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25 May 2019
Bootstrapping of FHE over the integer with large message is a open problem, which is to evaluate double modulo $(c ~\text{mod}~ p )~\mod~ Q$ arithmetic homomorphically for large $Q$. In this paper, we express this double modulo reduction circuit as a arithmetic circuit of degree at most $\theta^2 \log^2\theta/2$, with $O(\theta \log^2\theta)$ multiplication gates, where $\theta= \frac{\lambda}{\log \lambda}$ and $\lambda$ is the security parameter. The complexity of decryption circuit is independent of the message space size $Q$ with a constraint $Q> \theta \log^2\theta/2$.
ePrint Report Solutions of $x^{q^k}+\cdots+x^{q}+x=a$ in $GF(2^n)$ Kwang Ho Kim, Jong Hyok Choe, Dok Nam Lee, Dae Song Go, Sihem Mesnager
Though it is well known that the roots of any affine polynomial over finite field can be computed by a system of linear equations by using a normal base of the field, such solving approach appears to be difficult to apply when the field is fairly large. Thus, it may be of great interest to find explicit representation of the solutions independently of the field base. This was previously done only for quadratic equations over binary finite field. This paper gives explicit representation of solutions for much wider class of affine polynomials over binary prime field.
Recently one new key recovery method for a filter generator was proposed. It is based on so-called planar approximations of such a generator. This paper contains the numerical part of the research of the Boolean functions properties which allow to protect the generator against this method. The main theoretical part of this research is presented at the CTCrypt 2019 conference.
ePrint Report How to not break SIDH Chloe Martindale, Lorenz Panny
We give a number of approaches which, to a newcomer, may seem like natural ways to attack the SIDH/SIKE protocol, and explain why each of these approaches seems to fail, at least with the specific setup and parameters of SIKE. Our aim is to save some time for others who are looking to assess the security of SIDH/SIKE. We include methods that fail to attack the pure isogeny problem, namely: looking at the $\mathbb F_p$-subgraph, lifting to characteristic zero, and using Weil restrictions. We also include methods that fail to make use of the public 2-power and 3-power torsion points, namely: interpolation techniques, any purely group-theoretic approaches, and constructing an endomorphism à la Petit to exploit the auxiliary points, but with balanced parameters.
ePrint Report Identity-Based Encryption from $e$-th Power Residue Symbols Xiaopeng Zhao, Jinwen Zheng, Nanyuan Cao, Zhenfu Cao, Xiaolei Dong
This paper generalizes the notable Galbrath's test by introducing the general reciprocity law on function fields. With the help of the extended Galbrath's test, we show the scheme of Boneh, LaVigne and Sabin (BLS) is not anonymous in general. BLS's scheme naturally generalizes Cocks' scheme to higher power residue symbols, but it is less efficient, bandwidth-wise because computing $e$-th power residue symbols is really time-consuming and ciphertexts are expressed as polynomials. We improve the efficiency of BLS's scheme through taking off the part of computing $e$-th power residue symbols in the encryption phase. Our construction also widens BLS's scheme to the case $e$ is square-free. Finally, we provide some methods for computing $e$-th power residue symbols in order to make our scheme more efficient.
How much we say, to whom, and when, is inherently telling, even if the contents of our communication is unclear. In other words: encryption is not enough; neither to secure privacy, nor to maintain confidentiality. Years ago Adi Shamir already predicted that encryption will be bypassed. And it has. The modern dweller of cyber space is routinely violated via her data behavior. Also, often an adversary has the power to compel release of cryptographic keys over well-exposed communication. The front has shifted, and now technology must build cryptographic shields beyond content, and into pattern, even as to existence of communication. We present here tools, solutions, methods to that end. They are based on equivocation. If a message is received by many recipients, it hides the intended one. If a protocol calls for decoy messages, then it protects the identity of the sender of the contents-laden message. BitGrey is a protocol that creates a "grey hole" (of various shades) around the communicating community, so that very little information leaks out. In addition the BitLoop protocol constructs a fixed rate circulating bit flow, traversing through all members of a group. The looping bits appear random, and effectively hide the pattern, even the existence of communication within the group.
In this paper we present a comprehensive comparison between pairing-friendly elliptic curves, considering different curve forms and twists where possible. We define a measure of the efficiency of a parametrized pairing-friendly family that takes into account the number field sieve (NFS) attacks (unlike the $\rho$-value). This measure includes an approximation of the security of the discrete logarithm problem in $\mathbb F_{p^k}^*$, computed via the method of Barbulescu and Duquesne [4]. We compute the security of the families presented by Fotiadis and Konstantinou in [13], compute some new families, and compare the efficiency of both of these with the (adjusted) BLS, KSS, and BN families, and with the new families of [19]. Finally, we present an optimal pairing-friendly elliptic curve for security level 128 and recommend two pairing-friendly elliptic curves for security level 192.
24 May 2019
Pseudorandom functions are traditionally built upon block ciphers, but with the trend of permutation based cryptography, it is a natural question to investigate the design of pseudorandom functions from random permutations. We present a generic study of how to build beyond birthday bound secure pseudorandom functions from public random permutations. We first show that a pseudorandom function based on a single permutation call cannot be secure beyond the $2^{n/2}$ birthday bound, where n is the state size of the function. We next consider the Sum of Even-Mansour (SoEM) construction, that instantiates the sum of permutations with the Even-Mansour construction. We prove that SoEM achieves tight $2n/3$-bit security if it is constructed from two independent permutations and two randomly drawn keys. We also demonstrate a birthday bound attack if either the permutations or the keys are identical. Finally, we present the Sum of Key Alternating Ciphers (SoKAC) construction, a translation of Encrypted Davies-Meyer Dual to a public permutation based setting, and show that SoKAC achieves tight $2n/3$-bit security even when a single key is used.
ePrint Report Towards post-quantum symmetric cryptography John Gregory Underhill, Stiepan Aure&#769;lien Kovac, Xenia Bogomolec
Withthiswork, weintendondemonstratingtheneedfor improvements to the currently standardized AES family of cryptosystems, and provide a solution that meets the requirements of long-term security in the rapidly evolving threat landscape. The solution proposed is flexible, dramatically increases the potential security of the cipher, and strongly mitigates many of the most serious attacks on the AES family of cryptosystems. Further, our solution can be easily integrated into existing AES cryptosystem deployments, with only a few small changes required, thus preserving the large investments in this cipher both in hardware and software.
ePrint Report Continuous Space-Bounded Non-Malleable Codes from Stronger Proofs-of-Space Binyi Chen, Yilei Chen, Kristina Hosta&#769;kova&#769;, Pratyay Mukherjee
Non-malleable codes are encoding schemes that provide protections against various classes of tampering attacks. Recently Faust et al. (CRYPTO 2017) initiated the study of space- bounded non-malleable codes that provide such protections against tampering within small- space devices. They put forward a construction based on any non-interactive proof-of-space (NIPoS). However, the scheme only protects against an a priori bounded number of tampering attacks.

We construct non-malleable codes that are resilient to an unbounded polynomial number of space-bounded tamperings. Towards that we introduce a stronger variant of NIPoS called proof-extractable NIPoS (PExt-NIPoS), and propose two approaches of constructing such a primitive. Using a new proof strategy we show that the generic encoding scheme of Faust et al. achieves unbounded tamper-resilience when instantiated with a PExt-NIPoS. We show two methods to construct PExt-NIPoS:

1. The first method uses a special family of “memory-hard” graphs, called challenge-hard graphs (CHG), a notion we introduce here. We instantiate such family of graphs based on an extension of stack of localized expanders (first used by Ren and Devadas in the context of proof-of-space). In addition, we show that the graph construction used as a building block for the proof-of-space by Dziembowski et al. (CRYPTO 2015) satisfies challenge-hardness as well. These two CHG-instantiations lead to continuous space-bounded NMC with different features in the random oracle model.

2. Our second instantiation relies on a new measurable property, called uniqueness of NIPoS. We show that standard extractability can be upgraded to proof-extractability if the NIPoS also has uniqueness. We propose a simple heuristic construction of NIPoS, that achieves (partial) uniqueness, based on a candidate memory-hard function in the standard model and a publicly verifiable computation with small-space verification. Instantiating the encoding scheme of Faust et al. with this NIPoS, we obtain a continuous space-bounded NMC that supports the “most practical” parameters, complementing the provably secure but “relatively impractical” CHG-based constructions. Additionally, we revisit the construction of Faust et al. and observe that due to the lack of uniqueness of their NIPoS, the resulting encoding schemes yield “highly impractical” parameters in the continuous setting.

We conclude the paper with a comparative study of all our non-malleable code constructions with an estimation of concrete parameters.
This paper is focused on an open question regarding the correlation and the power of the NIST statistical test suite. If we found some correlation between these statistical tests, then we can improve the testing strategy by executing only one of the tests that are correlated. Using the Galton-Pearson “product-moment correlation coefficient”, by simulation, we found a high correlation between five couples of this statistical tests: (frequency, cumulative sums forward), (frequency, cumulative sums reverse), (cumulative sums forward, cumulative sums reverse), (random excursions, random excursions variant), and (serial 1, serial 2).
23 May 2019
This paper describes a new public coin, succinct interactive zero-knowledge argument for NP under standard cryptographic hardness assumptions—without requiring a trusted setup. In particular, our argument enables a prover to prove the satisfiability of arithmetic circuits over a large finite field (an NP-complete language for which there exist efficient reductions from high-level programs of practical interest) to a verifier. We construct this argument through a novel synthesis of techniques from prior work on short PCPs, MIPs, and doubly-efficient IPs. Specifically, our interactive argument is a succinct variant of the sum-check protocol where the protocol is run with a carefully-constructed low-degree polynomial that encodes a given circuit satisfiability instance. Since our interactive argument is public coin, we make it non-interactive in the random oracle model, thereby obtaining a zero-knowledge succinct non-interactive argument of knowledge (zkSNARK), which we call Spartan.

Spartan is the first zkSNARK without trusted setup (i.e., a “transparent” zkSNARK) where verifying a proof incurs sub-linear costs without requiring data parallelism (or other homogeneity) in the structure of an arithmetic circuit for which a proof is produced. To achieve this, Spartan introduces a notion of computation commitments—a primitive to create a short cryptographic commitment to a mathematical description of an arithmetic circuit. Finally, Spartan is asymptotically efficient with small constants: the prover performs $O(n)$ cryptographic operations to produce a proof of size $O(n^{1/c})$ that can be verified in $O(n^{1-1/c})$ time (after a one-time, public preprocessing of the circuit to create a computation commitment that takes $O(n)$ time), where $n$ denotes the size of an arithmetic circuit and $c \geq 2$ (Spartan can produce $O(\log{n})$-sized proofs, but the verifier incurs $O(n)$ costs).
ePrint Report Finding a Nash Equilibrium Is No Easier Than Breaking Fiat-Shamir Arka Rai Choudhuri, Pavel Hubacek, Chethan Kamath, Krzysztof Pietrzak, Alon Rosen, Guy N. Rothblum
The Fiat-Shamir heuristic transforms a public-coin interactive proof into a non-interactive argument, by replacing the verifier with a cryptographic hash function that is applied to the protocol’s transcript. Constructing hash functions for which this transformation is sound is a central and long-standing open question in cryptography.

We show that solving the End-of-Metered-Line problem is no easier than breaking the soundness of the Fiat-Shamir transformation when applied to the sumcheck protocol. In particular, if the transformed protocol is sound, then any hard problem in #P gives rise to a hard distribution in the class CLS, which is contained in PPAD.

Our main technical contribution is a stateful incrementally verifiable procedure that, given a SAT instance over n variables, counts the number of satisfying assignments. This is accomplished via an exponential sequence of small steps, each computable in time poly(n). Incremental verifiability means that each intermediate state includes a sumcheck-based proof of its correctness, and the proof can be updated and verified in time poly(n).

Combining our construction with a hash family proposed by Canetti et al. [STOC 2019] gives rise to a distribution in the class CLS, which is provably hard under the assumption that any one of a class of fully homomorphic encryption (FHE) schemes has almost-optimal security against quasi-polynomial time adversaries, and under the additional worst-case assumption that there is no polynomial time algorithm for counting the number of satisfying assignments for formulas over a polylogarithmic number of variables.
ePrint Report About Wave Implementation and its Leakage Immunity Thomas Debris-Alazard, Nicolas Sendrier, Jean-Pierre Tillich
Wave is a recent digital signature scheme. It is based on a family of trapdoor one-way Preimage Sampleable Functions and is proven EUF-CMA in the random oracle model under two code-based computational assumptions. One of its key properties is to produce signatures uniformly distributed of fixed Hamming weight. This property implies that, if properly implemented, Wave is immune to leakage attack. We describe here the key stages for the implementation of the Wave trapdoor inverse function to integrate all the features to achieve leakage-freeness. A proof of concept implementation was made in SageMath. It allowed us to check that properly generated Wave signatures are uniformly distributed. In particular, we show that the signatures produced by this implementation defeat the Barreto-Persichetti attack. We show which features of the Wave specification were improperly put aside and explain why the claim of breaking Wave is incorrect.
ePrint Report Linearly-Homomorphic Signatures and Scalable Mix-Nets Chloé Hébant, Duong Hieu Phan, David Pointcheval
Anonymity is a primary ingredient for our digital life. Several tools have been designed to address it such as, for authentication, blind signatures, group signatures or anonymous credentials and, for confidentiality, randomizable encryption or mix-nets. When it comes to complex electronic voting schemes, random shuffling of ciphertexts with mix-nets is the only known tool. However, it requires huge and complex zero-knowledge proofs to guarantee the actual permutation of the initial ciphertexts.

In this paper, we propose a new approach for proving correct shuffling: the mix-servers can simply randomize individual ballots, which means the ciphertexts, the signatures, and the verification keys, with an additional global proof of constant size, and the output will be publicly verifiable. The computational complexity for the mix-servers is linear in the number of ciphertexts. Verification is also linear in the number of ciphertexts, independently of the number of rounds of mixing. This leads to the most efficient technique, that is highly scalable. Our constructions make use of linearly-homomorphic signatures, with new features, that are of independent interest.
22 May 2019
Zero-Knowledge Proof-of-Identity from trusted public certificates (e.g., national identity cards and/or ePassports; eSIM) is introduced here to permissionless blockchains in order to remove the inefficiencies of Sybil-resistant mechanisms such as Proof-of-Work (i.e., high energy and environmental costs) and Proof-of-Stake (i.e., capital hoarding and lower transaction volume). The proposed solution effectively limits the number of mining nodes a single individual would be able to run while keeping membership open to everyone, circumventing the impossibility of full decentralization and the blockchain scalability trilemma when instantiated on a blockchain with a consensus protocol based on the cryptographic random selection of nodes. Resistance to collusion is also considered. Solving one of the most pressing problems in blockchains, a zk-PoI cryptocurrency is proved to have the following advantageous properties: - an incentive-compatible protocol for the issuing of cryptocurrency rewards based on a unique Nash equilibrium - strict domination of mining over all other PoW/PoS cryptocurrencies, thus the zk-PoI cryptocurrency becoming the preferred choice by miners is proved to be a Nash equilibrium and the Evolutionarily Stable Strategy - PoW/PoS cryptocurrencies are condemned to pay the Price of Crypto-Anarchy, redeemed by the optimal efficiency of zk-PoI as it implements the social optimum - the circulation of a zk-PoI cryptocurrency Pareto dominates other PoW/PoS cryptocurrencies - the network effects arising from the social networks inherent to national identity cards and ePassports dominate PoW/PoS cryptocurrencies - the lower costs of its infrastructure imply the existence of a unique equilibrium where it dominates other forms of payment
ePrint Report Transform-and-Encode: A Countermeasure Framework for Statistical Ineffective Fault Attacks on Block Ciphers Sayandeep Saha, Dirmanto Jap, Debapriya Basu Roy, Avik Chakraborti, Shivam Bhasin, Debdeep Mukhopadhyay
Right from its introduction by Boneh et al., fault attacks (FA) have been established to be one of the most practical threats to both public key and symmetric key based cryptosystems. Statistical Ineffective Fault Analysis (SIFA) is a recently proposed class of fault attacks introduced at CHES 2018. The fascinating feature of this attack is that it exploits the correct ciphertexts obtained during a fault injection campaign, instead of the faulty ciphertexts. The SIFA has been shown to bypass almost all of the existing fault attack countermeasures even when they are combined with provably secure masking schemes for side-channel resistance. The goal of this work is to propose a countermeasure for SIFA. It has been observed that a randomized domain transformation of the intermediate computation combined with bit-level error correction can throttle SIFA. The randomized domain transformation can be achieved by standard masking schemes. In fact, we prove that if biased faults are injected at the state register of a block cipher at a target round, then masking is sufficient to protect against SIFA, until all the shares for a specific bit are corrupted. However, masking alone cannot prevent SIFA if the faults are injected at certain specific locations inside the S-Boxes. To address this issue, we incorporate a bit-level error-correction mechanism. The strongest advantage of the proposed countermeasure, called AntiSIFA, is that it provides provable and quantifiable security guarantees. Proof-of-concept evaluations were performed on software implementations of the block cipher PRESENT, which correlates with the theoretical results.
ePrint Report Evaluation of Code-based Signature Schemes Partha Sarathi Roy, Kirill Morozov, Kazuhide Fukushima, Shinsaku Kiyomoto
Code-based cryptographic schemes recently raised to prominence as quantum-safe alternatives to the currently employed number-theoretic constructions, which do not resist quantum attacks. In this article, we discuss the Courtois-Finiasz-Sendrier signature scheme and derive code-based signature schemes using the Fiat-Shamir transformation from code-based zero-knowledge identification schemes, namely the Stern scheme, the Jain-Krenn-Pietrzak-Tentes scheme, and the Cayrel-Veron-El Yousfi scheme. We analyze the security of these code-based signature schemes and derive the security parameters to achieve the 80-bit and 128-bit level of classical security. To derive the secure parameters, we have studied the hardness of Syndrome Decoding Problem. Furthermore, we implement the signature schemes, based on the Fiat-Shamir transform, which were mentioned above, and compare their performance on a PC.
ePrint Report TMPS: Ticket-Mediated Password Strengthening John Kelsey, Dana Dachman-Soled, Sweta Mishra, Meltem Sonmez Turan
We introduce the notion of Ticket-Mediated Password Strengthening (TMPS), a technique for allowing users to derive keys from passwords while imposing a strict limit on the number of guesses of their password any attacker can make, and strongly protecting the users' privacy. We describe the security requirements of TMPS, and then a set of efficient and practical protocols to implement a TMPS scheme, requiring only hash functions, CCA2-secure encryption, and blind signatures. We provide several variant protocols, including an offline symmetric-only protocol that uses a local trusted computing environment, and online variants that use group signatures or stronger trust assumptions instead of blind signatures. We formalize the security of our scheme by defining an ideal functionality in the Universal Composability (UC) framework, and by providing game-based definitions of security. We prove that our protocol realizes the ideal functionality in the random oracle model (ROM) under adaptive corruptions with erasures, and prove that security with respect to the ideal/real definition implies security with respect to the game-based definitions.
ePrint Report Formally Verified Cryptographic Web Applications in WebAssembly Jonathan Protzenko, Benjamin Beurdouche, Denis Merigoux, Karthikeyan Bhargavan
After suffering decades of high-profile attacks, the need for formal verification of security-critical software has never been clearer. Verification-oriented programming languages like F* are now being used to build high-assurance cryptographic libraries and implementations of standard protocols like TLS. In this paper, we seek to apply these verification techniques to modern Web applications, like WhatsApp, that embed sophisticated custom cryptographic components. The problem is that these components are often implemented in JavaScript, a language that is both hostile to cryptographic code and hard to reason about. So we instead target WebAssebmy, a new instruction set that is supported by all major JavaScript runtimes.

We present a new toolchain that compiles Low*, a low-level subset of the F* programming language, into WebAssembly. Unlike other WebAssembly compilers like Emscripten, our compilation pipeline is focused on compactness and auditability: we formalize the full translation rules in the paper and implement it in a few thousand lines of OCaml. Using this toolchain, we present two case studies. First, we build WHACL*, a WebAssembly version of the existing, verified HACL* cryptographic library. Then, we present LibSignal*, a brand new, verified implementation of the Signal protocol in WebAssembly, that can be readily used by messaging applications like WhatsApp, Skype, and Signal.
We present a protocol for a cryptoeconomic fair exchange of data previously owned by the purchaser for tokens that functions even when both parties are anonymous. This enables peer-to-peer data storage without identity verification. We use a smart contract on a decentralized ledger as a trusted third party. Actual data transfer can take place with any standard anonymous exchange channel. Due to the anonymity of the parties, the smart contract cannot punish either party's off-ledger reputation. Furthermore, the contract has limited power to arbitrate fault in off-ledger disputes. Thus, an important feature of our protocol is a collateral mechanism that collectively punishes both Alice and Bob if either of them abandons the protocol or cheats. However, we prove that parameters can be chosen such that the collateral can be made, subject to data size, arbitrarily low and still result in an expected financial loss if either Alice or Bob cheats. We are able to achieve this due to our non-standard use of error-correcting codes. In addition, the protocol allows those storing the data to exchange it without the client's participation.
I am making this work from August 1998 available for historical reasons. It has been cited as an unpublished manuscript'' more than two dozen times over the years -- even though it has not been publicly available anywhere for almost 20 years. The short memo describes a simple non-intrusive reverse engineering technique against Russian GOST chips. The technique is based on a slide attack. This may be historically interesting since slide attacks had not been invented yet'', at least in formal sense.

The brief original abstract: We show that a simple black box'' chosen-key attack against GOST can recover secret S-boxes with approximately $2^{32}$ encryptions.
In this draft, the internal keyed permutation of FlexAEAD has been analysed. In our analysis, we have first reported an iterated truncated differential for one round which holds with a probability of $2^{-7}$ and can penetrate same number of rounds as claimed by the designers with much less complexity which can be easily converted to a key-recovery attack. We have also reported a Super-Sbox construction in the internal permutation, which has been exploited using the Yoyo game to devise a 6-round deterministic distinguisher and a 7-round key recovery attack for 128-bit internal permutation. Similar attacks can be mounted for 64-bit and 256-bit internal permutation.
It has been 70 years since the publication of the seminal outstanding work of Claude Elwood Shannon, in which he first gave a mathematical definition of the cryptosystem and introduced the concept of perfect ciphers. He also examined the conditions in which such a ciphers exist. Shannon's results in one form or another are presented in almost all books on cryptography. One of his result deals with so-called endomorphic ciphers in which the cardinalities of the message space $\mathcal{M}$ and the ciphertexts $\mathcal{C}$ are the same. The Vernam cipher (one-time pad) is the most famous representative of such ciphers. Moreover, it's the only one known to be perfect.

Surprisingly, we have found a mistake in the Shannon's result. Namely, Shannon stated that an endomorphic cipher, in which the keyspace $\mathcal{K}$ has the same cardinality as message space, is perfect if and only if two conditions are satisfied. The first suggests that for any pair plaintext - ciphertext there exists only one key that translates this plaintext into this ciphertext. The second argues that the key distribution must be uniform. We show, that these two conditions are not really enough. We prove in three different ways that the plaintexts must also be equally probable. Moreover, we study the general endomorphic cipher and get the same result. It follows, that in practice perfect endomorphic ciphers do not exist.
ePrint Report Efficient Search for Optimal Diffusion Layers of Generalized Feistel Networks Patrick Derbez, Pierre-Alain Fouque, Baptiste Lambin, Victor Mollimard
The Feistel construction is one of the most studied ways of building block ciphers. Several generalizations were then proposed in the literature, leading to the Generalized Feistel Network, where the round function first applies a classical Feistel operation in parallel on an even number of blocks, and then a permutation is applied to this set of blocks. In 2010 at FSE, Suzaki and Minematsu studied the diffusion of such construction, raising the question of how many rounds are required so that each block of the ciphertext depends on all blocks of the plaintext. They thus gave some optimal permutations, with respect to this diffusion criteria, for a Generalized Feistel Network consisting of 2 to 16 blocks, as well as giving a good candidate for 32 blocks. Later at FSE'19, Cauchois et al. went further and were able to propose optimal even-odd permutations for up to 26 blocks.

In this paper, we complete the literature by building optimal even-odd permutations for 28, 30, 32, 36 blocks which to the best of our knowledge were unknown until now. The main idea behind our constructions and impossibility proof is a new characterization of the total diffusion of a permutation after a given number of rounds. In fact, we propose an efficient algorithm based on this new characterization which constructs all optimal even-odd permutations for the 28, 30, 32, 36 blocks cases and proves a better lower bound for the 34, 38, 40 and 42 blocks cases. In particular, we improve the 32 blocks case by exhibiting optimal even-odd permutations with diffusion round of 9. The existence of such a permutation was an open problem for almost 10 years and the best known permutation in the literature had a diffusion round of 10. Moreover, our characterization can be implemented very efficiently and allows us to easily re-find all optimal even-odd permutations for up to 26 blocks with a basic exhaustive search.
ePrint Report Protecting against Statistical Ineffective Fault Attacks Joan Daemen, Christoph Dobraunig, Maria Eichlseder, Hannes Gross, Florian Mendel, Robert Primas
At ASIACRYPT 2018 it was shown that Statistical Ineffective Fault Attacks (SIFA) pose a threat for many practical implementations of symmetric cryptography. In particular, countermeasures against both power analysis and fault attacks typically do not prevent straightforward SIFA attacks that require very limited knowledge about the concrete attacked implementation. Consequently, the exploration of countermeasures against SIFA that do not rely on protocols or physical protection mechanisms is of particular interest. In this paper, we explore different countermeasure strategies against SIFA. First, we thoroughly analyze the conditions for an attack to be successful. We then show that by building the implementation from invertible building blocks rather than binary gates we can create circuits where a single fault in the computation does not cancel out. This property, when combined with a typical redundancy-based countermeasure, then results in a single-fault SIFA-secure implementation. This approach can be implemented efficiently and we show how it can be applied to 3-bit, 4-bit, and 5-bit S-boxes. Additionally, we also present an alternative countermeasure strategy based on fine-grained detection. Although this approach may lead to a higher implementation cost, it can be used to protect arbitrary circuits and can be generalized to cover multi-fault SIFA.
ePrint Report SIKE Round 2 Speed Record on ARM Cortex-M4 Hwajeong soe, Amir Jalali, Reza Azarderakhsh
We present the first practical software implementation of Supersingular Isogeny Key Encapsulation (SIKE) round 2, targeting NIST’s 1, 2, and 5 security levels on 32-bit ARM Cortex-M4 microcontrollers. The proposed library introduces a new speed record of SIKE protocol on the target platform. We achieved this record by adopting several state-of-the-art engineering techniques as well as highly-optimized hand-crafted assembly implementation of finite field arithmetic. In particular, we carefully redesign the previous optimized implementations of filed arithmetic on 32-bit ARM Cortex-M4 platform and propose a set of novel techniques which are explicitly suitable for SIKE/SIDH primes. Moreover, the proposed arithmetic implementations are fully scalable to larger bit-length integers and can be adopted over different security levels. The benchmark result on STM32F4 Discovery board equipped with 32-bit ARM Cortex-M4 microcontrollers shows that the entire key encapsulation over p434 takes about 326 million clock cycles (i.e. 1.94 seconds @168MHz). In contrast to the previous optimized implementation of the isogeny-based key exchange on low-power 32-bit ARM Cortex-M4, our performance evaluation shows feasibility of using SIKE mechanism on the target platform. In comparison to the most of the post-quantum candidates, SIKE requires an excessive number of arithmetic operations, resulting in significantly slower timings. However, its small key size makes this scheme as a promising candidate on low-end microcontrollers in the quantum era by ensuring the lower energy consumption for key transmission than other schemes.
ePrint Report Theoretical and Practical Approaches for Hardness Amplification of PUFs Fatemeh Ganji, Shahin Tajik, Pascal Stauss, Jean-Pierre Seifert, Domenic Forte, Mark Tehranipoor
The era of PUFs has been characterized by the efforts put into research and the development of PUFs that are robust against attacks, in particular, machine learning (ML) attacks. In the lack of systematic and provable methods for this purpose, we have witnessed the ever-continuing competition between PUF designers/ manufacturers, cryptanalysts, and of course, adversaries that maliciously break the security of PUFs. This is despite a series of acknowledged principles developed in cryptography and complexity theory, under the umbrella term hardness amplification." The goal of studies on the hardness amplification is to build a strongly secure construction out of considerably weaker primitives. This paper aims at narrowing the gap between these studies and hardware security, specifically for applications in the domain of PUFs. To this end, we first review an example of practical efforts made to construct more secure PUFs, namely the concept of rolling PUFs. Based on what can be learned from this and central insights provided by the ML and complexity theory, we propose a new PUF-based scheme built around the idea of using a new function, namely, the Tribes function, which combines the outputs of a set of PUFs to generate the final response. Our theoretical findings are discussed in an exhaustive manner and supported by the results of experiments, conducted extensively on real-world PUFs.
ePrint Report Stopping time signatures for some algorithms in cryptography Percy Deift, Stephen D. Miller, Thomas Trogdon
We consider the normalized distribution of the overall running times of some cryptographic algorithms, and what information they reveal about the algorithms. Recent work of Deift, Menon, Olver, Pfrang, and Trogdon has shown that certain numerical algorithms applied to large random matrices exhibit a characteristic distribution of running times, which depends only on the algorithm but are independent of the choice of probability distributions for the matrices. Different algorithms often exhibit different running time distributions, and so the histograms for these running time distributions provide a "time-signature" for the algorithms, making it possible, in many cases, to distinguish one algorithm from another. In this paper we extend this analysis to cryptographic algorithms, and present examples of such algorithms with time-signatures that are indistinguishable, and others with time-signatures that are clearly distinct.
In this work we present a new interactive Zero-Knowledge Argument of knowledge for general arithmetic circuits. Our protocol is based on the MPC-in-the-head''-paradigm of Ishai et al. (STOC 2009) and uses MPC with preprocessing such as recently proposed by Katz, Kolesnikov and Wang (ACM CCS 2018). Our argument system uses only symmetric-key primitives and utilizes a version of the so-called SPDZ-protocol which has efficiency benefits for arithmetic circuits compared to other approaches.

Based on specific properties of our protocol we then show how it can be used to construct an efficient Zero-Knowledge Argument of Knowledge for instances of the Short Integer Solution (SIS) problem. We present different protocols that are tailored to specific uses of SIS and show how our solution compares in terms of argument size to existing work. We moreover implemented our Zero-Knowledge argument for SIS and show that using our protocols it is possible to run a complete interactive proof, even for general SIS instances which result in a circuit with $>10^6$ gates, in less than 0.5 seconds. To the best of our knowledge, our construction outperforms all known approaches for the SIS problem with post-quantum security either in terms of computation or communication complexity.