloom presented a (t, n)-threshold SS scheme based on the Chinese Remainder Theorem (CRT) for integers in 1983. However, compared with the most popular Shamir’s thresholdtn SS scheme, existing CRT based schemes have a lower information rate, moreover, they are harder to construct due to the stringent condition on moduli. To overcome these shortcomings of CRT based schemes, (1) we first propose a generalized (t, n)-threshold SS scheme based on the CRT for polynomial ring over a finite field. We show that our scheme is ideal, i.e., it is perfect in security and has the information rate 1. Comparison show that our scheme has a better information rate and is easier to construct compared with the existing threshold SS schemes based on the CRT for integers. (2) We prove that Shamir’s scheme, which is based on the Lagrange interpolation, is a special case of our scheme. Therefore, we establish the connection among threshold schemes based on the Lagrange interpolation, schemes based on the CRT for integers and our scheme. (3) As a natural extension of our threshold scheme, we present a weighted threshold SS scheme based on the CRT for polynomial rings, which inherits the above advantages of our threshold scheme over existing weighted schemes based on the CRT for integers.
2018
ASIACRYPT
Optimal Linear Multiparty Conditional Disclosure of Secrets Protocols
In a k-party CDS protocol, each party sends one message to a referee (without seeing the other messages) such that the referee will learn a secret held by the parties if and only if the inputs of the parties satisfy some condition (e.g., if the inputs are all equal). This simple primitive is used to construct attribute based encryption, symmetrically-private information retrieval, priced oblivious transfer, and secret-sharing schemes for any access structure. Motivated by these applications, CDS protocols have been recently studied in many papers.In this work, we study linear CDS protocols, where each of the messages of the parties is a linear function of the secret and random elements taken from some finite field. Linearity is an important property of CDS protocols as many applications of CDS protocols required it.Our main result is a construction of linear k-party CDS protocols for an arbitrary function $f:[N]^{k}\rightarrow \left\{ 0,1 \right\}$ with messages of size $O(N^{(k-1)/2})$ (a similar result was independently and in parallel proven by Liu et al. [27]). By a lower bound of Beimel et al. [TCC 2017], this message size is optimal. We also consider functions with few inputs that return 1, and design more efficient CDS protocols for them.CDS protocols can be used to construct secret-sharing schemes for uniform access structures, where for some k all sets of size less than k are unauthorized, all sets of size greater than k are authorized, and each set of size k can be either authorized or unauthorized. We show that our results imply that every k-uniform access structure with n parties can be realized by a linear secret-sharing scheme with share size $\min \left\{ (O(n/k))^{(k-1)/2},O(n \cdot 2^{n/2}) \right\}$. Furthermore, the linear k-party CDS protocol with messages of size $O(N^{(k-1)/2})$ was recently used by Liu and Vaikuntanathan [STOC 2018] to construct a linear secret-sharing scheme with share size $O(2^{0.999n})$ for any n-party access structure.
2018
ASIACRYPT
Towards Practical Key Exchange from Ordinary Isogeny Graphs
We revisit the ordinary isogeny-graph based cryptosystems of Couveignes and Rostovtsev–Stolbunov, long dismissed as impractical. We give algorithmic improvements that accelerate key exchange in this framework, and explore the problem of generating suitable system parameters for contemporary pre- and post-quantum security that take advantage of these new algorithms. We also prove the session-key security of this key exchange in the Canetti–Krawczyk model, and the IND-CPA security of the related public-key encryption scheme, under reasonable assumptions on the hardness of computing isogeny walks. Our systems admit efficient key-validation techniques that yield CCA-secure encryption, thus providing an important step towards efficient post-quantum non-interactive key exchange (NIKE).
2018
ASIACRYPT
CSIDH: An Efficient Post-Quantum Commutative Group Action
We propose an efficient commutative group action suitable for non-interactive key exchange in a post-quantum setting. Our construction follows the layout of the Couveignes–Rostovtsev–Stolbunov cryptosystem, but we apply it to supersingular elliptic curves defined over a large prime field $\mathbb F_p$, rather than to ordinary elliptic curves. The Diffie–Hellman scheme resulting from the group action allows for public-key validation at very little cost, runs reasonably fast in practice, and has public keys of only 64 bytes at a conjectured AES-128 security level, matching NIST’s post-quantum security category I.
2018
ASIACRYPT
Computing Supersingular Isogenies on Kummer Surfaces
We apply Scholten’s construction to give explicit isogenies between the Weil restriction of supersingular Montgomery curves with full rational 2-torsion over $\mathbb {F}_{p^2}$ and corresponding abelian surfaces over $\mathbb {F}_{p}$. Subsequently, we show that isogeny-based public key cryptography can exploit the fast Kummer surface arithmetic that arises from the theory of theta functions. In particular, we show that chains of 2-isogenies between elliptic curves can instead be computed as chains of Richelot (2, 2)-isogenies between Kummer surfaces. This gives rise to new possibilities for efficient supersingular isogeny-based cryptography.
2018
ASIACRYPT
Robustly Reusable Fuzzy Extractor from Standard Assumptions
A fuzzy extractor (FE) aims at deriving and reproducing (almost) uniform cryptographic keys from noisy non-uniform sources. To reproduce an identical key R from subsequent readings of a noisy source, it is necessary to eliminate the noises from those readings. To this end, a public helper string P, together with the key R, is produced from the first reading of the source during the initial enrollment phase.In this paper, we consider computational fuzzy extractor. We formalize robustly reusable fuzzy extractor (rrFE) which considers reusability and robustness simultaneously in the Common Reference String (CRS) model. Reusability of rrFE deals with source reuse. It guarantees that the key R output by fuzzy extractor is pseudo-random even if the initial enrollment is applied to the same source several times, generating multiple public helper strings and keys $(P_i,R_i)$. Robustness of rrFE deals with active probabilistic polynomial-time adversaries, who may manipulate the public helper string $P_i$ to affect the reproduction of $R_i$. Any modification of ${P}_i$ by the adversary will be detected by the robustness of rrFE. We show how to construct an rrFE from a Symmetric Key Encapsulation Mechanism (SKEM), a Secure Sketch (SS), an Extractor (Ext), and a Lossy Algebraic Filter (LAF). We characterize the key-shift security notion of SKEM and the homomorphic properties of SS, Ext and LAF, which enable our construction of rrFE to achieve both reusability and robustness.We present an instantiation of SKEM from the DDH assumption. Combined with the LAF by Hofheinz (EuroCrypt 2013), homomorphic SS and Ext, we obtain the first rrFE based on standard assumptions.
2018
ASIACRYPT
Simple and More Efficient PRFs with Tight Security from LWE and Matrix-DDH
We construct efficient and tightly secure pseudorandom functions (PRFs) with only logarithmic security loss and short secret keys. This yields very simple and efficient variants of well-known constructions, including those of Naor-Reingold (FOCS 1997) and Lewko-Waters (ACM CCS 2009). Most importantly, in combination with the construction of Banerjee, Peikert and Rosen (EUROCRYPT 2012) we obtain the currently most efficient LWE-based PRF from a weak LWE-assumption with a much smaller modulus than the original construction. In comparison to the only previous construction with this property, which is due to Döttling and Schröder (CRYPTO 2015), we use a modulus of similar size, but only a single instance of the underlying PRF, instead of parallel instances, where is the security parameter. Like Döttling and Schröder, our security proof is only almost back-box, due to the fact that the number of queries made by the adversary and its advantage must be known a-priori.Technically, we introduce all-prefix universal hash functions (APUHFs), which are hash functions that are (almost-)universal, even if any prefix of the output is considered. We give simple and very efficient constructions of APUHFs, and show how they can be combined with the augmented cascade of Boneh et al. (ACM CCS 2010) to obtain our results. Along the way, we develop a new and more direct way to prove security of PRFs based on the augmented cascade.
2018
ASIACRYPT
Simulatable Channels: Extended Security that is Universally Composable and Easier to Prove
Ever since the foundational work of Goldwasser and Micali, simulation has proven to be a powerful and versatile construct for formulating security in various areas of cryptography. However security definitions based on simulation are generally harder to work with than game based definitions, often resulting in more complicated proofs. In this work we challenge this viewpoint by proposing new simulation-based security definitions for secure channels that in many cases lead to simpler proofs of security. We are particularly interested in definitions of secure channels which reflect real-world requirements, such as, protecting against the replay and reordering of ciphertexts, accounting for leakage from the decryption of invalid ciphertexts, and retaining security in the presence of ciphertext fragmentation. Furthermore we show that our proposed notion of channel simulatability implies a secure channel functionality that is universally composable. To the best of our knowledge, we are the first to study universally composable secure channels supporting these extended security goals. We conclude, by showing that the Dropbear implementation of SSH-CTR is channel simulatable in the presence of ciphertext fragmentation, and therefore also realises a universally composable secure channel. This is intended, in part, to highlight the merits of our approach over prior ones in admitting simpler security proofs in comparable settings.
2018
ASIACRYPT
Block Cipher Invariants as Eigenvectors of Correlation Matrices
Best Paper Award
A new approach to invariant subspaces and nonlinear invariants is developed. This results in both theoretical insights and practical attacks on block ciphers. It is shown that, with minor modifications to some of the round constants, Midori-64 has a nonlinear invariant with $2^{96}$ corresponding weak keys. Furthermore, this invariant corresponds to a linear hull with maximal correlation. By combining the new invariant with integral cryptanalysis, a practical key-recovery attack on 10 rounds of unmodified Midori-64 is obtained. The attack works for $2^{96}$ weak keys and irrespective of the choice of round constants. The data complexity is $1.25 \cdot 2^{21}$ chosen plaintexts and the computational cost is dominated by $2^{56}$ block cipher calls. Finally, it is shown that similar techniques lead to a practical key-recovery attack on MANTIS-4. The full key is recovered using 640 chosen plaintexts and the attack requires about $2^{56}$ block cipher calls.
2018
ASIACRYPT
Practical Attacks Against the Walnut Digital Signature Scheme
Recently, NIST started the process of standardizing quantum-resistant public-key cryptographic algorithms. WalnutDSA, the subject of this paper, is one of the 20 proposed signature schemes that are being considered for standardization. Walnut relies on a one-way function called E-Multiplication, which has a rich algebraic structure. This paper shows that this structure can be exploited to launch several practical attacks against the Walnut cryptosystem. The attacks work very well in practice; it is possible to forge signatures and compute equivalent secret keys for the 128-bit and 256-bit security parameters submitted to NIST in less than a second and in less than a minute respectively.
2018
ASIACRYPT
Two Attacks on Rank Metric Code-Based Schemes: RankSign and an IBE Scheme
RankSign [30] is a code-based signature scheme proposed to the NIST competition for quantum-safe cryptography [5] and, moreover, is a fundamental building block of a new Identity-Based-Encryption (IBE) [26]. This signature scheme is based on the rank metric and enjoys remarkably small key sizes, about 10KBytes for an intended level of security of 128 bits. Unfortunately we will show that all the parameters proposed for this scheme in [5] can be broken by an algebraic attack that exploits the fact that the augmented LRPC codes used in this scheme have very low weight codewords. Therefore, without RankSign the IBE cannot be instantiated at this time. As a second contribution we will show that the problem is deeper than finding a new signature in rank-based cryptography, we also found an attack on the generic problem upon which its security reduction relies. However, contrarily to the RankSign scheme, it seems that the parameters of the IBE scheme could be chosen in order to avoid our attack. Finally, we have also shown that if one replaces the rank metric in the [26] IBE scheme by the Hamming metric, then a devastating attack can be found.
2018
ASIACRYPT
An Efficient Structural Attack on NIST Submission DAGS
We present an efficient key recovery attack on code based encryption schemes using some quasi-dyadic alternant codes with extension degree 2. This attack permits to break the proposal DAGS recently submitted to NIST.
2018
ASIACRYPT
Pattern Matching on Encrypted Streams
Pattern matching is essential in applications such as deep-packet inspection (DPI), searching on genomic data, or analyzing medical data. A simple task to do on plaintext data, pattern matching is much harder to do when the privacy of the data must be preserved. Existent solutions involve searchable encryption mechanisms with at least one of these three drawbacks: requiring an exhaustive (and static) list of keywords to be prepared before the data is encrypted (like in symmetric searchable encryption); requiring tokenization, i.e., breaking up the data to search into substrings and encrypting them separately (e.g., like BlindBox); relying on symmetric-key cryptography, thus implying a token-regeneration step for each encrypted-data source (e.g., user). Such approaches are ill-suited for pattern-matching with evolving patterns (e.g., updating virus signatures), variable searchword lengths, or when a single entity must filter ciphertexts from multiple parties.In this work, we introduce Searchable Encryption with Shiftable Trapdoors (SEST): a new primitive that allows for pattern matching with universal tokens (usable by all entities), in which keywords of arbitrary lengths can be matched to arbitrary ciphertexts. Our solution uses public-key encryption and bilinear pairings.In addition, very minor modifications to our solution enable it to take into account regular expressions, such as fully- or partly-unknown characters in a keyword (wildcards and interval/subset searches). Our trapdoor size is at most linear in the keyword length (and independent of the plaintext size), and we prove that the leakage to the searcher is only the trivial one: since the searcher learns whether the pattern occurs and where, it can distinguish based on different search results of a single trapdoor on two different plaintexts.To better show the usability of our scheme, we implemented it to run DPI on all the SNORT rules. We show that even for very large plaintexts, our encryption algorithm scales well. The pattern-matching algorithm is slower, but extremely parallelizable, and it can thus be run even on very large data. Although our proofs use a (marginally) interactive assumption, we argue that this is a relatively small price to pay for the flexibility and privacy that we are able to attain.
2018
ASIACRYPT
SQL on Structurally-Encrypted Databases
We show how to encrypt a relational database in such a way that it can efficiently support a large class of SQL queries. Our construction is based solely on structured encryption (STE) and does not make use of any property-preserving encryption (PPE) schemes such as deterministic and order-preserving encryption. As such, our approach leaks considerably less than PPE-based solutions which have recently been shown to reveal a lot of information in certain settings (Naveed et al., CCS ’15). Our construction is efficient and—under some conditions on the database and queries—can have asymptotically-optimal query complexity. We also show how to extend our solution to be dynamic while maintaining the scheme’s optimal query complexity.
2018
ASIACRYPT
Parameter-Hiding Order Revealing Encryption
Order-revealing encryption (ORE) is a primitive for outsourcing encrypted databases which allows for efficiently performing range queries over encrypted data. Unfortunately, a series of works, starting with Naveed et al. (CCS 2015), have shown that when the adversary has a good estimate of the distribution of the data, ORE provides little protection. In this work, we consider the case that the database entries are drawn identically and independently from a distribution of known shape, but for which the mean and variance are not (and thus the attacks of Naveed et al. do not apply). We define a new notion of security for ORE, called parameter-hiding ORE, which maintains the secrecy of these parameters. We give a construction of ORE satisfying our new definition from bilinear maps.
2018
ASIACRYPT
Revisiting Key-Alternating Feistel Ciphers for Shorter Keys and Multi-user Security
Key-Alternating Feistel (KAF) ciphers, a.k.a. Feistel-2 models, refer to Feistel networks with round functions of the form $F_i(k_i\oplus x_i)$, where $k_i$ is the (secret) round-key and $F_i$ is a public random function. This model roughly captures the structures of many famous Feistel ciphers, and the most prominent instance is DES.Existing provable security results on KAF assumed independent round-keys and round functions (ASIACRYPT 2004 & FSE 2014). In this paper, we investigate how to achieve security under simpler and more realistic assumptions: with round-keys derived from a short main-key, and hopefully with identical round functions.For birthday-type security, we consider 4-round KAF, investigate the minimal conditions on the way to derive the four round-keys, and prove that when such adequately derived keys and the same round function are used, the 4-round KAF is secure up to $2^{n/2}$ queries.For beyond-birthday security, we focus on 6-round KAF. We prove that when the adjacent round-keys are independent, and independent round-functions are used, the 6 round KAF is secure up to $2^{2n/3}$ queries. To our knowledge, this is the first beyond-birthday security result for KAF without assuming completely independent round-keys.Our results hold in the multi-user setting as well, constituting the first non-trivial multi-user provable security results on Feistel ciphers. We finally demonstrate applications of our results on designing key-schedules and instantiating keyed sponge constructions.
2018
ASIACRYPT
Short Variable Length Domain Extenders with Beyond Birthday Bound Security
Length doublers are cryptographic functions that transform an n-bit cryptographic primitive into an efficient and secure cipher that length-preservingly encrypts strings of length in $[n,2n-1]$. All currently known constructions are only proven secure up to the birthday bound, and for all but one construction this bound is known to be tight. We consider the remaining candidate, $\mathrm {LDT}$ by Chen et al. (ToSC 2017(3)), and prove that it achieves beyond the birthday bound security for the domain [n, 3n / 2). We generalize the construction to multiple rounds and demonstrate that by adding one more encryption layer to $\mathrm {LDT}$, beyond the birthday bound security can be achieved for all strings of length in $[n,2n-1]$: security up to around $2^{2n/3}$ for the encryption of strings close to n and security up to around $2^{n}$ for strings of length close to 2n. The security analysis of both schemes is performed in a modular manner through the introduction and analysis of a new concept called “harmonic permutation primitives.”
2018
ASIACRYPT
Building Quantum-One-Way Functions from Block Ciphers: Davies-Meyer and Merkle-Damgård Constructions
We present hash functions that are almost optimally one-way in the quantum setting. Our hash functions are based on the Merkle-Damgård construction iterating a Davies-Meyer compression function, which is built from a block cipher. The quantum setting that we use is a natural extention of the classical ideal cipher model. Recent work has revealed that symmetric-key schemes using a block cipher or a public permutation, such as CBC-MAC or the Even-Mansour cipher, can get completely broken with quantum superposition attacks, in polynomial time of the block size. Since many of the popular schemes are built from a block cipher or a permutation, the recent findings motivate us to study such schemes that are provably secure in the quantum setting. Unfortunately, no such schemes are known, unless one relies on certain algebraic assumptions. In this paper we present hash constructions that are provably one-way in the quantum setting without algebraic assumptions, solely based on the assumption that the underlying block cipher is ideal. To do this, we reduce one-wayness to a problem of finding a fixed point and then bound its success probability with a distinguishing advantage. We develop a generic tool that helps us prove indistinguishability of two quantum oracle distributions.
2018
ASIACRYPT
Tweakable Block Ciphers Secure Beyond the Birthday Bound in the Ideal Cipher Model
We propose a new construction of tweakable block ciphers from standard block ciphers. Our construction, dubbed $\mathsf {XHX2}$, is the cascade of two independent $\mathsf {XHX}$ block ciphers, so it makes two calls to the underlying block cipher using tweak-dependent keys. We prove the security of $\mathsf {XHX2}$ up to $\min \{2^{2(n+m)/3},2^{n+m/2}\}$ queries (ignoring logarithmic factors) in the ideal cipher model, when the block cipher operates on n-bit blocks using m-bit keys. The $\mathsf {XHX2}$ tweakable block cipher is the first construction that achieves beyond-birthday-bound security with respect to the input size of the underlying block cipher in the ideal cipher model.
2018
ASIACRYPT
ZCZ – Achieving n-bit SPRP Security with a Minimal Number of Tweakable-Block-Cipher Calls
Strong Pseudo-random Permutations (SPRPs) are important for various applications. In general, it is desirable to base an SPRP on a single-keyed primitive for minimizing the implementation costs. For constructions built on classical block ciphers, Nandi showed at ASIACRYPT’15 that at least two calls to the primitive per processed message block are required for SPRP security, assuming that all further operations are linear. The ongoing trend of using tweakable block ciphers as primitive has already led to MACs or encryption modes with high security and efficiency properties. Thus, three interesting research questions are hovering in the domain of SPRPs: (1) if and to which extent the bound of two calls per block can be reduced with a tweakable block cipher, (2) how concrete constructions could be realized, and (3) whether full n-bit security is achievable from primitives with n-bit state size.The present work addresses all three questions. Inspired by Iwata et al.’s ZHash proposal at CRYPTO’17, we propose the ZCZ (ZHash-Counter-ZHash) construction, a single-key variable-input-length SPRP based on a single tweakable block cipher whose tweak length is at least its state size. ZCZ possesses close to optimal properties with regards to both performance and security: not only does it require only asymptotically $3\ell /2$ calls to the primitive for $\ell$-block messages; we show that this figure is close to the minimum by an PRP distinguishing attack on any construction with tweak size of $\tau = n$ bits and fewer than $(3\ell -1)/2$ calls to the same primitive. Moreover, it provides optimal n-bit security for a primitive with n-bit state and tweak size.
2018
ASIACRYPT
Measuring, Simulating and Exploiting the Head Concavity Phenomenon in BKZ
The Blockwise-Korkine-Zolotarev (BKZ) lattice reduction algorithm is central in cryptanalysis, in particular for lattice-based cryptography. A precise understanding of its practical behavior in terms of run-time and output quality is necessary for parameter selection in cryptographic design. As the provable worst-case bounds poorly reflect the practical behavior, cryptanalysts rely instead on the heuristic BKZ simulator of Chen and Nguyen (Asiacrypt’11). It fits better with practical experiments, but not entirely. In particular, it over-estimates the norm of the first few vectors in the output basis. Put differently, BKZ performs better than its Chen–Nguyen simulation.In this work, we first report experiments providing more insight on this shorter-than-expected phenomenon. We then propose a refined BKZ simulator by taking the distribution of short vectors in random lattices into consideration. We report experiments suggesting that this refined simulator more accurately predicts the concrete behavior of BKZ. Furthermore, we design a new BKZ variant that exploits the shorter-than-expected phenomenon. For the same cost assigned to the underlying SVP-solver, the new BKZ variant produces bases of better quality. We further illustrate its potential impact by testing it on the SVP-120 instance of the Darmstadt lattice challenge.
2018
ASIACRYPT
Quantum Lattice Enumeration and Tweaking Discrete Pruning
Enumeration is a fundamental lattice algorithm. We show how to speed up enumeration on a quantum computer, which affects the security estimates of several lattice-based submissions to NIST: if T is the number of operations of enumeration, our quantum enumeration runs in roughly $\sqrt{T}$ operations. This applies to the two most efficient forms of enumeration known in the extreme pruning setting: cylinder pruning but also discrete pruning introduced at Eurocrypt ’17. Our results are based on recent quantum tree algorithms by Montanaro and Ambainis-Kokainis. The discrete pruning case requires a crucial tweak: we modify the preprocessing so that the running time can be rigorously proved to be essentially optimal, which was the main open problem in discrete pruning. We also introduce another tweak to solve the more general problem of finding close lattice vectors.
2018
ASIACRYPT
On the Hardness of the Computational Ring-LWR Problem and Its Applications
In this paper, we propose a new assumption, the Computational Learning With Rounding over rings, which is inspired by the computational Diffie-Hellman problem. Assuming the hardness of R-LWE, we prove this problem is hard when the secret is small, uniform and invertible. From a theoretical point of view, we give examples of a key exchange scheme and a public key encryption scheme, and prove the worst-case hardness for both schemes with the help of a random oracle. Our result improves both speed, as a result of not requiring Gaussian secret or noise, and size, as a result of rounding. In practice, our result suggests that decisional R-LWR based schemes, such as Saber, Round2 and Lizard, which are among the most efficient solutions to the NIST post-quantum cryptography competition, stem from a provable secure design. There are no hardness results on the decisional R-LWR with polynomial modulus prior to this work, to the best of our knowledge.
2018
ASIACRYPT
On the Statistical Leak of the GGH13 Multilinear Map and Some Variants
At EUROCRYPT 2013, Garg, Gentry and Halevi proposed a candidate construction (later referred as GGH13) of cryptographic multilinear map (MMap). Despite weaknesses uncovered by Hu and Jia (EUROCRYPT 2016), this candidate is still used for designing obfuscators.The naive version of the GGH13 scheme was deemed susceptible to averaging attacks, i.e., it could suffer from a statistical leak (yet no precise attack was described). A variant was therefore devised, but it remains heuristic. Recently, to obtain MMaps with low noise and modulus, two variants of this countermeasure were developed by Döttling et al. (EPRINT:2016/599).In this work, we propose a systematic study of this statistical leakage for all these GGH13 variants. In particular, we confirm the weakness of the naive version of GGH13. We also show that, among the two variants proposed by Döttling et al., the so-called conservative method is not so effective: it leaks the same value as the unprotected method. Luckily, the leakage is more noisy than in the unprotected method, making the straightforward attack unsuccessful. Additionally, we note that all the other methods also leak values correlated with secrets.As a conclusion, we propose yet another countermeasure, for which this leakage is made unrelated to all secrets. On our way, we also make explicit and tighten the hidden exponents in the size of the parameters, as an effort to assess and improve the efficiency of MMaps.
2018
ASIACRYPT
LWE Without Modular Reduction and Improved Side-Channel Attacks Against BLISS
This paper is devoted to analyzing the variant of Regev’s learning with errors (LWE) problem in which modular reduction is omitted: namely, the problem (ILWE) of recovering a vector $\mathbf {s}\in \mathbb {Z}^n$ given polynomially many samples of the form $(\mathbf {a},\langle \mathbf {a},\mathbf {s}\rangle + e)\in \mathbb {Z}^{n+1}$ where $\mathbf { a}$ and e follow fixed distributions. Unsurprisingly, this problem is much easier than LWE: under mild conditions on the distributions, we show that the problem can be solved efficiently as long as the variance of e is not superpolynomially larger than that of $\mathbf { a}$. We also provide almost tight bounds on the number of samples needed to recover $\mathbf {s}$.Our interest in studying this problem stems from the side-channel attack against the BLISS lattice-based signature scheme described by Espitau et al. at CCS 2017. The attack targets a quadratic function of the secret that leaks in the rejection sampling step of BLISS. The same part of the algorithm also suffers from a linear leakage, but the authors claimed that this leakage could not be exploited due to signature compression: the linear system arising from it turns out to be noisy, and hence key recovery amounts to solving a high-dimensional problem analogous to LWE, which seemed infeasible. However, this noisy linear algebra problem does not involve any modular reduction: it is essentially an instance of ILWE, and can therefore be solved efficiently using our techniques. This allows us to obtain an improved side-channel attack on BLISS, which applies to 100% of secret keys (as opposed to ${\approx }7\%$ in the CCS paper), and is also considerably faster.
2018
ASIACRYPT
Quantum Algorithms for the $k$-xor Problem
The $k$-xor (or generalized birthday) problem is a widely studied question with many applications in cryptography. It aims at finding k elements of n bits, drawn at random, such that the xor of all of them is 0. The algorithms proposed by Wagner more than fifteen years ago remain the best known classical algorithms for solving them, when disregarding logarithmic factors.In this paper we study these problems in the quantum setting, when considering that the elements are created by querying a random function (or k random functions) $H~: \{0,1\}^n \rightarrow \{0,1\}^n$. We consider two scenarios: in one we are able to use a limited amount of quantum memory (i.e. a number O(n) of qubits, the same as the one needed by Grover’s search algorithm), and in the other we consider that the algorithm can use an exponential amount of qubits. Our newly proposed algorithms are of general interest. In both settings, they provide the best known quantum time complexities.In particular, we are able to considerately improve the $3$-xor algorithm: with limited qubits, we reach a complexity considerably better than what is currently possible for quantum collision search. Furthermore, when having access to exponential amounts of quantum memory, we can take this complexity below $O(2^{n/3})$, the well-known lower bound of quantum collision search, clearly improving the best known quantum time complexity also in this setting.We illustrate the importance of these results with some cryptographic applications.
2018
ASIACRYPT
Hidden Shift Quantum Cryptanalysis and Implications
At Eurocrypt 2017 a tweak to counter Simon’s quantum attack was proposed: replace the common bitwise addition with other operations, as a modular addition. The starting point of our paper is a follow up of these previous results:First, we have developed new algorithms that improves and generalizes Kuperberg’s algorithm for the hidden shift problem, which is the algorithm that applies instead of Simon when considering modular additions. Thanks to our improved algorithm, we have been able to build a quantum attack in the superposition model on Poly1305, proposed at FSE 2005, widely used and claimed to be quantumly secure. We also answer an open problem by analyzing the effect of the tweak to the FX construction.We have also generalized the algorithm. We propose for the first time a quantum algorithm for solving the hidden problem with parallel modular additions, with a complexity that matches both Simon and Kuperberg in its extremes.In order to verify our theoretical analysis, and to get concrete estimates of the cost of the algorithms, we have simulated them, and were able to validate our estimated complexities.Finally, we analyze the security of some classical symmetric constructions with concrete parameters, to evaluate the impact and practicality of the proposed tweak. We concluded that the tweak does not seem to be efficient.
2018
ASIACRYPT
Arya: Nearly Linear-Time Zero-Knowledge Proofs for Correct Program Execution
There have been tremendous advances in reducing interaction, communication and verification time in zero-knowledge proofs but it remains an important challenge to make the prover efficient. We construct the first zero-knowledge proof of knowledge for the correct execution of a program on public and private inputs where the prover computation is nearly linear time. This saves a polylogarithmic factor in asymptotic performance compared to current state of the art proof systems.We use the TinyRAM model to capture general purpose processor computation. An instance consists of a TinyRAM program and public inputs. The witness consists of additional private inputs to the program. The prover can use our proof system to convince the verifier that the program terminates with the intended answer within given time and memory bounds. Our proof system has perfect completeness, statistical special honest verifier zero-knowledge, and computational knowledge soundness assuming linear-time computable collision-resistant hash functions exist. The main advantage of our new proof system is asymptotically efficient prover computation. The prover’s running time is only a superconstant factor larger than the program’s running time in an apples-to-apples comparison where the prover uses the same TinyRAM model. Our proof system is also efficient on the other performance parameters; the verifier’s running time and the communication are sublinear in the execution time of the program and we only use a log-logarithmic number of rounds.
2018
ASIACRYPT
Improved (Almost) Tightly-Secure Simulation-Sound QA-NIZK with Applications
We construct the first (almost) tightly-secure unbounded-simulation-sound quasi-adaptive non-interactive zero-knowledge arguments (USS-QA-NIZK) for linear-subspace languages with compact (number of group elements independent of the security parameter) common reference string (CRS) and compact proofs under standard assumptions in bilinear-pairings groups. In particular, under the SXDH assumption, the USS-QA-NIZK proof size is only seventeen group elements with a factor $O(\log {Q})$ loss in security reduction to SXDH. The USS-QA-NIZK primitive has many applications, including structure-preserving signatures (SPS), CCA2-secure publicly-verifiable public-key encryption (PKE), which in turn have applications to CCA-anonymous group signatures, blind signatures and unbounded simulation-sound Groth-Sahai NIZK proofs. We show that the almost tight security of our USS-QA-NIZK translates into constructions of all of the above applications with (almost) tight-security to standard assumptions such as SXDH and, more generally, $\mathcal{D}_k$-MDDH. Thus, we get the first publicly-verifiable (almost) tightly-secure multi-user/multi-challenge CCA2-secure PKE with practical efficiency under standard bilinear assumptions. Our (almost) tight SPS construction is also improved in the signature size over previously known constructions.
2018
ASIACRYPT
Programming the Demirci-Selçuk Meet-in-the-Middle Attack with Constraints
Cryptanalysis with SAT/SMT, MILP and CP has increased in popularity among symmetric-key cryptanalysts and designers due to its high degree of automation. So far, this approach covers differential, linear, impossible differential, zero-correlation, and integral cryptanalysis. However, the Demirci-Selçuk meet-in-the-middle ($\mathcal {DS}$-$\mathsf {MITM}$) attack is one of the most sophisticated techniques that has not been automated with this approach. By an in-depth study of Derbez and Fouque’s work on $\mathcal {DS}$-$\mathsf {MITM}$ analysis with dedicated search algorithms, we identify the crux of the problem and present a method for automatic $\mathcal {DS}$-$\mathsf {MITM}$ attack based on general constraint programming, which allows the cryptanalysts to state the problem at a high level without having to say how it should be solved. Our method is not only able to enumerate distinguishers but can also partly automate the key-recovery process. This approach makes the $\mathcal {DS}$-$\mathsf {MITM}$ cryptanalysis more straightforward and easier to follow, since the resolution of the problem is delegated to off-the-shelf constraint solvers and therefore decoupled from its formulation. We apply the method to SKINNY, TWINE, and LBlock, and we get the currently known best $\mathcal {DS}$-$\mathsf {MITM}$ attacks on these ciphers. Moreover, to demonstrate the usefulness of our tool for the block cipher designers, we exhaustively evaluate the security of $8! = 40320$ versions of LBlock instantiated with different words permutations in the F functions. It turns out that the permutation used in the original LBlock is one of the 64 permutations showing the strongest resistance against the $\mathcal {DS}$-$\mathsf {MITM}$ attack. The whole process is accomplished on a PC in less than 2 h. The same process is applied to TWINE, and similar results are obtained.
2018
ASIACRYPT
Cryptanalysis of MORUS
MORUS is a high-performance authenticated encryption algorithm submitted to the CAESAR competition, and recently selected as a finalist. There are three versions of MORUS: MORUS-640 with a 128-bit key, and MORUS-1280 with 128-bit or 256-bit keys. For all versions the security claim for confidentiality matches the key size. In this paper, we analyze the components of this algorithm (initialization, state update and tag generation), and report several results.As our main result, we present a linear correlation in the keystream of full MORUS, which can be used to distinguish its output from random and to recover some plaintext bits in the broadcast setting. For MORUS-1280, the correlation is $2^{-76}$, which can be exploited after around $2^{152}$ encryptions, less than what would be expected for a 256-bit secure cipher. For MORUS-640, the same attack results in a correlation of $2^{-73}$, which does not violate the security claims of the cipher.To identify this correlation, we make use of rotational invariants in MORUS using linear masks that are invariant by word-rotations of the state. This motivates us to introduce single-word versions of MORUS called MiniMORUS, which simplifies the analysis. The attack has been implemented and verified on MiniMORUS, where it yields a correlation of $2^{-16}$.We also study reduced versions of the initialization and finalization of MORUS, aiming to evaluate the security margin of these components. We show a forgery attack when finalization is reduced from 10 steps to 3, and a key-recovery attack in the nonce-misuse setting when initialization is reduced from 16 steps to 10. These additional results do not threaten the full MORUS, but studying all aspects of the design is useful to understand its strengths and weaknesses.
2018
ASIACRYPT
New MILP Modeling: Improved Conditional Cube Attacks on Keccak-Based Constructions
In this paper, we propose a new MILP modeling to find better or even optimal choices of conditional cubes, under the general framework of conditional cube attacks. These choices generally find new or improved attacks against the keyed constructions based on Keccak permutation and its variants, including Keccak-MAC, KMAC, Keyak, and Ketje, in terms of attack complexities or the number of attacked rounds. Interestingly, conditional cube attacks were applied to round-reduced Keccak-MAC, but not to KMAC despite the great similarity between Keccak-MAC and KMAC, and the fact that KMAC is the NIST standard way of constructing MAC from SHA-3. As examples to demonstrate the effectiveness of our new modeling, we report key recovery attacks against KMAC128 and KMAC256 reduced to 7 and 9 rounds, respectively; the best attack against Lake Keyak with 128-bit key is improved from 6 to 8 rounds in the nonce-respected setting and 9 rounds of Lake Keyak can be attacked if the key size is of 256 bits; attack complexity improvements are found generally on other constructions. Our new model is also applied to Keccak-based full-state keyed sponge and gives a positive answer to the open question proposed by Bertoni et al. whether cube attacks can be extended to more rounds by exploiting full-state absorbing. To verify the correctness of our attacks, reduced-variants of the attacks are implemented and verified on a PC practically. It is remarked that this work does not threaten the security of any full version of the instances analyzed in this paper.
2018
ASIACRYPT
On the Concrete Security of Goldreich’s Pseudorandom Generator
Local pseudorandom generators allow to expand a short random string into a long pseudo-random string, such that each output bit depends on a constant number d of input bits. Due to its extreme efficiency features, this intriguing primitive enjoys a wide variety of applications in cryptography and complexity. In the polynomial regime, where the seed is of size n and the output of size $n^{\textsf {s}}$ for $\textsf {s}> 1$ , the only known solution, commonly known as Goldreich’s PRG, proceeds by applying a simple d-ary predicate to public random size-d subsets of the bits of the seed.While the security of Goldreich’s PRG has been thoroughly investigated, with a variety of results deriving provable security guarantees against class of attacks in some parameter regimes and necessary criteria to be satisfied by the underlying predicate, little is known about its concrete security and efficiency. Motivated by its numerous theoretical applications and the hope of getting practical instantiations for some of them, we initiate a study of the concrete security of Goldreich’s PRG, and evaluate its resistance to cryptanalytic attacks. Along the way, we develop a new guess-and-determine-style attack, and identify new criteria which refine existing criteria and capture the security guarantees of candidate local PRGs in a more fine-grained way.
2018
ASIACRYPT
A Framework for Achieving KDM-CCA Secure Public-Key Encryption
We propose a framework for achieving a public-key encryption (PKE) scheme that satisfies key dependent message security against chosen ciphertext attacks (KDM-CCA security) based on projective hash function. Our framework can be instantiated under the decisional diffie-hellman (DDH), quadratic residuosity (QR), and decisional composite residuosity (DCR) assumptions. The constructed schemes are KDM-CCA secure with respect to affine functions and compatible with the amplification method shown by Applebaum (EUROCRYPT 2011). Thus, they lead to PKE schemes satisfying KDM-CCA security for all functions computable by a-priori bounded size circuits. They are the first PKE schemes satisfying such a security notion in the standard model using neither non-interactive zero knowledge proof nor bilinear pairing. The above framework based on projective hash function captures only KDM-CCA security in the single user setting. However, we can prove the KDM-CCA security in the multi user setting of our concrete instantiations by using their algebraic structures explicitly. Especially, we prove that our DDH based scheme satisfies KDM-CCA security in the multi user setting with the same parameter setting as in the single user setting.
2018
ASIACRYPT
Understanding and Constructing AKE via Double-Key Key Encapsulation Mechanism
Motivated by abstracting the common idea behind several implicitly authenticated key exchange (AKE) protocols, we introduce a primitive that we call double-key key encapsulation mechanism (2-key KEM). It is a special type of KEM involving two pairs of secret-public keys and satisfying some function and security property. Such 2-key KEM serves as the core building block and provides alternative approaches to simplify the constructions of AKE. To see the usefulness of 2-key KEM, we show how several existing constructions of AKE can be captured as 2-key KEM and understood in a unified framework, including widely used HMQV, NAXOS, Okamoto-AKE, and FSXY12-13 schemes. Then, we show (1) how to construct 2-key KEM from concrete assumptions, (2) how to adapt the classical Fujisaki-Okamoto transformation and KEM combiner to achieve the security requirement of 2-key KEM, (3) an elegant Kyber-AKE over lattice using the improved Fujisaki-Okamoto technique.
2018
ASIACRYPT
Identity-Based Encryption Tightly Secure Under Chosen-Ciphertext Attacks
We propose the first identity-based encryption (IBE) scheme that is (almost) tightly secure against chosen-ciphertext attacks. Our scheme is efficient, in the sense that its ciphertext overhead is only seven group elements, three group elements more than that of the state-of-the-art passively (almost) tightly secure IBE scheme. Our scheme is secure in a multi-challenge setting, i.e., in face of an arbitrary number of challenge ciphertexts. The security of our scheme is based upon the standard symmetric external Diffie-Hellman assumption in pairing-friendly groups, but we also consider (less efficient) generalizations under weaker assumptions.
2018
ASIACRYPT
Short Digital Signatures and ID-KEMs via Truncation Collision Resistance
Truncation collision resistance is a simple non-interactive complexity assumption that seems very plausible for standard cryptographic hash functions like SHA-3. We describe how this assumption can be leveraged to obtain standard-model constructions of public-key cryptosystems that previously seemed to require a programmable random oracle. This includes the first constructions of identity-based key encapsulation mechanisms (ID-KEMs) and digital signatures over bilinear groups with full adaptive security and without random oracles, where a ciphertext or signature consists of only a single element of a prime-order group. We also describe a generic construction of ID-KEMs with full adaptive security from a scheme with very weak security (“selective and non-adaptive chosen-ID security”), and a similar generic construction for digital signatures.
2018
ASIACRYPT
Tighter Security Proofs for GPV-IBE in the Quantum Random Oracle Model
In (STOC, 2008), Gentry, Peikert, and Vaikuntanathan proposed the first identity-based encryption (GPV-IBE) scheme based on a post-quantum assumption, namely, the learning with errors (LWE) assumption. Since their proof was only made in the random oracle model (ROM) instead of the quantum random oracle model (QROM), it remained unclear whether the scheme was truly post-quantum or not. In (CRYPTO, 2012), Zhandry developed new techniques to be used in the QROM and proved security of GPV-IBE in the QROM, hence answering in the affirmative that GPV-IBE is indeed post-quantum. However, since the general technique developed by Zhandry incurred a large reduction loss, there was a wide gap between the concrete efficiency and security level provided by GPV-IBE in the ROM and QROM. Furthermore, regardless of being in the ROM or QROM, GPV-IBE is not known to have a tight reduction in the multi-challenge setting. Considering that in the real-world an adversary can obtain many ciphertexts, it is desirable to have a security proof that does not degrade with the number of challenge ciphertext.In this paper, we provide a much tighter proof for the GPV-IBE in the QROM in the single-challenge setting. In addition, we also show that a slight variant of the GPV-IBE has an almost tight reduction in the multi-challenge setting both in the ROM and QROM, where the reduction loss is independent of the number of challenge ciphertext. Our proof departs from the traditional partitioning technique and resembles the approach used in the public key encryption scheme of Cramer and Shoup (CRYPTO, 1998). Our proof strategy allows the reduction algorithm to program the random oracle the same way for all identities and naturally fits the QROM setting where an adversary may query a superposition of all identities in one random oracle query. Notably, our proofs are much simpler than the one by Zhandry and conceptually much easier to follow for cryptographers not familiar with quantum computation. Although at a high level, the techniques used for the single and multi-challenge setting are similar, the technical details are quite different. For the multi-challenge setting, we rely on the Katz-Wang technique (CCS, 2003) to overcome some obstacles regarding the leftover hash lemma.
2018
ASIACRYPT
New Instantiations of the CRYPTO 2017 Masking Schemes
At CRYPTO 2017, Belaïd et al. presented two new private multiplication algorithms over finite fields, to be used in secure masking schemes. To date, these algorithms have the lowest known complexity in terms of bilinear multiplication and random masks respectively, both being linear in the number of shares $d+1$ . Yet, a practical drawback of both algorithms is that their safe instantiation relies on finding matrices satisfying certain conditions. In their work, Belaïd et al. only address these up to $d=2$ and 3 for the first and second algorithm respectively, limiting so far the practical usefulness of their constructions.In this paper, we use in turn an algebraic, heuristic, and experimental approach to find many more safe instances of Belaïd et al.’s algorithms. This results in explicit instantiations up to order $d = 6$ over large fields, and up to $d = 4$ over practically relevant fields such as $\mathbb {F}_{2^8}$ .
2018
ASIACRYPT
Statistical Ineffective Fault Attacks on Masked AES with Fault Countermeasures
Implementation attacks like side-channel and fault attacks are a threat to deployed devices especially if an attacker has physical access. As a consequence, devices like smart cards and IoT devices usually provide countermeasures against implementation attacks, such as masking against side-channel attacks and detection-based countermeasures like temporal or spacial redundancy against fault attacks. In this paper, we show how to attack implementations protected with both masking and detection-based fault countermeasures by using statistical ineffective fault attacks using a single fault induction per execution. Our attacks are largely unaffected by the deployed protection order of masking and the level of redundancy of the detection-based countermeasure. These observations show that the combination of masking plus error detection alone may not provide sufficient protection against implementation attacks.
2018
ASIACRYPT
Tight Private Circuits: Achieving Probing Security with the Least Refreshing
Masking is a common countermeasure to secure implementations against side-channel attacks. In 2003, Ishai, Sahai, and Wagner introduced a formal security model, named $t$-probing model, which is now widely used to theoretically reason on the security of masked implementations. While many works have provided security proofs for small masked components, called gadgets, within this model, no formal method allowed to securely compose gadgets with a tight number of shares (namely, $t+1$) until recently. In 2016, Barthe et al. filled this gap with maskComp, a tool checking the security of masking schemes composed of several gadgets. This tool can achieve provable security with tight number of shares by inserting mask-refreshing gadgets at carefully selected locations. However the method is not tight in the sense that there exists some compositions of gadgets for which it cannot exhibit a flaw nor prove the security. As a result, it is overconservative and might insert more refresh gadgets than actually needed to ensure $t$-probing security. In this paper, we exhibit the first tool, referred to as tightPROVE, able to clearly state whether a shared circuit composed of standard gadgets (addition, multiplication, and refresh) is $t$-probing secure or not. Given such a composition, our tool either produces a probing-security proof (valid at any order) or exhibits a security flaw that directly implies a probing attack at a given order. Compared to maskComp, tightPROVE can drastically reduce the number of required refresh gadgets to get a probing security proof, and thus the randomness requirement for some secure shared circuits. We apply our method to a recent AES implementation secured with higher-order masking in bitslice and we show that we can save all the refresh gadgets involved in the s-box layer, which results in an significant performance gain.
2018
ASIACRYPT
Attacks and Countermeasures for White-box Designs
In traditional symmetric cryptography, the adversary has access only to the inputs and outputs of a cryptographic primitive. In the white-box model the adversary is given full access to the implementation. He can use both static and dynamic analysis as well as fault analysis in order to break the cryptosystem, e.g. to extract the embedded secret key. Implementations secure in such model have many applications in industry. However, creating such implementations turns out to be a very challenging if not an impossible task.Recently, Bos et al. [7] proposed a generic attack on white-box primitives called differential computation analysis (DCA). This attack was applied to many white-box implementations both from academia and industry. The attack comes from the area of side-channel analysis and the most common method protecting against such attacks is masking, which in turn is a form of secret sharing. In this paper we present multiple generic attacks against masked white-box implementations. We use the term “masking” in a very broad sense. As a result, we deduce new constraints that any secure white-box implementation must satisfy.Based on the new constraints, we develop a general method for protecting white-box implementations. We split the protection into two independent components: value hiding and structure hiding. Value hiding must provide protection against passive DCA-style attacks that rely on analysis of computation traces. Structure hiding must provide protection against circuit analysis attacks. In this paper we focus on developing the value hiding component. It includes protection against the DCA attack by Bos et al. and protection against a new attack called algebraic attack.We present a provably secure first-order protection against the new algebraic attack. The protection is based on small gadgets implementing secure masked XOR and AND operations. Furthermore, we give a proof of compositional security allowing to freely combine secure gadgets. We derive concrete security bounds for circuits built using our construction.
2018
ASIACRYPT
Signatures with Flexible Public Key: Introducing Equivalence Classes for Public Keys
We introduce a new cryptographic primitive called signatures with flexible public key $(\mathsf{SFPK})$. We divide the key space into equivalence classes induced by a relation $\mathcal {R}$. A signer can efficiently change his or her key pair to a different representatives of the same class, but without a trapdoor it is hard to distinguish if two public keys are related. Our primitive is motivated by structure-preserving signatures on equivalence classes ($\mathsf{SPS\text {-}EQ}$), where the partitioning is done on the message space. Therefore, both definitions are complementary and their combination has various applications.We first show how to efficiently construct static group signatures and self-blindable certificates by combining the two primitives. When properly instantiated, the result is a group signature scheme that has a shorter signature size than the current state-of-the-art scheme by Libert, Peters, and Yung from Crypto’15, but is secure in the same setting.In its own right, our primitive has stand-alone applications in the cryptocurrency domain, where it can be seen as a straightforward formalization of so-called stealth addresses. Finally, it can be used to build the first efficient ring signature scheme in the plain model without trusted setup, where signature size depends only sub-linearly on the number of ring members. Thus, we solve an open problem stated by Malavolta and Schröder at ASIACRYPT’2017.
2018
ASIACRYPT
Compact Multi-signatures for Smaller Blockchains
We construct new multi-signature schemes that provide new functionality. Our schemes are designed to reduce the size of the Bitcoin blockchain, but are useful in many other settings where multi-signatures are needed. All our constructions support both signature compression and public-key aggregation. Hence, to verify that a number of parties signed a common message m, the verifier only needs a short multi-signature, a short aggregation of their public keys, and the message m. We give new constructions that are derived from Schnorr signatures and from BLS signatures. Our constructions are in the plain public key model, meaning that users do not need to prove knowledge or possession of their secret key.In addition, we construct the first short accountable-subgroup multi-signature (ASM) scheme. An ASM scheme enables any subset $S$ of a set of n parties to sign a message m so that a valid signature discloses which subset generated the signature (hence the subset $S$ is accountable for signing m). We construct the first ASM scheme where signature size is only $O(\kappa )$ bits over the description of $S$, where $\kappa$ is the security parameter. Similarly, the aggregate public key is only $O(\kappa )$ bits, independent of n. The signing process is non-interactive. Our ASM scheme is very practical and well suited for compressing the data needed to spend funds from a t-of-n Multisig Bitcoin address, for any (polynomial size) t and n.
2018
ASIACRYPT
Multi-key Homomorphic Signatures Unforgeable Under Insider Corruption
Homomorphic signatures (HS) allows the derivation of the signature of the message-function pair (m, g), where $m = g(m_1, \ldots , m_K)$, given the signatures of each of the input messages $m_k$ signed under the same key. Multi-key HS (M-HS) introduced by Fiore et al.  (ASIACRYPT’16) further enhances the utility by allowing evaluation of signatures under different keys. The unforgeability of existing M-HS notions assumes that all signers are honest. We consider a setting where an arbitrary number of signers can be corrupted, called unforgeability under corruption, which is typical for natural applications (e.g., verifiable multi-party computation) of M-HS. Surprisingly, there is a huge gap between M-HS (for arbitrary circuits) with and without unforgeability under corruption: While the latter can be constructed from standard lattice assumptions (ASIACRYPT’16), we show that the former likely relies on non-falsifiable assumptions. Specifically, we propose a generic construction of M-HS with unforgeability under corruption from zero-knowledge succinct non-interactive argument of knowledge (ZK-SNARK) (and other standard assumptions), and then show that such M-HS implies zero-knowledge succinct non-interactive arguments (ZK-SNARG). Our results leave open the pressing question of what level of authenticity and utility can be achieved in the presence of corrupt signers under standard assumptions.
2018
ASIACRYPT
Attribute-Based Signatures for Unbounded Languages from Standard Assumptions
Attribute-based signature (ABS) schemes are advanced signature schemes that simultaneously provide fine-grained authentication while protecting privacy of the signer. Previously known expressive ABS schemes support either the class of deterministic finite automata and circuits from standard assumptions or Turing machines from the existence of indistinguishability obfuscations.In this paper, we propose the first ABS scheme for a very general policy class, all deterministic Turing machines, from a standard assumption, namely, the Symmetric External Diffie-Hellman (SXDH) assumption. We also propose the first ABS scheme that allows nondeterministic finite automata (NFA) to be used as policies. Although the expressiveness of NFAs are more restricted than Turing machines, this is the first scheme that supports nondeterministic computations as policies.Our main idea lies in abstracting ABS constructions and presenting the concept of history of computations; this allows a signer to prove possession of a policy that accepts the string associated to a message in zero-knowledge while also hiding the policy, regardless of the computational model being used. With this abstraction in hand, we are able to construct ABS for Turing machines and NFAs using a surprisingly weak NIZK proof system. Essentially we only require a NIZK proof system for proving that a (normal) signature is valid. Such a NIZK proof system together with a base signature scheme are, in turn, possible from bilinear groups under the SXDH assumption, and hence so are our ABS schemes.
2018
ASIACRYPT
Learning Strikes Again: The Case of the DRS Signature Scheme
Lattice signature schemes generally require particular care when it comes to preventing secret information from leaking through signature transcript. For example, the Goldreich-Goldwasser-Halevi (GGH) signature scheme and the NTRUSign scheme were completely broken by the parallelepiped-learning attack of Nguyen and Regev (Eurocrypt 2006). Several heuristic countermeasures were also shown vulnerable to similar statistical attacks.At PKC 2008, Plantard, Susilo and Win proposed a new variant of GGH, informally arguing resistance to such attacks. Based on this variant, Plantard, Sipasseuth, Dumondelle and Susilo proposed a concrete signature scheme, called DRS, that has been accepted in the round 1 of the NIST post-quantum cryptography project.In this work, we propose yet another statistical attack and demonstrate a weakness of the DRS scheme: one can recover some partial information of the secret key from sufficiently many signatures. One difficulty is that, due to the DRS reduction algorithm, the relation between the statistical leak and the secret seems more intricate. We work around this difficulty by training a statistical model, using a few features that we designed according to a simple heuristic analysis.While we only recover partial information on the secret key, this information is easily exploited by lattice attacks, significantly decreasing their complexity. Concretely, we claim that, provided that $100\,000$ signatures are available, the secret key may be recovered using BKZ-138 for the first set of DRS parameters submitted to the NIST. This puts the security level of this parameter set below 80-bits (maybe even 70-bits), to be compared to an original claim of 128-bits.
2018
ASIACRYPT
How to Securely Compute with Noisy Leakage in Quasilinear Complexity
Since their introduction in the late 90’s, side-channel attacks have been considered as a major threat against cryptographic implementations. This threat has raised the need for formal leakage models in which the security of implementations can be proved. At Eurocrypt 2013, Prouff and Rivain introduced the noisy leakage model which has been argued to soundly capture the physical reality of power and electromagnetic leakages. In their work, they also provide the first formal security proof for a masking scheme in the noisy leakage model. However their work has two important limitations: (i) the security proof relies on the existence of a leak-free component, (ii) the tolerated amount of information in the leakage (aka leakage rate) is of O(1 / n) where n is the security parameter (i.e. the number of shares in the underlying masking scheme). The first limitation was nicely tackled by Duc, Dziembowski and Faust one year later (Eurocrypt 2014). Their main contribution was to show a security reduction from the noisy leakage model to the conceptually simpler random-probing model. They were then able to prove the security of the well-known Ishai-Sahai-Wagner scheme (Crypto 2003) in the noisy leakage model. The second limitation was addressed in a paper by Andrychowicz, Dziembowski and Faust (Eurocrypt 2016) which makes use of a construction due to Ajtai (STOC 2011) to achieve security in the strong adaptive probing model with a leakage rate of $O(1/\log n)$. The authors argue that their result can be translated into the noisy leakage model with a leakage rate of O(1) by using secret sharing based on algebraic geometric codes. In terms of complexity, the protected program scales from |P| arithmetic instructions to $\tilde{O}(|P| \, n^2)$. According to the authors, this $\tilde{O}(n^2)$ blow-up could be reduced to $\tilde{O}(n)$ using packed secret sharing but no details are provided. Moreover, such an improvement would only be possible for a program of width at least linear in n. The issue of designing an explicit scheme achieving $\tilde{O}(n)$ complexity blow-up for any arithmetic program is hence left open.In this paper, we tackle the above issue: we show how to securely compute in the presence of noisy leakage with a leakage rate $\tilde{O}(1)$ and complexity blow-up $\tilde{O}(n)$. Namely, we introduce a transform that turns any program P composed of arithmetic instructions on some filed $\mathbb {F}$ into a (functionally equivalent) program $\varPi$ composed of $|\varPi | = O(|P| n \log n)$ arithmetic instructions which can tolerate some (quasi-constant) amount of noisy leakage on its internal variables (while revealing negligible information). We use a polynomial encoding allowing quasilinear multiplication based on the fast Number Theoretic Transform (NTT). We first show that our scheme is secure in the random-probing model with leakage rate $O(1/\log n)$. Using the reduction by Duc et al. this result can be translated in the noisy leakage model with a $O(1/|\mathbb {F}|^2 \log n)$ leakage rate. However, a straight application of this reduction is not satisfactory since our construction requires $|\mathbb {F}| = O(n)$. In order to bypass this issue (which is shared with the construction of Andrychowicz et al.), we provide a generic security reduction from the noisy leakage model at the logical-instruction level to the random-probing model at the arithmetic level. This reduction allows us to prove the security of our construction in the noisy leakage model with leakage rate $\tilde{O}(1)$.
2018
ASIACRYPT
Leakage-Resilient Cryptography from Puncturable Primitives and Obfuscation
In this work, we develop a framework for building leakage-resilient cryptosystems in the bounded leakage model from puncturable primitives and indistinguishability obfuscation ( $i\mathcal {O}$ ). The major insight of our work is that various types of puncturable pseudorandom functions (PRFs) can achieve leakage resilience on an obfuscated street.First, we build leakage-resilient weak PRFs from weak puncturable PRFs and $i\mathcal {O}$ , which readily imply leakage-resilient secret-key encryption. Then, we build leakage-resilient publicly evaluable PRFs (PEPRFs) from puncturable PEPRFs and $i\mathcal {O}$ , which readily imply leakage-resilient key encapsulation mechanism and thus public-key encryption. As a building block of independent interest, we realize puncturable PEPRFs from either newly introduced puncturable objects such as puncturable trapdoor functions and puncturable extractable hash proof systems or existing puncturable PRFs with $i\mathcal {O}$ . Finally, we construct the first leakage-resilient public-coin signature from selective puncturable PRFs, leakage-resilient one-way functions and $i\mathcal {O}$ . This settles the open problem posed by Boyle, Segev, and Wichs (Eurocrypt 2011).By further assuming the existence of lossy functions, all the above constructions achieve optimal leakage rate of $1 - o(1)$ . Such a leakage rate is not known to be achievable for weak PRFs, PEPRFs and public-coin signatures before. This also resolves the open problem posed by Dachman-Soled, Gordon, Liu, O’Neill, and Zhou (PKC 2016, JOC 2018).
2018
ASIACRYPT
Unbounded Inner Product Functional Encryption from Bilinear Maps
Inner product functional encryption (IPFE), introduced by Abdalla et al. (PKC2015), is a kind of functional encryption supporting only inner product functionality. All previous IPFE schemes are bounded schemes, meaning that the vector length that can be handled in the scheme is fixed in the setup phase. In this paper, we propose the first unbounded IPFE schemes, in which we do not have to fix the lengths of vectors in the setup phase and can handle (a priori) unbounded polynomial lengths of vectors. Our first scheme is private-key based and fully function hiding. That is, secret keys hide the information of the associated function. Our second scheme is public-key based and provides adaptive security in the indistinguishability based security definition. Both our schemes are based on SXDH, which is a well-studied standard assumption, and secure in the standard model. Furthermore, our schemes are quite efficient, incurring an efficiency loss by only a small constant factor from previous bounded function hiding schemes.
2018
ASIACRYPT
This paper demonstrates how to achieve simulation-based strong attribute hiding against adaptive adversaries for predicate encryption (PE) schemes supporting expressive predicate families under standard computational assumptions in bilinear groups. Our main result is a simulation-based adaptively strongly partially-hidingPE (PHPE) scheme for predicates computing arithmetic branching programs (ABP) on public attributes, followed by an inner-product predicate on private attributes. This simultaneously generalizes attribute-based encryption (ABE) for boolean formulas and ABP’s as well as strongly attribute-hiding PE schemes for inner products. The proposed scheme is proven secure for any a priori bounded number of ciphertexts and an unbounded (polynomial) number of decryption keys, which is the best possible in the simulation-based adaptive security framework. This directly implies that our construction also achieves indistinguishability-based strongly partially-hiding security against adversaries requesting an unbounded (polynomial) number of ciphertexts and decryption keys. The security of the proposed scheme is derived under (asymmetric version of) the well-studied decisional linear (DLIN) assumption. Our work resolves an open problem posed by Wee in TCC 2017, where his result was limited to the semi-adaptive setting. Moreover, our result advances the current state of the art in both the fields of simulation-based and indistinguishability-based strongly attribute-hiding PE schemes. Our main technical contribution lies in extending the strong attribute hiding methodology of Okamoto and Takashima [EUROCRYPT 2012, ASIACRYPT 2012] to the framework of simulation-based security and beyond inner products.
2018
ASIACRYPT
Improved Inner-Product Encryption with Adaptive Security and Full Attribute-Hiding
In this work, we propose two IPE schemes achieving both adaptive security and full attribute-hiding in the prime-order bilinear group, which improve upon the unique existing result satisfying both features from Okamoto and Takashima [Eurocrypt ’12] in terms of efficiency. Our first IPE scheme is based on the standard $k\textsc {-lin}$ assumption and has shorter master public key and shorter secret keys than Okamoto and Takashima’s IPE under weaker ${\textsc {dlin} }=2\textsc {-lin}$ assumption.Our second IPE scheme is adapted from the first one; the security is based on the ${\textsc {xdlin}}$ assumption (as Okamoto and Takashima’s IPE) but now it also enjoys shorter ciphertexts. Technically, instead of starting from composite-order IPE and applying existing transformation, we start from an IPE scheme in a very restricted setting but already in the prime-order group, and then gradually upgrade it to our full-fledged IPE scheme. This method allows us to integrate Chen et al.’s framework [Eurocrypt ’15] with recent new techniques [TCC ’17, Eurocrypt ’18] in an optimized way.
2018
ASIACRYPT
Decentralized Multi-Client Functional Encryption for Inner Product
We consider a situation where multiple parties, owning data that have to be frequently updated, agree to share weighted sums of these data with some aggregator, but where they do not wish to reveal their individual data, and do not trust each other. We combine techniques from Private Stream Aggregation (PSA) and Functional Encryption (FE), to introduce a primitive we call Decentralized Multi-Client Functional Encryption (DMCFE), for which we give a practical instantiation for Inner Product functionalities. This primitive allows various senders to non-interactively generate ciphertexts which support inner-product evaluation, with functional decryption keys that can also be generated non-interactively, in a distributed way, among the senders. Interactions are required during the setup phase only. We prove adaptive security of our constructions, while allowing corruptions of the clients, in the random oracle model.
2018
ASIACRYPT
Practical Fully Secure Unrestricted Inner Product Functional Encryption Modulo p
Functional encryption (FE) is a modern public-key cryptographic primitive allowing an encryptor to finely control the information revealed to recipients from a given ciphertext. Abdalla, Bourse, De Caro, and Pointcheval (PKC 2015) were the first to consider FE restricted to the class of linear functions, i.e. inner products. Though their schemes are only secure in the selective model, Agrawal, Libert, and Stehlé (CRYPTO 16) soon provided adaptively secure schemes for the same functionality. These constructions, which rely on standard assumptions such as the Decision Diffie-Hellman ( $\mathsf {DDH}$ ), the Learning-with-Errors ( $\mathsf {LWE}$ ), and Paillier’s Decision Composite Residuosity (DCR) problems, do however suffer of various practical drawbacks. Namely, the DCR based scheme only computes inner products modulo an RSA integer which is oversized for many practical applications, while the computation of inner products modulo a prime p either requires, for their $\mathsf {DDH}$ based scheme, that the inner product be contained in a sufficiently small interval for decryption to be efficient, or, as in the $\mathsf {LWE}$ based scheme, suffers of poor efficiency due to impractical parameters.In this paper, we provide adaptively secure FE schemes for the inner product functionality which are both efficient and allow for the evaluation of unbounded inner products modulo a prime p. Our constructions rely on new natural cryptographic assumptions in a cyclic group containing a subgroup where the discrete logarithm ( $\mathsf {DL}$ ) problem is easy which extend Castagnos and Laguillaumie’s assumption (RSA 2015) of a $\mathsf {DDH}$ group with an easy $\mathsf {DL}$ subgroup. Instantiating our generic constructions using class groups of imaginary quadratic fields gives rise to the most efficient FE for inner products modulo an arbitrary large prime p. One of our schemes outperforms the DCR variant of Agrawal et al.’s protocols in terms of size of keys and ciphertexts by factors varying between 2 and 20 for a 112-bit security.
2018
ASIACRYPT
On Multiparty Garbling of Arithmetic Circuits
We initiate a study of garbled circuits that contain both Boolean and arithmetic gates in secure multiparty computation. In particular, we incorporate the garbling gadgets for arithmetic circuits recently presented by Ball, Malkin, and Rosulek (ACM CCS 2016) into the multiparty garbling paradigm initially introduced by Beaver, Micali, and Rogaway (STOC ’90). This is the first work that studies arithmetic garbled circuits in the multiparty setting. Using mixed Boolean-arithmetic circuits allows more efficient secure computation of functions that naturally combine Boolean and arithmetic computations. Our garbled circuits are secure in the semi-honest model, under the same hardness assumptions as Ball et al., and can be efficiently and securely computed in constant rounds assuming an honest majority.We first extend free addition and multiplication by a constant to the multiparty setting. We then extend to the multiparty setting efficient garbled multiplication gates. The garbled multiplication gate construction we show was previously achieved only in the two-party setting and assuming a random oracle.We further present a new garbling technique, and show how this technique can improve efficiency in garbling selector gates. Selector gates compute a simple “if statement” in the arithmetic setting: the gate selects the output value from two input integer values, according to a Boolean selector bit; if the bit is 0 the output equals the first value, and if the bit is 1 the output equals the second value. Using our new technique, we show a new and designated garbled selector gate that reduces by approximately $33\%$ the evaluation time, for any number of parties, from the best previously known constructions that use existing techniques and are secure based on the same hardness assumptions.On the downside, we find that testing equality and computing exponentiation by a constant are significantly more complex to garble in the multiparty setting than in the two-party setting.
2018
ASIACRYPT
$\mathsf {Free\ }{} \mathtt{IF}$ : How to Omit Inactive Branches and Implement $\mathcal {S}$ -Universal Garbled Circuit (Almost) for Free
Two-party Secure Function Evaluation (SFE) allows two parties to evaluate a function known to both parties on their private inputs. In some settings, the input of one of the parties is the definition of the computed function, and requires protection as well. The standard solution for SFE of private functions (PF-SFE) is to rely on Universal Circuits (UC), which can be programmed to implement any circuit of size $s$ . Recent UC optimizations report the cost of UC for $s$ -gate Boolean circuits is $\approx 5 s \log s$ .Instead, we consider garbling that allows evaluating one of a given set $\mathcal {S}$ of circuits. We show how to evaluate one of the circuits in $\mathcal {S}$ at the communication cost comparable to that of evaluating the largest circuit in $\mathcal {S}$ . In other words, we show how to omit generating and sending inactive GC branches. Our main insight is that a garbled circuit is just a collection of garbled tables, and as such can be reused to emulate the throw-away computation of an inactive execution branch without revealing to the Evaluator whether it evaluates active or inactive branch.This cannot be proven within the standard BHR garbled circuits framework because the function description is inseparable from the garbling by definition. We carefully extend BHR in a general way, introducing topology-decoupling circuit garbling. We preserve all existing constructions and proofs of the BHR framework, while allowing this and other future constructions which may treat garbled tables separately from function description.Our construction is presented in the semi-honest model.
2018
TOSC
Towards Low Energy Stream Ciphers
Energy optimization is an important design aspect of lightweight cryptography. Since low energy ciphers drain less battery, they are invaluable components of devices that operate on a tight energy budget such as handheld devices or RFID tags. At Asiacrypt 2015, Banik et al. presented the block cipher family Midori which was designed to optimize the energy consumed per encryption and which reduces the energy consumption by more than 30% compared to previous block ciphers. However, if one has to encrypt/decrypt longer streams of data, i.e. for bulk data encryption/decryption, it is expected that a stream cipher should perform even better than block ciphers in terms of energy required to encrypt. In this paper, we address the question of designing low energy stream ciphers. To this end, we analyze for common stream cipher design components their impact on the energy consumption. Based on this, we give arguments why indeed stream ciphers allow for encrypting long data streams with less energy than block ciphers and validate our findings by implementations. Afterwards, we use the analysis results to identify energy minimizing design principles for stream ciphers.
2018
TOSC
ShiftRows Alternatives for AES-like Ciphers and Optimal Cell Permutations for Midori and Skinny
We study possible alternatives for ShiftRows to be used as cell permutations in AES-like ciphers. As observed during the design process of the block cipher Midori, when using a matrix with a non-optimal branch number for the MixColumns operation, the choice of the cell permutation, i.e., an alternative for ShiftRows, can actually improve the security of the primitive. In contrast, when using an MDS matrix it is known that one cannot increase the minimum number of active S-boxes by deviating from the ShiftRows-type permutation. However, finding the optimal choice for the cell permutation for a given, non-optimal, MixColumns operation is a highly non-trivial problem. In this work, we propose techniques to speed up the search for the optimal cell permutations significantly. As case studies, we apply those techniques to Midori and Skinny and provide possible alternatives for their cell permutations. We finally state an easy-to-verify sufficient condition on a cell permutation, to be used as an alternative in Midori, that attains a high number of active S-boxes and thus provides good resistance against differential and linear attacks.
2018
TOSC
MDS Matrices with Lightweight Circuits
MDS matrices are an important element for the design of block ciphers such as the AES. In recent years, there has been a lot of work on the construction of MDS matrices with a low implementation cost, in the context of lightweight cryptography. Most of the previous efforts focused on local optimization, constructing MDS matrices with coefficients that can be efficiently computed. In particular, this led to a matrix with a direct xor count of only 106, while a direct implementation of the MixColumn matrix of the AES requires 152 bitwise xors. More recently, techniques based on global optimization have been introduced, where the implementation can reuse some intermediate variables. In particular, Kranz et al. used optimization tools to find a good implementation from the description of an MDS matrix. They have lowered the cost of implementing the MixColumn matrix to 97 bitwise xors, and proposed a new matrix with only 72 bitwise xors, the lowest cost known so far. In this work we propose a different approach to global optimization. Instead of looking for an optimized circuit of a given matrix, we run a search through a space of circuits, to find optimal circuits yielding MDS matrices. This results in MDS matrices with an even lower cost, with only 67 bitwise xors.
2018
TOSC
Separable Statistics and Multidimensional Linear Cryptanalysis
Multidimensional linear cryptanalysis of block ciphers is improved in this work by introducing a number of new ideas. Firstly, formulae is given to compute approximate multidimensional distributions of the encryption algorithm internal bits. Conventional statistics like LLR (Logarithmic Likelihood Ratio) do not fit to work in Matsui’s Algorithm 2 for large dimension data, as the observation may depend on too many cipher key bits. So, secondly, a new statistic which reflects the structure of the cipher round is constructed instead. Thirdly, computing the statistic values that will fall into a critical region is presented as an optimisation problem for which an efficient algorithm is suggested. The algorithm works much faster than brute forcing all relevant key bits to compute the statistic. An attack for 16-round DES was implemented. We got an improvement over Matsui’s attack on DES in data and time complexity keeping success probability the same. With 241.81 plaintext blocks and success rate 0.83 (computed theoretically) we found 241.46 (which is close to the theoretically predicted number 241.81) key-candidates to 56-bit DES key. Search tree to compute the statistic values which fall into the critical region incorporated 245.45 nodes in the experiment and that is at least theoretically inferior in comparison with the final brute force. To get success probability 0.85, which is a fairer comparison to Matsui’s results, we would need 241.85 data and to brute force 241.85 key-candidates. That compares favourably with 243 achieved by Matsui.
2018
TOSC
Clustering Related-Tweak Characteristics: Application to MANTIS-6
The TWEAKEY/STK construction is an increasingly popular approach for designing tweakable block ciphers that notably uses a linear tweakey schedule. Several recent attacks have analyzed the implications of this approach for differential cryptanalysis and other attacks that can take advantage of related tweakeys. We generalize the clustering approach of a recent differential attack on the tweakable block cipher MANTIS5 and describe a tool for efficiently finding and evaluating such clusters. More specifically, we consider the set of all differential characteristics compatible with a given truncated characteristic, tweak difference, and optional constraints for the differential. We refer to this set as a semi-truncated characteristic and estimate its probability by analyzing the distribution of compatible differences at each step. We apply this approach to find a semi-truncated differential characteristic for MANTIS6 with probability about 2−67.73 and derive a key-recovery attack with a complexity of about 255.09 chosen-plaintext queries and 255.52 computations. The data-time product is 2110.61 &lt;&lt; 2126.
2018
TOSC
Mixture Differential Cryptanalysis: a New Approach to Distinguishers and Attacks on round-reduced AES
At Eurocrypt 2017 the first secret-key distinguisher for 5-round AES - based on the “multiple-of-8” property - has been presented. Although it allows to distinguish a random permutation from an AES-like one, it seems rather hard to implement a key-recovery attack different than brute-force like using such a distinguisher. In this paper we introduce “Mixture Differential Cryptanalysis” on round-reduced AESlike ciphers, a way to translate the (complex) “multiple-of-8” 5-round distinguisher into a simpler and more convenient one (though, on a smaller number of rounds). Given a pair of chosen plaintexts, the idea is to construct new pairs of plaintexts by mixing the generating variables of the original pair of plaintexts. Here we theoretically prove that for 4-round AES the corresponding ciphertexts of the original pair of plaintexts lie in a particular subspace if and only if the corresponding pairs of ciphertexts of the new pairs of plaintexts have the same property. Such secret-key distinguisher - which is independent of the secret-key, of the details of the S-Box and of the MixColumns matrix (except for the branch number equal to 5) - can be used as starting point to set up new key-recovery attacks on round-reduced AES. Besides a theoretical explanation, we also provide a practical verification both of the distinguisher and of the attack.
2018
TOSC
Cryptanalysis of AES-PRF and Its Dual
A dedicated pseudorandom function (PRF) called AES-PRF was proposed by Mennink and Neves at FSE 2018 (ToSC 2017, Issue 3). AES-PRF is obtained from AES by using the output of the 5-th round as the feed-forward to the output state. This paper presents extensive security analysis of AES-PRF and its variants. Specifically, we consider unbalanced variants where the output of the s-th round is used as the feed-forward. We also analyze the security of “dual” constructions of the unbalanced variants, where the input state is used as the feed-forward to the output of the s-th round. We apply an impossible differential attack, zero-correlation linear attack, traditional differential attack, zero correlation linear distinguishing attack and a meet-in-the-middle attack on these PRFs and reduced round versions. We show that AES-PRF is broken whenever s ≤ 2 or s ≥ 6, or reduced to 7 rounds, and Dual-AES-PRF is broken whenever s ≤ 4 or s ≥ 8. Our results on AES-PRF improve the initial security evaluation by the designers in various ways, and our results on Dual-AES-PRF give the first insight to its security.
2018
TOSC
SUNDAE: Small Universal Deterministic Authenticated Encryption for the Internet of Things
Lightweight cryptography was developed in response to the increasing need to secure devices for the Internet of Things. After significant research effort, many new block ciphers have been designed targeting lightweight settings, optimizing efficiency metrics which conventional block ciphers did not. However, block ciphers must be used in modes of operation to achieve more advanced security goals such as data confidentiality and authenticity, a research area given relatively little attention in the lightweight setting. We introduce a new authenticated encryption (AE) mode of operation, SUNDAE, specially targeted for constrained environments. SUNDAE is smaller than other known lightweight modes in implementation area, such as CLOC, JAMBU, and COFB, however unlike these modes, SUNDAE is designed as a deterministic authenticated encryption (DAE) scheme, meaning it provides maximal security in settings where proper randomness is hard to generate, or secure storage must be minimized due to expense. Unlike other DAE schemes, such as GCM-SIV, SUNDAE can be implemented efficiently on both constrained devices, as well as the servers communicating with those devices. We prove SUNDAE secure relative to its underlying block cipher, and provide an extensive implementation study, with results in both software and hardware, demonstrating that SUNDAE offers improved compactness and power consumption in hardware compared to other lightweight AE modes, while simultaneously offering comparable performance to GCM-SIV on parallel high-end platforms.
2018
TOSC
Double-block Hash-then-Sum: A Paradigm for Constructing BBB Secure PRF
SUM-ECBC (Yasuda, CT-RSA 2010) is the first beyond birthday bound (BBB) secure block cipher based deterministic MAC. After this work, some more BBB secure deterministic MACs have been proposed, namely PMAC_Plus (Yasuda, CRYPTO 2011), 3kf9 (Zhang et al., ASIACRYPT 2012) and LightMAC_Plus (Naito, ASIACRYPT 2017). In this paper, we have abstracted out the inherent design principle of all these BBB secure MACs and present a generic design paradigm to construct a BBB secure pseudo random function, namely Double-block Hash-then- Sum or in short (DbHtS). A DbHtS construction, as the name implies, computes a double block hash on the message and then sum the encrypted output of the two hash blocks. Our result renders that if the underlying hash function meets certain security requirements (namely cover-free and block-wise universal advantage is low), DbHtS construction provides 2n/3-bit security. We demonstrate the applicability of our result by instantiating all the existing beyond birthday secure deterministic MACs (e.g., SUM-ECBC, PMAC_Plus, 3kf9, LightMAC_Plus) as well as a simple two-keyed variant for each of them and some algebraic hash based constructions.
2018
TOSC
More Accurate Differential Properties of LED64 and Midori64
In differential cryptanalysis, a differential is more valuable than the single trail belonging to it in general. The traditional way to compute the probability of the differential is to sum the probabilities of all trails within it. The automatic tool for the search of differentials based on Mixed Integer Linear Programming (MILP) has been proposed and realises the task of finding multiple trails of a given differential. The problem is whether it is reliable to evaluate the probability of the differential traditionally. In this paper, we focus on two lightweight block ciphers – LED64 and Midori64 and show the more accurate estimation of differential probability considering the key schedule. Firstly, an automated tool based on Boolean Satisfiability Problem (SAT) is put forward to accomplish the automatic search of differentials for ciphers with S-boxes and is applied to LED64 and Midori64. Secondly, we provide an automatic approach to detect the right pairs following a given differential, which can be exploited to calculate the differential property. Applying this technique to the STEP function of LED64, we discover some differentials with enhanced probability. As a result, the previous attacks relying upon high probability differentials can be improved definitely. Thirdly, we present a method to compute an upper-bound of the weak-key ratio for a given differential, which is utilised to analyse 4-round differentials of Midori64. We detect two differentials whose weak-key ratios are much lower than the expected 50%. More than 78% of the keys will make these two differentials being impossible differentials. The idea of the estimation for an upper-bound of the weak-key ratio can be employed for other ciphers and allows us to launch differential attacks more reliably. Finally, we introduce how to compute the enhanced differential probability and evaluate the size of keys achieving the improved probability. Such a property may incur an efficient weak-key attack. For a 4-round differential of Midori64, we obtain an improved differential property for a portion of keys.
2018
TOSC
Cryptanalysis of Reduced round SKINNY Block Cipher
SKINNY is a family of lightweight tweakable block ciphers designed to have the smallest hardware footprint. In this paper, we present zero-correlation linear approximations and the related-tweakey impossible differential characteristics for different versions of SKINNY .We utilize Mixed Integer Linear Programming (MILP) to search all zero-correlation linear distinguishers for all variants of SKINNY, where the longest distinguisher found reaches 10 rounds. Using a 9-round characteristic, we present 14 and 18-round zero correlation attacks on SKINNY-64-64 and SKINNY- 64-128, respectively. Also, for SKINNY-n-n and SKINNY-n-2n, we construct 13 and 15-round related-tweakey impossible differential characteristics, respectively. Utilizing these characteristics, we propose 23-round related-tweakey impossible differential cryptanalysis by applying the key recovery attack for SKINNY-n-2n and 19-round attack for SKINNY-n-n. To the best of our knowledge, the presented zero-correlation characteristics in this paper are the first attempt to investigate the security of SKINNY against this attack and the results on the related-tweakey impossible differential attack are the best reported ones.
2018
TOSC
Cryptanalysis of Low-Data Instances of Full LowMCv2
LowMC is a family of block ciphers designed for a low multiplicative complexity. The specification allows a large variety of instantiations, differing in block size, key size, number of S-boxes applied per round and allowed data complexity. The number of rounds deemed secure is determined by evaluating a number of attack vectors and taking the number of rounds still secure against the best of these. In this paper, we demonstrate that the attacks considered by the designers of LowMC in the version 2 of the round-formular were not sufficient to fend off all possible attacks. In the case of instantiations of LowMC with one of the most useful settings, namely with few applied S-boxes per round and only low allowable data complexities, efficient attacks based on difference enumeration techniques can be constructed. We show that it is most effective to consider tuples of differences instead of simple differences, both to increase the range of the distinguishers and to enable key recovery attacks. All applications for LowMC we are aware of, including signature schemes like Picnic and more recent (ring/group) signature schemes have used version 3 of the roundformular for LowMC, which takes our attack already into account.
2018
TOSC
Cube-Attack-Like Cryptanalysis of Round-Reduced Keccak Using MILP
Cube-attack-like cryptanalysis on round-reduced Keccak was proposed by Dinur et al. at EUROCRYPT 2015. It recovers the key through two phases: the preprocessing phase for precomputing a look-up table and online phase for querying the output and getting the cube sum with which the right key can be retrieved by looking up the precomputed table. It was shown that such attacks are efficient specifically for Keccak-based constructions with small nonce or message block size. In this paper, we provide a mixed integer linear programming (MILP) model for cubeattack- like cryptanalysis on keyed Keccak, which does not impose any unnecessary constraint on cube variables and finds almost optimal cubes by balancing the two phases of cube-attack-like cryptanalysis. Our model is applied to Ketje Jr, Ketje Sr, a Xoodoo-based authenticated encryption and Keccak-MAC-512, all of which have a relatively small nonce or message block size. As a result, time complexities of 5-round attacks on Ketje Jr and 7-round attacks on Ketje Sr can be improved significantly. Meanwhile, 6-round attacks, one more round than the previous best attack, are possible if the key size of Ketje V1 (V2) is reduced to 72 (80) bits. For Xoodoo-based AE in Ketje style, the attack reaches 6 rounds. Additionally, a 7-round attack of Keccak-MAC-512 is achieved. To verify the correctness of our attacks, a 5-round attack on Ketje V1 is implemented and tested practically. It is noted that this work does not threaten the security of any Keccak-based construction.
2018
TOSC
Conditional Linear Cryptanalysis – Cryptanalysis of DES with Less Than 242 Complexity
In this paper we introduce a new extension of linear cryptanalysis that may reduce the complexity of attacks by conditioning linear approximations on other linear approximations. We show that the bias of some linear approximations may increase under such conditions, so that after discarding the known plaintexts that do not satisfy the conditions, the bias of the remaining known plaintexts increases. We show that this extension can lead to improvements of attacks, which may require fewer known plaintexts and time of analysis. We present several types of such conditions, including one that is especially useful for the analysis of Feistel ciphers. We exemplify the usage of such conditions for attacks by a careful application of our extension to Matsui’s attack on the full 16-round DES, which succeeds to reduce the complexity of the best attack on DES to less than 242. We programmed a test implementation of our attack and verified our claimed results with a large number of runs. We also introduce a new type of approximations, to which we call scattered approximations, and discuss its applications.
2018
TOSC
Generating Graphs Packed with Paths Estimation of Linear Approximations and Differentials
When designing a new symmetric-key primitive, the designer must show resistance to known attacks. Perhaps most prominent amongst these are linear and differential cryptanalysis. However, it is notoriously difficult to accurately demonstrate e.g. a block cipher’s resistance to these attacks, and thus most designers resort to deriving bounds on the linear correlations and differential probabilities of their design. On the other side of the spectrum, the cryptanalyst is interested in accurately assessing the strength of a linear or differential attack.While several tools have been developed to search for optimal linear and differential trails, e.g. MILP and SAT based methods, only few approaches specifically try to find as many trails of a single approximation or differential as possible. This can result in an overestimate of a cipher’s resistance to linear and differential attacks, as was for example the case for PRESENT.In this work, we present a new algorithm for linear and differential trail search. The algorithm represents the problem of estimating approximations and differentials as the problem of finding many long paths through a multistage graph. We demonstrate that this approach allows us to find a very large number of good trails for each approximation or differential. Moreover, we show how the algorithm can be used to efficiently estimate the key dependent correlation distribution of a linear approximation, facilitating advanced linear attacks. We apply the algorithm to 17 different ciphers, and present new and improved results on several of these.
2018
TOSC
On the Boomerang Uniformity of Cryptographic Sboxes
The boomerang attack is a cryptanalysis technique against block ciphers which combines two differentials for the upper part and the lower part of the cipher. The dependency between these two differentials then highly affects the complexity of the attack and all its variants. Recently, Cid et al. introduced at Eurocrypt’18 a new tool, called the Boomerang Connectivity Table (BCT) that permits to simplify this complexity analysis, by storing and unifying the different switching probabilities of the cipher’s Sbox in one table. In this seminal paper a brief analysis of the properties of these tables is provided and some open questions are raised. It is being asked in particular whether Sboxes with optimal BCTs exist for even dimensions, where optimal means that the maximal value in the BCT equals the lowest known differential uniformity. When the dimension is even and differs from 6, such optimal Sboxes correspond to permutations such that the maximal value in their DDT and in their BCT equals 4 (unless APN permutations for such dimensions exist). We provide in this work a more in-depth analysis of boomerang connectivity tables, by studying more closely differentially 4-uniform Sboxes. We first completely characterize the BCT of all differentially 4-uniform permutations of 4 bits and then study these objects for some cryptographically relevant families of Sboxes, as the inverse function and quadratic permutations. These two families provide us with the first examples of differentially 4-uniform Sboxes optimal against boomerang attacks for an even number of variables, answering the above open question.
2018
TOSC
Lightweight and Side-channel Secure 4 × 4 S-Boxes from Cellular Automata Rules
This work focuses on side-channel resilient design strategies for symmetrickey cryptographic primitives targeting lightweight applications. In light of NIST’s lightweight cryptography project, design choices for block ciphers must consider not only security against traditional cryptanalysis, but also side-channel security, while adhering to low area and power requirements. In this paper, we explore design strategies for substitution-permutation network (SPN)-based block ciphers that make them amenable to low-cost threshold implementations (TI) - a provably secure strategy against side-channel attacks. The core building blocks for our strategy are cryptographically optimal 4×4 S-Boxes, implemented via repeated iterations of simple cellular automata (CA) rules. We present highly optimized TI circuits for such S-Boxes, that consume nearly 40% less area and power as compared to popular lightweight S-Boxes such as PRESENT and GIFT. We validate our claims via implementation results on ASIC using 180nm technology. We also present a comparison of TI circuits for two popular lightweight linear diffusion layer choices - bit permutations and MixColumns using almost-maximum-distance-separable (almost-MDS) matrices. We finally illustrate design paradigms that combine the aforementioned TI circuits for S-Boxes and diffusion layers to obtain fully side-channel secure SPN block cipher implementations with low area and power requirements.
2018
TOSC
The design of Xoodoo and Xoofff
This paper presents Xoodoo, a 48-byte cryptographic permutation with excellent propagation properties. Its design approach is inspired by Keccak-p, while it is dimensioned like Gimli for efficiency on low-end processors. The structure consists of three planes of 128 bits each, which interact per 3-bit columns through mixing and nonlinear operations, and which otherwise move as three independent rigid objects. We analyze its differential and linear propagation properties and, in particular, prove lower bounds on the weight of trails using the tree search-based technique of Mella et al. (ToSC 2017). Xoodoo’s primary target application is in the Farfalle construction that we instantiate for the doubly-extendable cryptographic keyed (or deck) function Xoofff. Combining a relatively narrow permutation with the parallelism of Farfalle results in very efficient schemes on a wide range of platforms, from low-end devices to high-end processors with vector instructions.
2018
TOSC
Adiantum: length-preserving encryption for entry-level processors
We present HBSH, a simple construction for tweakable length-preserving encryption which supports the fastest options for hashing and stream encryption for processors without AES or other crypto instructions, with a provable quadratic advantage bound. Our composition Adiantum uses NH, Poly1305, XChaCha12, and a single AES invocation. On an ARM Cortex-A7 processor, Adiantum decrypts 4096-byte messages at 10.6 cycles per byte, over five times faster than AES-256-XTS, with a constant-time implementation. We also define HPolyC which is simpler and has excellent key agility at 13.6 cycles per byte.
2018
TOSC
Generalized Nonlinear Invariant Attack and a New Design Criterion for Round Constants
The nonlinear invariant attack was introduced at ASIACRYPT 2016 by Todo et al.. The attack has received extensive attention of cryptographic community due to its practical application on the full-round block ciphers SCREAM, iSCREAM, and Midori64. However, the attack heavily relies on the choice of round constants and it becomes inefficient in the case these constants nonlinearly affect the so-called nonlinear invariants. In this article, to eliminate the impact from the round constants, a generalized nonlinear invariant attack which uses a pair of constants in the input of nonlinear invariants is proposed. The efficiency of this extended framework is practically confirmed by mounting a distinguishing attack on a variant of full-round iSCREAM cipher under a class of 280 weak keys. The considered variant of iSCREAM is however resistant against nonlinear invariant attack of Todo et al.. Furthermore, we investigate the resistance of block ciphers against generalized nonlinear invariant attacks with respect to the choice of round constants in an extended framework. We introduce a useful concept of closed-loop invariants of the substitution box (S-box) and show that the choice of robust round constants is closely related to the existence of linear structure of the closed-loop invariants of the substitution layer. In particular, we demonstrate that the design criteria for the round constants in Beierle et al.’s work at CRYPTO 2017 is not an optimal strategy. The round constants selected using this method may induce certain weaknesses that can be exploited in our generalized nonlinear invariant attack model. This scenario is efficiently demonstrated in the case of a slightly modified variant of the Midori64 block cipher.
2018
TOSC
Nonlinear Approximations in Cryptanalysis Revisited
This work studies deterministic and non-deterministic nonlinear approximations for cryptanalysis of block ciphers and cryptographic permutations and embeds it into the well-understood framework of linear cryptanalysis. For a deterministic (i.e., with correlation ±1) nonlinear approximation we show that in many cases, such a nonlinear approximation implies the existence of a highly-biased linear approximation. For non-deterministic nonlinear approximations, by transforming the cipher under consideration by conjugating each keyed instance with a fixed permutation, we are able to transfer many methods from linear cryptanalysis to the nonlinear case. Using this framework we in particular show that there exist ciphers for which some transformed versions are significantly weaker with regard to linear cryptanalysis than their original counterparts.
2018
TOSC
New Yoyo Tricks with AES-based Permutations
In Asiacrypt 2017, Rønjom et al. reported some interesting generic properties of SPNs, leading to what they call the Yoyo trick, and applied it to find the most efficient distinguishers on AES. In this work, we explore the Yoyo idea in distinguishing public permutations for the first time. We introduce the notion of nested zero difference pattern which extends the Yoyo idea and helps to compose it using improbable and impossible differential strategies to penetrate higher number of rounds. We devise a novel inside-out application of Yoyo which enables us to start the Yoyo game from an internal round. As an application, we investigate the AES-based public permutation AESQ used inside the authenticated cipher PAEQ. We achieve the first deterministic distinguisher of AESQ up to 8 rounds and the first 9-round distinguisher of AESQ that start from the first round with a practical complexity of around 226. We manage to augment Yoyo with improbable and impossible differentials leading to distinguishers on 9, 10, 12 rounds with complexities of about 22, 228, 2126 respectively. Further, with impossible differentials and a bi-directional Yoyo strategy, we obtain a 16-round impossible differential distinguisher with a complexity of 2126. Our results outperform all previous records on AESQ by a substantial margin. As another application, we apply the proposed strategies on AES in the known-key setting leading to one of the best 8-round known-key distinguisher with a complexity of 230. Finally, this work amplifies the scope of the Yoyo technique as a generic cryptanalysis tool.
2018
TOSC
Key Prediction Security of Keyed Sponges
The keyed sponge is a well-accepted method for message authentication. It processes data at a certain rate by sequential evaluation of an underlying permutation. If the key size k is smaller than the rate, currently known bounds are tight, but if it exceeds the rate, state of the art only dictates security up to 2k/2. We take closer inspection at the key prediction security of the sponge and close the remaining gap in the existing security analysis: we confirm key security up to close to 2k, regardless of the rate. The result impacts all applications of the keyed sponge and duplex that process at a rate smaller than the key size, including the STROBE protocol framework, as well as the related constructions such as HMAC-SHA-3 and the sandwich sponge.
2018
TOSC
Key Assignment Scheme with Authenticated Encryption
The Key Assignment Scheme (KAS) is a well-studied cryptographic primitive used for hierarchical access control (HAC) in a multilevel organisation where the classes of people with higher privileges can access files of those with lower ones. Our first contribution is the formalization of a new cryptographic primitive, namely, KAS-AE that supports the aforementioned HAC solution with an additional authenticated encryption property. Next, we present three efficient KAS-AE schemes that solve the HAC and the associated authenticated encryption problem more efficiently – both with respect to time and memory – than the existing solutions that achieve it by executing KAS and AE separately. Our first KAS-AE construction is built by using the cryptographic primitive MLE (EUROCRYPT 2013) as a black box; the other two constructions (which are the most efficient ones) have been derived by cleverly tweaking the hash function FP (Indocrypt 2012) and the authenticated encryption scheme APE (FSE 2014). This high efficiency of our constructions is critically achieved by using two techniques: design of a mechanism for reverse decryption used for reduction of time complexity, and a novel key management scheme for optimizing storage requirements when organizational hierarchy forms an arbitrary access graph (instead of a linear graph). We observe that constructing a highly efficient KAS-AE scheme using primitives other than MLE, FP and APE is a non-trivial task. We leave it as an open problem. Finally, we provide a detailed comparison of all the KAS-AE schemes.
2018
TOSC
Sound Hashing Modes of Arbitrary Functions, Permutations, and Block Ciphers
Cryptographic hashing modes come in many flavors, including Merkle-Damgård with various types of strengthening, Merkle trees, and sponge functions. As underlying primitives, these functions use arbitrary functions, permutations, or block ciphers. In this work we provide three simple proofs, one per primitive type, that cover all modes where the input to the primitive consists of message bits, chaining value bits, and bits that only depend on the mode and message length. Our approach generalizes and simplifies over earlier attempts of Dodis et al. (FSE 2009) and Bertoni et al. (Int. J. Inf. Sec. 2014). We prove tight indifferentiability bounds for modes using each of these three primitive types provided that the mode satisfies some easy to verify conditions.
2019
TOSC
CRAFT: Lightweight Tweakable Block Cipher with Efficient Protection Against DFA Attacks
Traditionally, countermeasures against physical attacks are integrated into the implementation of cryptographic primitives after the algorithms have been designed for achieving a certain level of cryptanalytic security. This picture has been changed by the introduction of PICARO, ZORRO, and FIDES, where efficient protection against Side-Channel Analysis (SCA) attacks has been considered in their design. In this work we present the tweakable block cipher CRAFT: the efficient protection of its implementations against Differential Fault Analysis (DFA) attacks has been one of the main design criteria, while we provide strong bounds for its security in the related-tweak model. Considering the area footprint of round-based hardware implementations, CRAFT outperforms the other lightweight ciphers with the same state and key size. This holds not only for unprotected implementations but also when fault-detection facilities, side-channel protection, and their combination are integrated into the implementation. In addition to supporting a 64-bit tweak, CRAFT has the additional property that the circuit realizing the encryption can support the decryption functionality as well with very little area overhead.
2019
TOSC
libInterMAC: Beyond Confidentiality and Integrity in Practice
Boldyreva et al. (Eurocrypt 2012) defined a fine-grained security model capturing ciphertext fragmentation attacks against symmetric encryption schemes. The model was extended by Albrecht et al. (CCS 2016) to include an integrity notion. The extended security model encompasses important security goals of SSH that go beyond confidentiality and integrity to include length hiding and denial-of-service resistance properties. Boldyreva et al. also defined and analysed the InterMAC scheme, while Albrecht et al. showed that InterMAC satisfies stronger security notions than all currently available SSH encryption schemes. In this work, we take the InterMAC scheme and make it fully ready for use in practice. This involves several steps. First, we modify the InterMAC scheme to support encryption of arbitrary length plaintexts and we replace the use of Encrypt-then-MAC in InterMAC with modern noncebased authenticated encryption. Second, we describe a reference implementation of the modified InterMAC scheme in the form of the library libInterMAC. We give a performance analysis of libInterMAC. Third, to test the practical performance of libInterMAC, we implement several InterMAC-based encryption schemes in OpenSSH and carry out a performance analysis for the use-case of file transfer using SCP. We measure the data throughput and the data overhead of using InterMAC-based schemes compared to existing schemes in OpenSSH. Our analysis shows that, for some network set-ups, using InterMAC-based schemes in OpenSSH only moderately affects performance whilst providing stronger security guarantees compared to existing schemes.
2019
TOSC
Constructing Low-latency Involutory MDS Matrices with Lightweight Circuits
MDS matrices are important building blocks providing diffusion functionality for the design of many symmetric-key primitives. In recent years, continuous efforts are made on the construction of MDS matrices with small area footprints in the context of lightweight cryptography. Just recently, Duval and Leurent (ToSC 2018/FSE 2019) reported some 32 × 32 binary MDS matrices with branch number 5, which can be implemented with only 67 XOR gates, whereas the previously known lightest ones of the same size cost 72 XOR gates.In this article, we focus on the construction of lightweight involutory MDS matrices, which are even more desirable than ordinary MDS matrices, since the same circuit can be reused when the inverse is required. In particular, we identify some involutory MDS matrices which can be realized with only 78 XOR gates with depth 4, whereas the previously known lightest involutory MDS matrices cost 84 XOR gates with the same depth. Notably, the involutory MDS matrix we find is much smaller than the AES MixColumns operation, which requires 97 XOR gates with depth 8 when implemented as a block of combinatorial logic that can be computed in one clock cycle. However, with respect to latency, the AES MixColumns operation is superior to our 78-XOR involutory matrices, since the AES MixColumns can be implemented with depth 3 by using more XOR gates.We prove that the depth of a 32 × 32 MDS matrix with branch number 5 (e.g., the AES MixColumns operation) is at least 3. Then, we enhance Boyar’s SLP-heuristic algorithm with circuit depth awareness, such that the depth of its output circuit is limited. Along the way, we give a formula for computing the minimum achievable depth of a circuit implementing the summation of a set of signals with given depths, which is of independent interest. We apply the new SLP heuristic to a large set of lightweight involutory MDS matrices, and we identify a depth 3 involutory MDS matrix whose implementation costs 88 XOR gates, which is superior to the AES MixColumns operation with respect to both lightweightness and latency, and enjoys the extra involution property.
2019
TOSC
Boomerang Connectivity Table Revisited. Application to SKINNY and AES
The boomerang attack is a variant of differential cryptanalysis which regards a block cipher E as the composition of two sub-ciphers, i.e., E = E1 o E0, and which constructs distinguishers for E with probability p2q2 by combining differential trails for E0 and E1 with probability p and q respectively. However, the validity of this attack relies on the dependency between the two differential trails. Murphy has shown cases where probabilities calculated by p2q2 turn out to be zero, while techniques such as boomerang switches proposed by Biryukov and Khovratovich give rise to probabilities greater than p2q2. To formalize such dependency to obtain a more accurate estimation of the probability of the distinguisher, Dunkelman et al. proposed the sandwich framework that regards E as Ẽ1 o Em o Ẽ0, where the dependency between the two differential trails is handled by a careful analysis of the probability of the middle part Em. Recently, Cid et al. proposed the Boomerang Connectivity Table (BCT) which unifies the previous switch techniques and incompatibility together and evaluates the probability of Em theoretically when Em is composed of a single S-box layer. In this paper, we revisit the BCT and propose a generalized framework which is able to identify the actual boundaries of Em which contains dependency of the two differential trails and systematically evaluate the probability of Em with any number of rounds. To demonstrate the power of this new framework, we apply it to two block ciphers SKINNY and AES. In the application to SKINNY, the probabilities of four boomerang distinguishers are re-evaluated. It turns out that Em involves5 or 6 rounds and the probabilities of the full distinguishers are much higher than previously evaluated. In the application to AES, the new framework is used to exclude incompatibility and find high probability distinguishers of AES-128 under the related-subkey setting. As a result, a 6-round distinguisher with probability 2−109.42 is constructed. Lastly, we discuss the relation between the dependency of two differential trails in boomerang distinguishers and the properties of components of the cipher.
2019
TOSC
Boomerang Switch in Multiple Rounds. Application to AES Variants and Deoxys
The boomerang attack is a cryptanalysis technique that allows an attacker to concatenate two short differential characteristics. Several research results (ladder switch, S-box switch, sandwich attack, Boomerang Connectivity Table (BCT), ...) showed that the dependency between these two characteristics at the switching round can have a significant impact on the complexity of the attack, or even potentially invalidate it. In this paper, we revisit the issue of boomerang switching effect, and exploit it in the case where multiple rounds are involved. To support our analysis, we propose a tool called Boomerang Difference Table (BDT), which can be seen as an improvement of the BCT and allows a systematic evaluation of the boomerang switch through multiple rounds. In order to illustrate the power of this technique, we propose a new related-key attack on 10-round AES-256 which requires only 2 simple related-keys and 275 computations. This is a much more realistic scenario than the state-of-the-art 10-round AES-256 attacks, where subkey oracles, or several related-keys and high computational power is needed. Furthermore, we also provide improved attacks against full AES-192 and reduced-round Deoxys.
2019
TOSC
A General Proof Framework for Recent AES Distinguishers
In this paper, a new framework is developed for proving and adapting the recently proposed multiple-of-8 property and mixture-differential distinguishers. The above properties are formulated as immediate consequences of an equivalence relation on the input pairs, under which the difference at the output of the round function is invariant. This approach provides a further understanding of these newly developed distinguishers. For example, it clearly shows that the branch number of the linear layer does not influence the validity of the property, on the contrary of what was previously believed. We further provide an extension of the mixture-differential distinguishers and multiple-of-8 property to any SPN and to a larger class of subspaces. These adapted properties can then be exhibited in a systematic way for other ciphers than the AES. We illustrate this with the examples of Midori, Klein, LED and Skinny.
2019
TOSC
Zero-Correlation Attacks on Tweakable Block Ciphers with Linear Tweakey Expansion
The design and analysis of dedicated tweakable block ciphers is a quite recent and very active research field that provides an ongoing stream of new insights. For instance, results of Kranz, Leander, and Wiemer from FSE 2017 show that the addition of a tweak using a linear tweak schedule does not introduce new linear characteristics. In this paper, we consider – to the best of our knowledge – for the first time the effect of the tweak on zero-correlation linear cryptanalysis for ciphers that have a linear tweak schedule. It turns out that the tweak can often be used to get zero-correlation linear hulls covering more rounds compared to just searching zero-correlation linear hulls on the data-path of a cipher. Moreover, this also implies the existence of integral distinguishers on the same number of rounds. We have applied our technique on round reduced versions of Qarma, Mantis, and Skinny. As a result, we can present – to the best of our knowledge – the best attack (with respect to number of rounds) on a round-reduced variant of Qarma.
2019
TOSC
Related-Tweak Statistical Saturation Cryptanalysis and Its Application on QARMA
Statistical saturation attack takes advantage of a set of plaintext with some bits fixed while the others vary randomly, and then track the evolution of a non-uniform plaintext distribution through the cipher. Previous statistical saturation attacks are all implemented under single-key setting, and there is no public attack models under related-key/tweak setting. In this paper, we propose a new cryptanalytic method which can be seen as related-key/tweak statistical saturation attack by revealing the link between the related-key/tweak statistical saturation distinguishers and KDIB (Key Difference Invariant Bias) / TDIB (Tweak Difference Invariant Bias) ones. KDIB cryptanalysis was proposed by Bogdanov et al. at ASIACRYPT’13 and utilizes the property that there can exist linear trails such that their biases are deterministically invariant under key difference. And this method can be easily extended to TDIB distinguishers if the tweak is also alternated. The link between them provides a new and more efficient way to find related-key/tweak statistical saturation distinguishers in ciphers. Thereafter, an automatic searching algorithm for KDIB/TDIB distinguishers is also given in this paper, which can be implemented to find word-level KDIB distinguishers for S-box based key-alternating ciphers. We apply this algorithm to QARMA-64 and give related-tweak statistical saturation attack for 10-round QARMA-64 with outer whitening key. Besides, an 11-round attack on QARMA-128 is also given based on the TDIB technique. Compared with previous public attacks on QARMA including outer whitening key, all attacks presented in this paper are the best ones in terms of the number of rounds.