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16 August 2017
In an accountable anonymous system, a user is guaranteed anonymity and unlinkability unless some well-defined condition is met. A line of research focus on schemes that do not rely on any trusted third party capable of de-anonymising users. Notable examples include $k$-times anonymous authentication ($k$-TAA), blacklistable anonymous credentials (BLAC) and linkable ring signatures (LRS). All instances of these schemes are based on traditional number theoretic assumptions, which are vulnerable to quantum attacks.

One common feature of these schemes is the need to limit the number of times a key can be (mis-)used. Traditionally, it is usually achieved through the use of a pseudorandom function (PRF) which maps a user's key to a pseudonym, along with a proof of correctness. However, existing lattice-based PRFs do not interact well with zero-knowledge proofs. To bridge this gap, we propose and develop the following techniques and primitives:

We formalize the notion of weak PRF with efficient protocols, which allows a prover to convince a verifier that the function $\mathsf{F}$ is evaluated correctly. Specifically, we provide an efficient construction based on the learning with rounding problem, which uses abstract Stern's Protocol to prove $y = \mathsf{F}_k(x)$ and $y \neq \mathsf{F}_k(x)$ without revealing $x$, $y$ or $k$.

We develop a general framework, which we call extended abstract Stern's protocol, to construct zero-knowledge arguments system for statements formed by conjunction and disjunction of sub-statements, who (or whose variants) are provable using abstract Stern's Protocol. Specifically, our system supports arbitrary monotonic propositions and allows a prover to argue polynomial relationships of the witnesses used in these sub-statements.

As many existing lattice-based primitives also admit proofs using abstract Stern's protocol, our techniques can easily glue different primitives together for privacy-enhancing applications in a simple and clean way. Indeed, we propose three new schemes, all of which are the first of its kind, in the lattice setting. They also enjoy additional advantages over instances of the number-theoretic counterpart. Our $k$-TAA and BLAC schemes support concurrent enrollment while our LRS features logarithmic signature size without relying on a trusted setup. Our techniques enrich the arsenal of privacy-enhancing techniques and could be useful in the constructions of other schemes such as e-cash, unique group signatures, public key encryption with verifiable decryption, etc.
The intractability of solving the LPN problem serves as the security source of many lightweight/post-quantum cryptographic schemes proposed over the past decade. There are several algorithms available so far to fulfill the solving task. In this paper, we present further algorithmic improvements to the existing work. We describe the first efficient algorithm for the single-list $k$-sum problem which naturally arises from the various BKW reduction settings, propose the hybrid mode of BKW reduction and show how to compute the matrix multiplication in the Gaussian elimination step with flexible and reduced time/memory complexities. The new algorithms yield the best known tradeoffs on the %time/memory/data complexity curve and clearly compromise the $80$-bit security of the LPN instances suggested in cryptographic schemes. Practical experiments on reduced LPN instances verified our results.
In this paper we consider both ``OR" and ``XOR" based monochrome random grid visual cryptographic schemes (RGVCS) for $t$-$(k,n)^*$ access structure which is a generalization of the threshold $(k,n)$ access structure in the sense that in all the successful attempts to recover the secret image, the $t$ essential participants must always be present, i.e., a group of $k$ or more participants can get back the secret if these $t$ essential participants are among them. Up to the best of our knowledge, the current proposed work is the first in the literature of RGVCS which provides efficient direct constructions for the $t$-$(k,n)^*$-RGVCS for both ``OR" and ``XOR" model. Finding the closed form of light contrast is a challenging work. However, in this paper we come up with the closed forms of the light contrasts for the ``OR" as well as for the ``XOR" model. As our proposed schemes are the first proposed schemes for $t$-$(k,n)^*$-RGVCS, it is not possible for us to compare our schemes directly with the existing schemes. However, we have constructed $t$-$(k,n)^*$-RGVCS, as a particular case, from the random grid based schemes for general access structures. Theoretical as well as simulation based data show that our proposed schemes work much efficiently than all these customized schemes.
ePrint Report MCMix: Anonymous Messaging via Secure Multiparty Computation Nikolaos Alexopoulos, Aggelos Kiayias, Thomas Zacharias, Riivo Talviste
We present ‘MCMix’, an anonymous messaging system that completely hides communication metadata and can scale in the order of hundreds of thousands of users. Our approach is to isolate two suitable functionalities, called dialing and conversation, that when used in succession realize anonymous messaging. With this as a starting point, we apply secure multiparty computation (``MC'' or MPC) and proceed to realize them. We present an implementation using a prevalent MPC system (Sharemind) that is competitive in terms of latency with previous messaging systems that only offer much weaker privacy guarantees. Our solution can be instantiated in a variety of different ways with different MPC implementations, overall illustrating how MPC is a viable and competitive alternative to mix-nets and DC-nets for anonymous communication.
ePrint Report Encrypting Messages for Incomplete Chains of Certificates Sanjit Chatterjee, Deepak Garg, Aniket Kate, Tobias Theobald
A public key infrastructure (PKI) binds public keys to the identities of their respective owners. It employs certificate authorities or a web of trust over social links to transitively build cryptographic trust across parties in the form of chains of certificates. In existing PKIs, Alice cannot send a message to Bob confidentially until a complete chain of trust from Alice to Bob exists. We observe that this temporal restriction---which may be severely limiting in some contexts like whistleblowing---can be eliminated by combining webs of trust with concepts from hierarchical identity-based encryption.

Specifically, we present a novel protocol that allows Alice to securely send a message to Bob, binding to any chain of social links, with the property that Bob can decrypt the message only after trust has been established on all links in the chain. This trust may be established either before or after Alice has sent the message, and it may be established in any order on the links. We prove the protocol's security relative to an ideal functionality, develop a prototypical implementation and evaluate the implementation's performance for a realistic environment obtained by harvesting data from an existing web of trust. We observe that our protocol is fast enough to be used in practice.
Most Multivariate Quadratic (MQ) signature schemes have a very large public key, which makes them unsuitable for many applications, despite attractive features such as speed and small signature sizes. In this paper we introduce a modification of the Unbalanced Oil and Vinegar (UOV) signature scheme that has public keys which are an order of magnitude smaller than other MQ signature schemes. The main idea is to choose UOV keys over the smallest field F2 in order to achieve small keys, but to lift the keys to a large extension field, where solving the MQ problem is harder. The resulting Lifted UOV signature scheme is very competitive with other post-quantum signature schemes in terms of key sizes, signature sizes and speed.
ePrint Report Proofs of Work for Blockchain Protocols Juan A. Garay, Aggelos Kiayias, Giorgos Panagiotakos
One of the most impactful applications of ``proofs of work'' (POW) currently is in the design of blockchain protocols such as Bitcoin. Yet, despite the wide recognition of POWs as the fundamental cryptographic tool in this context, there is no known cryptographic formulation that implies the security of the Bitcoin blockchain protocol. Indeed, all previous works formally arguing the security of the Bitcoin protocol relied on direct proofs in the random oracle model, thus circumventing the difficulty of isolating the required properties of the core POW primitive.

In this work we fill this gap by providing a formulation of the POW primitive that implies the security of the Bitcoin blockchain protocol in the standard model. Our primitive entails a number of properties that parallel an efficient non-interactive proof system: completeness and fast verification, security against malicious provers (termed ``hardness against tampering and chosen message attacks'') and security for honest provers (termed ``uniquely successful under chosen key and message attacks''). Interestingly, our formulation is incomparable with previous formulations of POWs that applied the primitive to contexts other than the blockchain. Our result paves the way for proving the security of blockchain protocols in the standard model assuming our primitive can be realized from computational assumptions.
14 August 2017
We give a brief survey of elliptic curve isogenies and the computational problems relevant for supersingular isogeny crypto. Supersingular isogeny cryptography is attracting attention due to the fact that there are no quantum attacks known against it that are significantly faster than classical attacks. However, the underlying computational problems have not been sufficiently studied by quantum algorithms researchers, especially since there are significant mathematical preliminaries needed to fully understand isogeny crypto. The main goal of the paper is to advertise various related computational problems, and to explain the relationships between them, in a way that is accessible to experts in quantum algorithms.
ePrint Report A Novel Cryptographic Framework for Cloud File Systems and CryFS, a Provably-Secure Construction Sebastian Messmer, Jochen Rill, Dirk Achenbach, J\"orn M\"uller-Quade
Using the cloud to store data offers many advantages for businesses and individuals alike. The cloud storage provider, however, has to be trusted not to inspect or even modify the data they are entrusted with. Encrypting the data offers a remedy, but current solutions have various drawbacks. Providers which offer encrypted storage themselves cannot necessarily be trusted, since they have no open implementation. Existing encrypted file systems are not designed for usage in the cloud and do not hide metadata like file sizes or directory structure, do not provide integrity, or are prohibitively inefficient. Most have no formal proof of security. Our contribution is twofold. We first introduce a comprehensive formal model for the security and integrity of cloud file systems. Second, we present CryFS, a novel encrypted file system specifically designed for usage in the cloud. Our file system protects confidentiality and integrity (including metadata), even in presence of an actively malicious cloud provider. We give a proof of security for these properties. Our implementation is easy and transparent to use and offers performance comparable to other state-of-the-art file systems.
13 August 2017
ePrint Report Oblivious Computation with Data Locality Gilad Asharov, T-H. Hubert Chan, Kartik Nayak, Rafael Pass, Ling Ren, Elaine Shi
Oblivious RAM compilers, introduced by Goldreich and Ostrovsky [JACM'96], compile any RAM program into one that is "memory-oblivious'' (i.e., the access pattern to the memory is independent of the input). All previous ORAM schemes, however, completely break the locality of data accesses (by shuffling the data to pseudorandom positions in memory).

In this work, we initiate the study of locality-friendly oblivious RAMs - Oblivious RAM compilers that preserve the locality of the accessed memory regions, while leaking only the lengths of contiguous memory regions accessed; we refer to such schemes as Range ORAMs. Our main results demonstrate the existence of a statistically-secure Range ORAM with only poly-logarithmic overhead (both in terms of the number of memory accesses, and in terms of locality). In our most optimized construction, the overhead is only a logarithmic factor greater than the best ORAM scheme (without locality).

To further improve the parameters, we also consider the weaker notion of a File ORAM: whereas a Range ORAM needs to support read/write access to arbitrary regions of the memory, a File ORAM only needs to support access to pre-defined non-overlapping regions (e.g., files being stored in memory). Assuming one-way functions, we present a computationally-secure File ORAM that, up to $\log \log n$ factors matches the best ORAM schemes (i.e., we essentially get "locality for free".)

As an intermediate result, we also develop a novel sorting algorithm which is also asymptotically optimal (up to $\log\log n$ factors) and enjoys good locality (can be implemented using $O(\log n)$ sequential accesses). This sorting algorithm can serve as a practical alternative to the previous sorting algorithms used in other oblivious RAM compilers and other applications, and might be of an independent interest.

To the best of our knowledge, before our work, the only works combining locality and obliviousness were for the special case of symmetric searchable encryption [Cash and Tessaro (EUROCRYPT'14), Asharov et al. (STOC'16)]. Searchable encryption can be viewed as a special case of a "read-only" File ORAM which leaks whether the same files are accessed again, and whether files contain the same keyword; this leakage, however, has been shown to be harmful in many applications, and is prevented by the definition of a File ORAM.
ePrint Report Post-quantum security of the sponge construction Jan Czajkowski, Leon Groot Bruinderink, Andreas H{\"u}lsing, Christian Schaffner, Dominique Unruh
We investigate the post-quantum security of hash functions based on the sponge construction. A crucial property for hash functions in the post-quantum setting is the collapsing property (a strengthening of collision-resistance). We show that the sponge construction is collapsing (and in consequence quantum collision-resistant) under suitable assumptions about the underlying block function. In particular, if the block function is a random function or a (non-invertible) random permutation, the sponge construction is collapsing.
12 August 2017
Over the past few years, the increased affordability of genome sequencing and the ensuing availability of genetic data have propelled important progress in precision medicine and enabled a market for personal genomic testing. This yields exciting new opportunities for faster and more accurate diagnosis, personalized treatments, and genetically tailored wellness plans. At the same time, however, it also creates important security and privacy threats.

In this paper, we present a new cryptographic protocol, PAPEETE (Private, Authorized, fast PErsonal gEnomic TEsting) suitable for running different types of tests on users' genetic data (specifically, SNPs). The protocol, which builds on top of additively homomorphic encryption, provides privacy for both users and test facilities, and it guarantees that the test is authorized by an appropriate authority such as the FDA. Finally, we present a prototype implementation of PAPEETE, and an experimental evaluation that attests to the real-world practicality of our techniques.
Private set intersection (PSI) allows two parties, who each hold a set of items, to compute the intersection of those sets without revealing anything about other items. Recent advances in PSI have significantly improved its performance for the case of semi-honest security, making semi-honest PSI a practical alternative to insecure methods for computing intersections. However, the semi-honest security model is not always a good fit for real-world problems.

In this work, we introduce a new PSI protocol that is secure in the presence of malicious adversaries. Our protocol is based entirely on fast symmetric-key primitives and inherits important techniques from state-of-the-art protocols in the semi-honest setting. Our novel technique to strengthen the protocol for malicious adversaries is inspired by the dual execution technique of Mohassel \& Franklin (PKC 2006). Our protocol is optimized for the random-oracle model, but can also be realized (with a performance penalty) in the standard model.

We demonstrate our protocol's practicality with a prototype implementation. To securely compute the intersection of two sets of size $2^{20}$ requires only 13 seconds with our protocol, which is $\sim 12\times$ faster than the previous best malicious-secure protocol (Rindal \& Rosulek, Eurocrypt 2017), and only $3\times$ slower than the best semi-honest protocol (Kolesnikov et al., CCS 2016).
ePrint Report An Efficient Certificateless Proxy Re-Encryption Scheme without Pairing S.Sharmila Deva Selvi, Arinjita Paul, C. Pandu Rangan
Proxy re-encryption (PRE) is a cryptographic primitive introduced by Blaze, Bleumer and Strauss to provide delegation of decryption rights. PRE allows re-encryption of a ciphertext intended for Alice (delegator) to a ciphertext for Bob (delegatee) via a semi-honest proxy, who should not learn anything about the underlying message. In 2003, Al-Riyami and Patterson introduced the notion of certificateless public key cryptography which offers the advantage of identity-based cryptography without suffering from the key escrow problem. The existing certificateless PRE (CLPRE) schemes rely on costly bilinear pairing operations. In ACM ASIA-CCS SCC 2015, Srinivasan et al. proposed the first construction of a certificateless PRE scheme without resorting to pairing in the random oracle model. However, in this work, we demonstrate a flaw in the CCA-security proof of their scheme. Also, we present the first construction of a CLPRE scheme without pairing which meets CCA security under the computational Diffie-Hellman hardness assumption in the random oracle model.
8 August 2017
AEZ is an authenticated encryption algorithm, submitted to the CAESAR competition. It has been selected for the third round of the competition. While some classical analysis on the algorithm have been published, the cost of these attacks is beyond the security claimed by the designers. In this paper, we show that all the versions of AEZ are completely broken against a quantum adversary. For this, we propose a generalisation of Simon's algorithm for quantum period finding that allows to build efficient attacks.
In 2012 Guneysu, et al. proposed GLP, a practical and efficient post-quantum digital signature scheme based on the computational hardness of the Ring Learning With Errors problem. It has some advantages over more recent efficient post-quantum digital signature proposals such as BLISS and Ring-TESLA, but Ring Learning With Errors hardness is more fully understood now than when GLP was published a half decade ago. Although not broken, GLP as originally proposed is no longer considered to offer strong levels of security.

We propose GLYPH, a new instantiation of GLP, parametrised for 128 bits of security under the very conservative assumptions proposed in [2], which gives a strong assurance that it will be secure against forgery even if there are further developments in lattice cryptanalysis. Parameters to obtain this strong security level in an efficient manner were not possible within the original formulation of GLP, as they are not compatible with a signature compression algorithm, and to address this we also propose a new form of the compression algorithm which works efficiently with wider ranges of parameters.
After the introduction of some stream ciphers with the minimal internal state, the design idea of these ciphers (i.e. the design of stream ciphers by using a secret key, not only in the initialization but also permanently in the keystream generation) has been developed. The idea lets to design lighter stream ciphers that they are suitable for devices with limited resources such as RFID, WSN. We present necessary conditions for designing a secure stream cipher with the minimal internal state. Based on the conditions, we propose Fruit-128 stream cipher for 128-bit security against all types of attacks. Our implementations showed that the area size of Fruit-128 is about 25.2% smaller than that of Grain-128a. The discussions are presented that Fruit-128 is more resistant than Grain-128a to some attacks such as Related key chosen IV attack. Sprout, Fruit-v2 and Plantlet ciphers are vulnerable to time-memory-data trade-off (TMDTO) distinguishing attacks. For the first time, IV bits were permanently used to strengthen Fruit-128 against TMDTO attacks. We will show that if IV bits are not permanently available during the keystream production step, we can eliminate the IV mixing function from it. In this case, security level decreases to 69-bit against TMDTO distinguishing attacks (that based on the application might be tolerable). Dynamic initialization is another contribution of the paper (that it can strengthen initialization of all stream ciphers with low area cost).
ePrint Report Categorising and Comparing Cluster-Based DPA Distinguishers Xinping Zhou, Carolyn Whitnall, Elisabeth Oswald, Degang Sun, Zhu Wang
Side-channel distinguishers play an important role in differential power analysis, where real world leakage information is compared against hypothetical predictions in order to guess at the underlying secret key. A class of distinguishers which can be described as `cluster-based' have the advantage that they are able to exploit multi-dimensional leakage samples in scenarios where only loose, `semi-profiled' approximations of the true leakage forms are available. This is by contrast with univariate distinguishers exploiting only single points (e.g.\ correlation), and Template Attacks requiring concise fitted models which can be overly sensitive to mismatch between the profiling and attack acquisitions. This paper collects together---to our knowledge, for the first time---the various different proposals for cluster-based DPA (concretely, Differential Cluster Analysis, First Principal Components Analysis, and Linear Discriminant Analysis), and shows how they fit within the robust `semi-profiling' attack procedure proposed by Whitnall et al.\ at CHES 2015. We provide discussion of the theoretical similarities and differences of the separately proposed distinguishers as well as an empirical comparison of their performance in a range of (real and simulated) leakage scenarios and with varying parameters. Our findings have application for practitioners constrained to rely on `semi-profiled' models who wish to make informed choices about the best known procedures to exploit such information.
Gentry’s bootstrapping technique is the most famous method of obtaining fully homomorphic encryption. In previous work I proposed a fully homomorphic encryption without bootstrapping which has the weak point in the enciphering function. In this paper I propose the improved fully homomorphic public-key encryption scheme on non-associative octonion ring over finite field without bootstrapping technique. The plaintext p consists of two sub-plaintext u and v. The proposed fully homomorphic public-key encryption scheme is immune from the “p and -p attack”. The cipher text consists of three sub-cipher texts. As the scheme is based on computational difficulty to solve the multivariate algebraic equations of high degree while the almost all multivariate cryptosystems proposed until now are based on the quadratic equations avoiding the explosion of the coefficients. Because proposed fully homomorphic encryption scheme is based on multivariate algebraic equations with high degree or too many variables, it is against the Gröbner basis attack, the differential attack, rank attack and so on.
ePrint Report Private Collaborative Neural Network Learning Melissa Chase, Ran Gilad-Bachrach, Kim Laine, Kristin Lauter, Peter Rindal
Machine learning algorithms, such as neural networks, create better predictive models when having access to larger datasets. In many domains, such as medicine and finance, each institute has only access to limited amounts of data, and creating larger datasets typically requires collaboration. However, there are privacy related constraints on these collaborations for legal, ethical, and competitive reasons. In this work, we present a feasible protocol for learning neural networks in a collaborative way while preserving the privacy of each record. This is achieved by combining Differential Privacy and Secure Multi-Party Computation with Machine Learning.
Logic locking is a technique that's proposed to protect outsourced IC designs from piracy and counterfeiting by untrusted foundries. A locked IC preserves the correct functionality only when a correct key is provided. Recently, the security of logic locking is threatened by a new attack called SAT attack, which can decipher the correct key of most logic locking techniques within a few hours even for a reasonably large key-size. This attack iteratively solves SAT formulas which progressively eliminate the incorrect keys till the circuit is unlocked. In this paper, we present a circuit block (referred to as Anti-SAT block) to enhance the security of existing logic locking techniques against the SAT attack. We show using a mathematical proof that the number of SAT attack iterations to reveal the correct key in a circuit comprising an Anti-SAT block is an exponential function of the key-size thereby making the SAT attack computationally infeasible. Besides, we address the vulnerability of the Anti-SAT block to various removal attacks and investigate obfuscation techniques to prevent these removal attacks. More importantly, we provide a proof showing that these obfuscation techniques for making Anti-SAT un-removable would not weaken the Anti-SAT block's resistance to SAT attack. Through our experiments, we illustrate the effectiveness of our approach to securing modern chips fabricated in untrusted foundries.
7 August 2017
ePrint Report GIFT: A Small Present (Full version) Subhadeep Banik, Sumit Kumar Pandey, Thomas Peyrin, Yu Sasaki, Siang Meng Sim, Yosuke Todo
In this article, we revisit the design strategy of PRESENT, leveraging all the advances provided by the research community in construction and cryptanalysis since its publication, to push the design up to its limits. We obtain an improved version, named GIFT, that provides a much increased efficiency in all domains (smaller and faster), while correcting the well-known weakness of PRESENT with regards to linear hulls.

GIFT is a very simple and clean design that outperforms even SIMON or SKINNY for round-based implementations, making it one of the most energy efficient ciphers as of today. It reaches a point where almost the entire implementation area is taken by the storage and the Sboxes, where any cheaper choice of Sbox would lead to a very weak proposal. In essence, GIFT is composed of only Sbox and bit-wiring, but its natural bitslice data flow ensures excellent performances in all scenarios, from area-optimised hardware implementations to very fast software implementation on high-end platforms.

We conducted a thorough analysis of our design with regards to state-of-the-art cryptanalysis, and we provide strong bounds with regards to differential/linear attacks.
For a public value $y$ and a linear function $f$, giving a zero-knowledge proof of knowledge of a secret value $x$ that satisfies $f(x)=y$ is a key ingredient in many cryptographic protocols. Lattice-based constructions, in addition, require proofs of ``shortness'' of $x$. Of particular interest are constructions where $f$ is a function over polynomial rings, since these are the ones that result in efficient schemes with short keys and outputs.

All known approaches for such lattice-based zero-knowledge proofs are not very practical because they involve a basic protocol that needs to be repeated many times in order to achieve negligible soundness error. In the amortized setting, where one needs to give zero-knowledge proofs for many equations for the same function $f$, the situation is more promising, though still not yet fully satisfactory. Current techniques either result in proofs of knowledge of $x$'s that are exponentially larger than the $x$'s actually used for the proof (i.e. the \emph{slack} is exponential), or they have polynomial slack but require the number of proofs to be in the several thousands before the amortization advantages ``kick in''.

In this work, we give a new approach for constructing amortized zero-knowledge proofs of knowledge of short solutions over polynomial rings. Our proof has small polynomial slack and is practical even when the number of relations is as small as the security parameter.
The number field sieve is the best-known algorithm for factoring integers and solving the discrete logarithm problem in prime fields. In this paper, we present some new improvements to various steps of the number field sieve. We apply these improvements on the current 768-bit discrete logarithm record and show that we are able to perform the overall computing time in about 1260 core$\cdot$years using these improvements instead of 2350 core$\cdot$years using the best known parameters for this problem. Moreover, we show that the pre-computation phase for a 768-bit discrete logarithm problem, that allows for example to build a massive decryption tool of IPsec traffic protected by the Oakley group~1, was feasible in reasonable time using technologies available before the year 2000.
ePrint Report CAKE: Code-based Algorithm for Key Encapsulation Paulo S. L. M. Barreto, Shay Gueron, Tim Gueneysu, Rafael Misoczki, Edoardo Persichetti, Nicolas Sendrier, Jean-Pierre Tillich
Current widely-used key-exchange (KE) mechanisms will be vulnerable to quantum attacks when sufficiently strong quantum computers become available. Therefore, devising quantum-resistant replacements that combine efficiency with solid security guarantees is an important and challenging task. This paper proposes several contributions towards this goal. First, we introduce ``{\em CAKE}'', a key-encapsulation algorithm based on the QC-MDPC McEliece encryption scheme, with two major improvements: a) the use of ephemeral keys that defeats a recent reaction-attack against MDPC decoding of the corresponding encryption scheme and b) a highly efficient key-generation procedure for QC-MDPC-based cryptosystems. Then, we present an authenticated key-exchange protocol based on CAKE, which is suitable for the Internet Key-Exchange (IKE) standard. We prove that CAKE is IND-CCA secure, that the protocol is SK-Secure, and suggest practical parameters. Compared to other post-quantum schemes, we believe that CAKE is a promising candidate for post-quantum key-exchange standardization.
ePrint Report Verifiable Private Polynomial Evaluation Xavier Bultel, Manik Lal Das, Hardik Gajera, David Gérault, Matthieu Giraud, Pascal Lafourcade
Delegating the computation of a polynomial to a server in a verifiable way is challenging. An even more challenging problem is ensuring that this polynomial remains hidden to clients who are able to query such a server. In this paper, we formally define the notion of \emph{Private Polynomial Evaluation} (PPE). Our main contribution is to design a rigorous security model along with relations between the different security properties. We define \emph{polynomial protection} (PP), \emph{proof unforgeability} (UNF), and \emph{indistinguishability against chosen function attack} (INDCFA), which formalizes the resistance of a PPE against attackers trying to guess which polynomial is used among two polynomials of their choice. As a second contribution, we give a cryptanalysis of two PPE schemes of the literature. Finally, we design a PPE scheme called PIPE and we prove that it is PP-, UNF- and INDCFA-secure under the decisional Diffie-Hellman assumption in the random oracle model.
ePrint Report Efficient, Reusable Fuzzy Extractors from LWE Daniel Apon, Congwon Cho, Karim Eldefrawy, Jonathan Katz
A fuzzy extractor (FE), proposed for deriving cryptographic keys from biometric data, enables reproducible generation of high-quality randomness from noisy inputs having sufficient min-entropy. FEs rely in their operation on a public \helper string" that is guaranteed not to leak too much information about the original input. Unfortunately, this guarantee may not hold when multiple independent helper strings are generated from correlated inputs as would occur if a user registers their biometric data with multiple servers; reusable FEs are needed in that case. Although the notion of reusable FEs was introduced in 2004, it has received relatively little attention since then.

We first analyze an FE proposed by Fuller et al. (Asiacrypt 2013) based on the learning-with-errors (LWE) assumption, and show that it is not reusable. We then show how to adapt their construction to obtain a weakly reusable FE. We also show a generic technique for turning any weakly reusable FE to a strongly reusable one, in the random-oracle model. Finally, we give a direct construction of a strongly reusable FE based on the LWE assumption, that does not rely on random oracles.
Commonly used digital signature schemes have a limited lifetime because their security is based on computational assumptions that will potentially break in the future when more powerful computers are available. In 1993, Bayer et al.\ proposed a method for prolonging the lifetime of a digital signature by time-stamping the signature together with the signed document. Based on their idea long-term timestamp schemes have been developed that generate renewable timestamps. To minimize the risk of a design failure that affects the security of these schemes, it is important to formally analyze their security. However, many of the proposed schemes have not been subject to a formal security analysis yet. In this paper, we address this issue by formally analyzing the security of a hash-based long-term timestamp scheme that is based on the ideas of Bayer et al. Our analysis shows that the security level of this scheme degrades cubic over time, a security loss that needs to be taken into account when the scheme is used in practice.
ePrint Report CryptHOL: Game-based Proofs in Higher-order Logic David A. Basin, Andreas Lochbihler, S. Reza Sefidgar
Game-based proofs are a well-established paradigm for structuring security arguments and simplifying their understanding. We present a novel framework, CryptHOL, for rigorous game-based proofs that is supported by mechanical theorem proving. CryptHOL is based on a new semantic domain with an associated functional programming language for expressing games. We embed our framework in the Isabelle/HOL theorem prover and, using the theory of relational parametricity, we tailor Isabelle’s existing proof automation to game-based proofs.

By basing our framework on a conservative extension of higher-order logic and providing sufficient automation support, the resulting proofs are trustworthy and comprehensible, and the framework is extensible and widely applicable. We evaluate our framework by formalizing different game-based proofs from the literature and comparing the results with existing formal-methods tools.
Group Homomorphic Encryption (GHE), formally defined by Armknecht, Katzenbeisser and Peter, is a public-key encryption primitive where the decryption algorithm is a group homomorphism. Hence it suports homomorphic evaluation of a single algebraic operation such as modular addition or modular multiplication. Most classical homomorphic encryption schemes such as as Goldwasser-Micali and Paillier are instances of GHE. In this work, we extend GHE to the attribute-based setting. We introduce and formally define the notion of Attribute-Based GHE (ABGHE) and explore its properties. Our main result is the construction of an Identity-Based Encryption (IBE) scheme supporting homomorphic addition modulo a poly-sized prime $e$, which is an instance of ABGHE. Our construction builds upon the IBE scheme of Boneh, LaVigne and Sabin (BLS). BLS relies on a hash function that maps identities to $e^{\text{th}}$ residues. However there is no known way to securely instantiate such a function. Our construction extends BLS so that it can use a hash function that can be securely instantiated. We prove our scheme IND-ID-CPA secure under the (slightly modified) $e^{\text{th}}$ residuosity assumption in the random oracle model and show that it supports a (modular) additive homomorphism. By using multiple instances of the scheme with distinct primes and leveraging the Chinese Remainder Theorem, we can support homomorphic addition modulo a ``large'' (i.e. superpolynomial) integer, the first such IBE scheme. We also show that our scheme for $e > 2$ is anonymous assuming the hardness of deciding solvability of a special system of multivariate polynomial equations. Finally, we define a primitive for attribute-based group homomorphisms in the multi-key setting, introduce an important security property and present a generic construction of the primitive meeting this security property.

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