All papers in 2023 (1971 results)

Last updated:  2023-12-31
Combinatorially Homomorphic Encryption
Yuval Ishai, Eyal Kushnir, and Ron D. Rothblum
Homomorphic encryption enables public computation over encrypted data. In the past few decades, homomorphic encryption has become a staple of both the theory and practice of cryptography. Nevertheless, while there is a general loose understanding of what it means for a scheme to be homomorphic, to date there is no single unifying minimal definition that captures all schemes. In this work, we propose a new definition, which we refer to as combinatorially homomorphic encryption, which attempts to give a broad base that captures the intuitive meaning of homomorphic encryption and draws a clear line between trivial and nontrivial homomorphism. Our notion relates the ability to accomplish some task when given a ciphertext, to accomplishing the same task without the ciphertext, in the context of communication complexity. Thus, we say that a scheme is combinatorially homomorphic if there exists a communication complexity problem $f(x,y)$ (where $x$ is Alice's input and $y$ is Bob's input) which requires communication $c$, but can be solved with communication less than $c$ when Alice is given in addition also an encryption $E_k(y)$ of Bob's input (using Bob's key $k$). We show that this definition indeed captures pre-existing notions of homomorphic encryption and (suitable variants are) sufficiently strong to derive prior known implications of homomorphic encryption in a conceptually appealing way. These include constructions of (lossy) public-key encryption from homomorphic private-key encryption, as well as collision-resistant hash functions and private information retrieval schemes.
Last updated:  2023-12-31
Hard Languages in $\mathsf{NP} \cap \mathsf{coNP}$ and NIZK Proofs from Unstructured Hardness
Riddhi Ghosal, Yuval Ishai, Alexis Korb, Eyal Kushilevitz, Paul Lou, and Amit Sahai
The existence of "unstructured" hard languages in $\mathsf{NP} \,\cap\,\mathsf{coNP}$ is an intriguing open question. Bennett and Gill (SICOMP, 1981) asked whether $\mathsf{P}$ is separated from $\mathsf{NP} \cap \mathsf{coNP}$ relative to a random oracle, a question that remained open ever since. While a hard language in $\mathsf{NP} \,\cap\,\mathsf{coNP}$ can be constructed in a black-box way from a one-way permutation, for which only few (structured) candidates exist, Bitansky et al. (SICOMP, 2021) ruled out such a construction based on an injective one-way function, an unstructured primitive that is easy to instantiate heuristically. In fact, the latter holds even with a black-box use of indistinguishability obfuscation. We give the first evidence for the existence of unstructured hard languages in $\mathsf{NP} \,\cap\,\mathsf{coNP}$ by showing that if $\mathsf{UP} \not \subseteq \mathsf{RP}$, which follows from the existence of injective one-way functions, the answer to Bennett and Gill's question is affirmative: with probability 1 over a random oracle $\cal O$, we have that $\mathsf{P}^{\cal O} \neq \mathsf{NP}^{\cal O} \cap \mathsf{coNP}^{\cal O}$. Our proof gives a constructive non-black-box approach for obtaining candidate hard languages in $\mathsf{NP} \,\cap\,\mathsf{coNP}$ from cryptographic hash functions. The above conditional separation builds on a new construction of non-interactive zero-knowledge (NIZK) proofs, with a computationally unbounded prover, to convert a hard promise problem into a hard language. We obtain such NIZK proofs for $\mathsf{NP}$, with a uniformly random reference string, from a special kind of hash function which is implied by (an unstructured) random oracle. This should be contrasted with previous constructions of such NIZK proofs that are based on one-way permutations or other structured primitives, as well as with (computationally sound) NIZK arguments in the random oracle model.
Last updated:  2024-03-07
The Planck Constant and Quantum Fourier Transformation
Zhengjun Cao and Zhenfu Cao
Quantum Fourier Transformation (QFT) plays a key role in quantum computation theory. But its transform size has never been discussed. In practice, the Xilinx LogiCORE IP Fast Fourier Transform core has the maximum transform size $N=2^{16}$. Taking into account the Planck constant $\hbar=6.62607015\times 10^{-34}$ and the difficulty to physically implement basic operator $\left[ \begin{array}{cc} 1& 0\\ 0 & \exp(-2\pi\,i/N)\\ \end{array} \right]$ on a qubit, we think $N=2^{120}$ could be an upper bound for the transform size of QFT.
Last updated:  2024-05-10
Efficient Hardware Implementation for Maiorana-McFarland type Functions
Anupam Chattopadhyay, Subhamoy Maitra, Bimal Mandal, Manmatha Roy, and Deng Tang
Maiorana--McFarland type constructions are basically concatenating the truth tables of linear functions on a smaller number of variables to obtain highly nonlinear ones on larger inputs. Such functions and their different variants have significant cryptology and coding theory applications. The straightforward hardware implementation of such functions using decoders (Khairallah et al., WAIFI 2018; Tang et al., SIAM Journal on Discrete Mathematics, 2019) requires exponential resources on the number of inputs. In this paper, we study such constructions in detail and provide implementation strategies for a selected subset of this class with polynomial many gates over the number of inputs. We demonstrate that such implementations cover the requirement of cryptographic primitives to a great extent. Several existing constructions are revisited in this direction, and exact implementations are provided with specific depth and gate counts for hardware implementation. Related combinatorial results of theoretical nature are also analyzed in this regard. Finally, we present a novel construction of a new class of balanced Boolean functions with very low absolute indicators and very high nonlinearity that can be implemented in polynomial-size circuits over the number of inputs. We underline that these constructions have immediate applications to resist the signature generation in Differential Fault Attack (DFA) and to implement functions on a large number of variables in designing ciphers for the paradigm of Fully Homomorphic Encryption (FHE).
Last updated:  2023-12-29
Secure and Practical Functional Dependency Discovery in Outsourced Databases
Xinle Cao, Yuhan Li, Dmytro Bogatov, Jian Liu, and Kui Ren
The popularity of cloud computing has made outsourced databases prevalent in real-world applications. To protect data security, numerous encrypted outsourced databases have been proposed for this paradigm. However, the maintenance of encrypted databases has scarcely been addressed. In this paper, we focus on a typical maintenance task --- functional dependency (FD) discovery. We develop novel FD protocols in encrypted databases while guaranteeing minimal leakages: nothing is revealed besides the database size and the actual discovered FDs. As far as we know, we are the first to formally define secure FD discovery with minimal leakage. We present two oblivious FD protocols and prove them secure in the presence of the persistent adversary (monitoring processes on the server). The first protocol leverages Oblivious RAM (ORAM) and is suitable for dynamic databases. The second protocol relies on oblivious sorting and is more practical in static databases due to high parallelism. We also present a thorough experimental evaluation of the proposed methods.
Last updated:  2024-03-07
Evaluating the security of CRYSTALS-Dilithium in the quantum random oracle model
Kelsey A. Jackson, Carl A. Miller, and Daochen Wang
In the wake of recent progress on quantum computing hardware, the National Institute of Standards and Technology (NIST) is standardizing cryptographic protocols that are resistant to attacks by quantum adversaries. The primary digital signature scheme that NIST has chosen is CRYSTALS-Dilithium. The hardness of this scheme is based on the hardness of three computational problems: Module Learning with Errors (MLWE), Module Short Integer Solution (MSIS), and SelfTargetMSIS. MLWE and MSIS have been well-studied and are widely believed to be secure. However, SelfTargetMSIS is novel and, though classically as hard as MSIS, its quantum hardness is unclear. In this paper, we provide the first proof of the hardness of SelfTargetMSIS via a reduction from MLWE in the Quantum Random Oracle Model (QROM). Our proof uses recently developed techniques in quantum reprogramming and rewinding. A central part of our approach is a proof that a certain hash function, derived from the MSIS problem, is collapsing. From this approach, we deduce a new security proof for Dilithium under appropriate parameter settings. Compared to the previous work by Kiltz, Lyubashevsky, and Schaffner (EUROCRYPT 2018) that gave the only other rigorous security proof for a variant of Dilithium, our proof has the advantage of being applicable under the condition $q = 1 \text{ mod } 2n$, where $q$ denotes the modulus and $n$ the dimension of the underlying algebraic ring. This condition is part of the original Dilithium proposal and is crucial for the efficient implementation of the scheme. We provide new secure parameter sets for Dilithium under the condition $q = 1 \text{ mod } 2n$, finding that our public key size and signature size are about $2.9\times$ and $1.3\times$ larger, respectively, than those proposed by Kiltz et al. at the same security level.
Last updated:  2024-02-15
Monotone Policy BARGs from BARGs and Additively Homomorphic Encryption
Shafik Nassar, Brent Waters, and David J. Wu
A monotone policy batch $\mathsf{NP}$ language $\mathcal{L}_{\mathcal{R}, P}$ is parameterized by a monotone policy $P \colon \{0,1\}^k \to \{0,1\}$ and an $\mathsf{NP}$ relation $\mathcal{R}$. A statement $(x_1, \ldots, x_k)$ is a YES instance if there exists $w_1, \ldots, w_k$ where $P(\mathcal{R}(x_1, w_1), \ldots, \mathcal{R}(x_k, w_k)) = 1$. For example, we might say that an instance $(x_1, \ldots, x_k)$ is a YES instance if a majority of the statements are true. A monotone policy batch argument (BARG) for $\mathsf{NP}$ allows a prover to prove that $(x_1, \ldots, x_k) \in \mathcal{L}_{\mathcal{R}, P}$ with a proof of size $\mathsf{poly}(\lambda, |\mathcal{R}|, \log k)$, where $\lambda$ is the security parameter, $|\mathcal{R}|$ is the size of the Boolean circuit that computes $\mathcal{R}$, and $k$ is the number of instances. Recently, Brakerski, Brodsky, Kalai, Lombardi, and Paneth (CRYPTO 2023) gave the first monotone policy BARG for $\mathsf{NP}$ from the learning with errors (LWE) assumption. In this work, we describe a generic approach for constructing monotone policy BARGs from any BARG for $\mathsf{NP}$ together with an additively homomorphic encryption scheme. This yields the first constructions of monotone policy BARGs from the $k$-$\mathsf{Lin}$ assumption in prime-order pairing groups as well as the (subexponential) DDH assumption in pairing-free groups. Central to our construction is a notion of a zero-fixing hash function, which is a relaxed version of a predicate-extractable hash function from the work of Brakerski et al. Our relaxation enables a direct realization of zero-fixing hash functions from BARGs for $\mathsf{NP}$ and additively homomorphic encryption, whereas the previous notion relied on leveled homomorphic encryption, and by extension, the LWE assumption. As an application, we also show how to combine a monotone policy BARG with a puncturable signature scheme to obtain a monotone policy aggregate signature scheme. Our work yields the first (statically-secure) monotone policy aggregate signatures that supports general monotone Boolean circuits from standard pairing-based assumptions. Previously, this was only known from LWE.
Last updated:  2024-05-06
How to Make Rational Arguments Practical and Extractable
Matteo Campanelli, Chaya Ganesh, and Rosario Gennaro
We investigate proof systems where security holds against rational parties instead of malicious ones. Our starting point is the notion of rational arguments, a variant of rational proofs (Azar and Micali, STOC 2012) where security holds against rational adversaries that are also computationally bounded. Rational arguments are an interesting primitive because they generally allow for very efficient protocols, and in particular sublinear verification (i.e. where the Verifier does not have to read the entire input). In this paper we aim at narrowing the gap between literature on rational schemes and real world applications. Our contribution is two-fold. We provide the first construction of rational arguments for the class of polynomial computations that is practical (i.e., it can be applied to real-world computations on reasonably common hardware) and with logarithmic communication. Techniques-wise, we obtain this result through a compiler from information-theoretic protocols and rational proofs for polynomial evaluation. The latter could be of independent interest. As a second contribution, we propose a new notion of extractability for rational arguments. Through this notion we can obtain arguments where knowledge of a witness is incentivized (rather than incentivizing mere soundness). We show how our aforementioned compiler can also be applied to obtain efficient extractable rational arguments for $\mathsf{NP}$.
Last updated:  2023-12-28
More Efficient Public-Key Cryptography with Leakage and Tamper Resilience
Shuai Han, Shengli Liu, and Dawu Gu
In this paper, we study the design of efficient signature and public-key encryption (PKE) schemes in the presence of both leakage and tampering attacks. Firstly, we formalize the strong leakage and tamper-resilient (sLTR) security model for signature, which provides strong existential unforgeability, and deals with bounded leakage and restricted tampering attacks, as a counterpart to the sLTR security introduced by Sun et al. (ACNS 2019) for PKE. Then, we present direct constructions of signature and chosen-ciphertext attack (CCA) secure PKE schemes in the sLTR model, based on the matrix decisional Diffie-Hellman (MDDH) assumptions (which covers the standard symmetric external DH (SXDH) and k-Linear assumptions) over asymmetric pairing groups. Our schemes avoid the use of heavy building blocks such as the true-simulation extractable non-interactive zero-knowledge proofs (tSE-NIZK) proposed by Dodis et al. (ASIACRYPT 2010), which are usually needed in constructing schemes with leakage and tamper-resilience. Especially, our SXDH-based signature and PKE schemes are more efficient than the existing schemes in the leakage and tamper-resilient setting: our signature scheme has only 4 group elements in the signature, which is about 5×~8× shorter, and our PKE scheme has only 6 group elements in the ciphertext, which is about 1.3×~3.3× shorter. Finally, we note that our signature scheme is the {\it first} one achieving strong existential unforgeability in the leakage and tamper-resilient setting, where strong existential unforgeability has important applications in building more complex primitives such as signcryption and authenticated key exchange.
Last updated:  2023-12-27
Maypoles: Lightning Striking Twice
Clara Shikhelman
The Lightning Network (LN) is a second layer solution built on top of Bitcoin, aimed to solve Bitcoin's long transaction waiting times and high transaction fees. Empirical and theoretical studies show that the LN is tending towards the hub and spoke network topology. In this topology most of the nodes, the spokes, open a single channel to one of the few well-connected nodes, the hubs. This topology is known to be prone to failures, attacks, and privacy issues. In this work we introduce the Maypoles protocol in which most nodes open two channels instead of one. We show that this protocol benefits the network significantly by enhancing its stability, privacy, and resilience to attacks. We also examine the economic incentives of nodes to take part in Maypoles.
Last updated:  2023-12-27
A Small Serving of Mash: (Quantum) Algorithms for SPDH-Sign with Small Parameters
Andrew Mendelsohn, Edmund Dable-Heath, and Cong Ling
We find an efficient method to solve the semidirect discrete logarithm problem (SDLP) over finite nonabelian groups of order $p^3$ and exponent $p^2$ for certain exponentially large parameters. This implies an attack on SPDH-Sign, a signature scheme based on the SDLP, for such parameters. We also take a step toward proving the quantum polynomial time equivalence of SDLP and SCDH.
Last updated:  2024-06-11
SoK: Polynomial Multiplications for Lattice-Based Cryptosystems
Vincent Hwang
We survey various mathematical tools used in software works multiplying polynomials in $\mathbb{Z}_q[x] / ⟨xn −αx−β⟩$. In particular, we survey implementation works targeting polynomial multiplications in lattice-based cryptosystems Dilithium, Kyber, NTRU, NTRU Prime, and Saber with instruction set architectures/extensions Armv7-M, Armv7E-M, Armv8-A, and AVX2. There are three emphases in this paper: (i) modular arithmetic, (ii) homomorphisms, and (iii) vectorization. For modular arithmetic, we survey Montgomery, Barrett, and Plantard multiplications. For homomorphisms, we survey (a) various homomorphisms such as Cooley–Tukey FFT, Good–Thomas FFT, Bruun’s FFT, Rader’s FFT, Karatsuba, and Toom–Cook; (b) various algebraic techniques for adjoining nice properties to the coefficient rings, including localization, Schönhage’s FFT, Nussbaumer’s FFT, and coefficient ring switching; and (c) various algebraic techniques related to the polynomial moduli, including twisting, composed multiplication, evaluation at ∞, truncation, incomplete transformation, striding, and Toeplitz matrix-vector product. For vectorization, we survey the relations between homomorphisms and vector arithmetic. We then go through several case studies: We compare the implementations of modular multiplications used in Dilithium and Kyber, explain how the matrix-to-vector structure was exploited in Saber, and review the design choices of transformations for NTRU and NTRU Prime with vectorization. Finally, we outline several interesting implementation projects.
Last updated:  2023-12-26
On The Practical Advantage of Committing Challenges in Zero-Knowledge Protocols
David Naccache and Ofer Yifrach-Stav
The Fiat-Shamir transform is a classical technique for turning any zero-knowledge $\Sigma$-protocol into a signature scheme. In essence, the idea underlying this transform is that deriving the challenge from the digest of the commitment suppresses simulatability and hence provides non-interactive proofs of interaction. It follows from that observation that if one wishes to preserve deniability the challenge size (per round) must be kept low. For instance in the original Fiat-Shamir protocol the authors recommend 18 bits but suggest that the challenge size can be made larger to reduce communication overhead, e.g. the value of 20 is proposed in \cite{micali}. We show that even with relatively small challenge sizes \textsl{practical} deniability can be destroyed by having the verifier artificially impose upon himself the use of slowed-down hash function or by resorting to a trusted agency proposing an on-line deniability enforcement service against the provers community's will.
Last updated:  2023-12-31
Post Quantum Sphinx
David Anthony Stainton
This paper introduces two designs of Sphinx variants with corresponding im- plementations for use in post-quantum threat models with a specific focus on Mix networks. We introduce an obvious variant of Sphinx with CSIDH/CTIDH and we additionally introduce ’KEM Sphinx’, an enhanced version of the Sphinx packet format, designed to improve performance through modifications that increase packet header size. Unlike its predecessor, KEM Sphinx addresses performance limitations inherent in the original design, offering a solution that doubles processing speed. Our analysis extends to the adaptation of KEM Sphinx in a post-quantum cryptographic context, showing a transition with minimal performance degradation. The study concludes that the trade-off be- tween increased size and improved speed and security is justifiable, especially in scenarios demanding higher security. These findings suggest KEM Sphinx as a promising direction for efficient, secure communication protocols in an increas- ingly post-quantum cryptographic landscape.
Last updated:  2023-12-25
On the notion of carries of numbers $2^n-1$ and Scholz conjecture
Theophilus Agama
Applying the pothole method on the factors of numbers of the form $2^n-1$, we prove that if $2^n-1$ has carries of degree at most $$\kappa(2^n-1)=\frac{1}{2(1+c)}\lfloor \frac{\log n}{\log 2}\rfloor-1$$ for $c>0$ fixed, then the inequality $$\iota(2^n-1)\leq n-1+(1+\frac{1}{1+c})\lfloor\frac{\log n}{\log 2}\rfloor$$ holds for all $n\in \mathbb{N}$ with $n\geq 4$, where $\iota(\cdot)$ denotes the length of the shortest addition chain producing $\cdot$. In general, we show that all numbers of the form $2^n-1$ with carries of degree $$\kappa(2^n-1):=(\frac{1}{1+f(n)})\lfloor \frac{\log n}{\log 2}\rfloor-1$$ with $f(n)=o(\log n)$ and $f(n)\longrightarrow \infty$ as $n\longrightarrow \infty$ for $n\geq 4$ then the inequality $$\iota(2^n-1)\leq n-1+(1+\frac{2}{1+f(n)})\lfloor\frac{\log n}{\log 2}\rfloor$$ holds.
Last updated:  2023-12-25
Revisiting Pairing-friendly Curves with Embedding Degrees 10 and 14
Uncategorized
Yu Dai, Debiao He, Cong Peng, Zhijian Yang, and Chang-an Zhao
Show abstract
Uncategorized
Since 2015, there has been a significant decrease in the asymptotic complexity of computing discrete logarithms in finite fields. As a result, the key sizes of many mainstream pairing-friendly curves have to be updated to maintain the desired security level. In PKC'20, Guillevic conducted a comprehensive assessment of the security of a series of pairing-friendly curves with embedding degrees ranging from $9$ to $17$. In this paper, we focus on pairing-friendly curves with embedding degrees of 10 and 14. First, we extend the optimized formula of the optimal pairing on BW13-310, a 128-bit secure curve with a prime $p$ in 310 bits and embedding degree $13$, to our target curves. This generalization allows us to compute the optimal pairing in approximately $\log r/2\varphi(k)$ Miller iterations, where $r$ and $k$ are the order of pairing groups and the embedding degree respectively. Second, we develop optimized algorithms for cofactor multiplication for $\mathbb{G}_1$ and $\mathbb{G}_2$, as well as subgroup membership testing for $\mathbb{G}_2$ on these curves. Based on these theoretical results a new 128-bit secure curve emerges: BW14-351. Finally, we provide detailed performance comparisons between BW14-351 and other popular curves on a 64-bit platform in terms of pairing computation, hashing to $\mathbb{G}_1$ and $\mathbb{G}_2$, group exponentiations and subgroup membership testings. Our results demonstrate that BW14-351 is a strong candidate for building pairing-based cryptographic protocols.
Last updated:  2023-12-25
Chosen Ciphertext Security via BARGs
Takahiro Matsuda
In this paper, we show a new set of cryptographic primitives that generically leads to chosen ciphertext secure (CCA secure) public-key encryption (PKE). Specifically, we show how a (non-interactive, publicly verifiable) batch argument (BARG) for NP can be combined with a chosen plaintext secure PKE scheme to achieve a CCA secure one. The requirement of the succinctness of the proof size of a BARG in our result is rather mild: The proof size is $O(k^{\epsilon})$ for some non-negative constant $\epsilon < 1$ when the correctness of $k$ statements is simultaneously proved.
Last updated:  2023-12-24
A Signature Scheme from Full-Distance Syndrome Decoding
Abdelhaliem Babiker
In this paper we propose a new hash-and-sign digital signature scheme whose security against existential forgery under adaptive chosen message attack is based on the hardness of full-distance syndrome decoding. We propose parameter sets for three security levels (128-bits, 192-bits, and 256-bits) based on concrete estimations for hardness of the syndrome decoding problem and estimate the corresponding sizes of the keys and the signature for each level. The scheme has large public and private keys but very small signatures.
Last updated:  2023-12-25
Barrett Multiplication for Dilithium on Embedded Devices
Vincent Hwang, YoungBeom Kim, and Seog Chung Seo
We optimize the number-theoretic transforms (NTTs) in Dilithium — a digital signature scheme recently standardized by the National Institute of Standards and Technology (NIST) — on Cortex-M3 and 8-bit AVR. The core novelty is the exploration of micro-architectural insights for modular multiplications. Recent work [Becker, Hwang, Kannwischer, Yang and Yang, Volume 2022 (1), Transactions on Cryptographic Hardware and Embedded Systems, 2022] found a correspondence between Montgomery and Barrett multiplications by relating modular reductions to integer approximations and demonstrated that Barrett multiplication is more favorable than Montgomery multiplication by absorbing the subtraction to the low multiplication. We first point out the benefit of Barrett multiplication when long and high multiplication instructions are unavailable, unusable, or slow. We then generalize the notion of integer approximations and improve the emulation of high multiplications used in Barrett multiplication. Compared to the state-of-the-art assembly-optimized implementations on Cortex-M3, our constant-time NTT/iNTT are 1.38−1.51 times faster and our variable-time NTT/iNTT are 1.10−1.21 times faster. On our 8-bit AVR, we outperform Montgomery-based C implementations of NTT/iNTT by 6.37−7.27 times by simply switching to the proposed Barrett-based implementation. We additionally implement Barrett-based NTT/iNTT in assembly and obtain 14.10− 14.42 times faster code. For the overall scheme, we provide speed-optimized implementations for Dilithium parameter sets dilithium2 and dilithium3 on Cortex-M3, and stack-optimized implementations for all parameter sets on Cortex-M3 and 8-bit AVR. We briefly compare the performance of speed-optimized dilithium3. Compared to the state-of-the-art assembly implementation on Cortex-M3, our assembly implementation reduces the key generation, signature generation, and signature verification cycles by 2.30%, 23.29%, and 0.69%. In the 8-bit AVR environment, our Barrett-based C implementation reduces the key generation, signature generation, and signature verification cycles by 45.09%, 56.80%, and 50.40%, respectively, and our assembly-optimized implementation reduces the cycles of each operation by 48.85%, 61.70%, and 55.08%, respectively.
Last updated:  2023-12-27
Fiat-Shamir Goes Tropical
Rémi Géraud-Stewart, David Naccache, and Ofer Yifrach-Stav
In a recent ePrint, Brown and Monico propose new attacks on the tropical signature scheme of Chen, Grigoriev and Shpilrain. This note provides a new countermeasures against those attacks. Thereby, we (temporarily?) shift the fire from the signature algorithm to redirect attacks on the key and on tropical polynomial factorization.
Last updated:  2023-12-24
Efficient quantum algorithms for some instances of the semidirect discrete logarithm problem
Muhammad Imran and Gábor Ivanyos
The semidirect discrete logarithm problem (SDLP) is the following analogue of the standard discrete logarithm problem in the semidirect product semigroup $G\rtimes \mathrm{End}(G)$ for a finite semigroup $G$. Given $g\in G, \sigma\in \mathrm{End}(G)$, and $h=\prod_{i=0}^{t-1}\sigma^i(g)$ for some integer $t$, the SDLP$(G,\sigma)$, for $g$ and $h$, asks to determine $t$. As Shor's algorithm crucially depends on commutativity, it is believed not to be applicable to the SDLP. Previously, the best known algorithm for the SDLP was based on Kuperberg's subexponential time quantum algorithm. Still, the problem plays a central role in the security of certain proposed cryptosystems in the family of $\textit{semidirect product key exchange}$. This includes a recently proposed signature protocol called SPDH-Sign. In this paper, we show that the SDLP is even easier in some important special cases. Specifically, for a finite group $G$, we describe quantum algorithms for the SDLP in $G\rtimes \mathrm{Aut}(G)$ for the following two classes of instances: the first one is when $G$ is solvable and the second is when $G$ is a matrix group and a power of $\sigma$ with a polynomially small exponent is an inner automorphism of $G$. We further extend the results to groups composed of factors from these classes. A consequence is that SPDH-Sign and similar cryptosystems whose security assumption is based on the presumed hardness of the SDLP in the cases described above are insecure against quantum attacks. The quantum ingredients we rely on are not new: these are Shor's factoring and discrete logarithm algorithms and well-known generalizations.
Last updated:  2023-12-25
Overview and Discussion of Attacks on CRYSTALS-Kyber
Stone Li
This paper reviews common attacks in classical cryptography and plausible attacks in the post-quantum era targeted at CRYSTALS-Kyber. Kyber is a recently standardized post-quantum cryptography scheme that relies on the hardness of lattice problems. Although it has undergone rigorous testing by the National Institute of Standards and Technology (NIST), there have recently been studies that have successfully executed attacks against Kyber while showing their applicability outside of controlled settings. The attacks discussed in the paper include common attacks, side-channel attacks, SCA-assisted CCA, and fault injections. In the common attacks section, attacks on symmetric primitives, multi-target attacks, and attacks exploiting decryption failures can all be deemed inviable, while recent data on attacks on module-LWE questions Kyber's security level. In the side-channel attacks section, timing attacks are proven useless due to the constant-time nature of Kyber, but SASCA attacks are still viable, though easily defended against with minimal drawbacks. Attacks targeting message encoding and attacks using deep learning, however, both prove effective, even with high-order masking. LDPC has also been proposed as a new framework for attack, proving itself potent with room for growth. In the SCA-assisted CCA section, EM attacks and CPA attacks have also both shown potential while remaining difficult to defend against. In the fault injection section, Roulette and error-tolerant key recovery have both recently been proposed, with data demonstrating their effectiveness and difficulty to defend against. This paper aims to provide future researchers insight into what areas should be focused on to strengthen current as well as future cryptosystems.
Last updated:  2023-12-23
Protection Against Subversion Corruptions via Reverse Firewalls in the plain Universal Composability Framework
Paula Arnold, Sebastian Berndt, Jörn Müller-Quade, and Astrid Ottenhues
While many modern cryptographic primitives have stood the test of time, attacker have already begun to expand their attacks beyond classical cryptanalysis by specifically targeting implementations. One of the most well-documented classes of such attacks are subversion (or substitution) attacks, where the attacker replaces the Implementation of the cryptographic primitive in an undetectable way such that the subverted implementation leaks sensitive information of the user during a protocol execution. The revelations of Snowden have shown that this is not only a dangerous theoretical attack, but an attack deployed by intelligence services. Several possible solutions for protection against these attacks are proposed in current literature. Among the most widely studied ones are cryptographic reverse firewalls that aim to actively remove the covert channel leaking the secret. While different protocols supporting such firewalls have been proposed, they do no guarantee security in the presence of concurrent runs. This situation was resolved by a recent work of Chakraborty et al. (EUROCRYPT 2022) that presented the first UC-model of such firewalls. Their model allows to provide security if a subverted party uses an honest firewall. However, using such a firewall also provides a possible new target for the attacker and in the case that an honest party uses a corrupted firewall, they were not able to prove any security guarantees. Furthermore, their model is quite complex and does not fit into the plain UC model. Hence, the authors needed to reprove fundamental theorems such as the composition theorem. Finally, the high complexity of their model also makes designing corresponding protocols a challenging task, as one also needs to reprove the security of the underlying protocol. In this paper, we present a simpler model capturing cryptographic reverse firewalls in the plain UC model. The simplicity of our model allows to also reason about corrupted firewalls and still maintain strong security guarantees. Furthermore, we resolve the open question by Chakraborty et al. (EUROCRYPT 2022) and by Chakraborty et al. (EUROCRYPT 2023) and present the first direct UC-secure oblivious transfer protocol along with a cryptographic reverse firewall.
Last updated:  2024-01-04
GigaDORAM: Breaking the Billion Address Barrier
Brett Falk, Rafail Ostrovsky, Matan Shtepel, and Jacob Zhang
We design and implement GigaDORAM, a novel 3-server Distributed Oblivious Random Access Memory (DORAM) protocol. Oblivious RAM allows a client to read and write to memory on an untrusted server while ensuring the server itself learns nothing about the client's access pattern. Distributed Oblivious RAM (DORAM) allows a group of servers to efficiently access a secret-shared array at a secret-shared index. A recent generation of DORAM implementations (e.g. FLORAM, DuORAM) has focused on building DORAM protocols based on Function Secret-Sharing (FSS). These protocols have low communication complexity and low round complexity but linear computational complexity of the servers. Thus, they work for moderate-size databases, but at a certain size, these FSS-based protocols become computationally inefficient. In this work, we introduce GigaDORAM, a hierarchical-solution-based DORAM featuring poly-logarithmic computation and communication, but with an over $100\times$ reduction in rounds per query compared to previous hierarchical DORAM protocols. In our implementation, we show that for moderate to large databases where FSS-based solutions become computation-bound, our protocol is orders of magnitude more efficient than the best existing DORAM protocols. When $N = 2^{31}$, our DORAM is able to perform over 700 queries per second.
Last updated:  2023-12-22
HELIOPOLIS: Verifiable Computation over Homomorphically Encrypted Data from Interactive Oracle Proofs is Practical
Diego F. Aranha, Anamaria Costache, Antonio Guimarães, and Eduardo Soria-Vazquez
Homomorphic encryption (HE) enables computation on encrypted data, which in turn facilitates the outsourcing of computation on private data. However, HE offers no guarantee that the returned result was honestly computed by the cloud. In order to have such guarantee, it is necessary to add verifiable computation (VC) into the system. The most efficient recent works in VC over HE focus on verifying operations on the ciphertext space of the HE scheme, which usually lacks the algebraic structure that would make it compatible with existing VC systems. For example, multiplication of ciphertexts in the current most efficient HE schemes requires non-algebraic operations such as real division and rounding. Therefore, existing works for VC over HE have to either give up on those efficient HE schemes, or incur a large overhead (an amount of constraints proportional to the ciphertext ring's size) in order to emulate these non-algebraic operations. In this work, we move away from that paradigm by placing the verification checks in the plaintext space of HE, all while the prover remains computing on ciphertexts. We achieve this by introducing a general transformation for Interactive Oracle Proofs (IOPs) to work over HE, whose result we denote as HE-IOPs. We apply this same transformation to the FRI [Ben-Sasson et al., ICALP 2018] IOP of proximity and we show how to compile HE-Reed Solomon-encoded IOPs and HE-$\delta$-correlated-IOPs with HE-FRI into HE-IOPs. Furthermore, our construction is compatible with a prover that provides input in zero-knowledge, and only relies on building blocks that are plausibly quantum-safe. Aligning the security parameters of HE and FRI is a difficult task for which we introduce several optimizations. We demonstrate their efficiency with a proof-of-concept implementation in Python and show that, for an encrypted Reed Solomon codeword with degree bound $2^{11}$ and rate $1/16$ in a (plaintext) field of size $2^{256}$, we can run FRI's commit phase in just 43 minutes on a single thread on a c6i.metal instance (which could be reduced to less than a minute in a multi-threaded implementation in a large server). Verification takes less than 0.2 seconds, and, based on micro-benchmarks of the employed techniques, we show it could be up to 100 times faster in a fully optimized implementation.
Last updated:  2024-04-19
PriDe CT: Towards Public Consensus, Private Transactions, and Forward Secrecy in Decentralized Payments
Yue Guo, Harish Karthikeyan, Antigoni Polychroniadou, and Chaddy Huussin
Anonymous Zether, proposed by Bunz et al. (FC, 2020) and subsequently improved by Diamond (IEEE S&P, 2021) is an account-based confidential payment mechanism that works by using a smart contract to achieve privacy (i.e. identity of receivers to transactions and payloads are hidden). In this work, we look at simplifying the existing protocol while also achieving batching of transactions for multiple receivers, while ensuring consensus and forward secrecy. To the best of our knowledge, this work is the first to formally study the notion of forward secrecy in the setting of blockchain, borrowing a very popular and useful idea from the world of secure messaging. Specifically, we introduce: - FUL-Zether, a forward-secure version of Zether (Bunz et al., FC, 2020). - PRIvate DEcentralized Confidental Transactions (PriDe CT), a much-simplified version of Anonymous Zether that achieves competitive performance and enables batching of transactions for multiple receivers. - PRIvate DEcentralized Forward-secure Until Last update Confidential Transactions (PriDeFUL CT), a forward-secure version of PriDe CT. We also present an open-source, Ethereum-based implementation of our system. PriDe CT uses linear homomorphic encryption as Anonymous Zether but with simpler zero-knowledge proofs. PriDeFUL CT uses an updatable public key encryption scheme to achieve forward secrecy by introducing a new DDH-based construction in the standard model. In terms of transaction sizes, Quisquis (Asiacrypt, 2019), which is the only cryptocurrency that supports batchability (albeit in the UTXO model), has 15 times more group elements than PriDe CT. Meanwhile, for a ring of $N$ receivers, Anonymous Zether requires $6\log N$ more terms even without accounting for the ability to batch in PriDe CT. Further, our implementation indicates that, for $N=32$, even if there were 7 intended receivers, PriDe CT outperforms Anonymous Zether in proving time and gas consumption.
Last updated:  2024-03-29
Using Predicate Extension for Predicate Encryption to Generically Obtain Chosen-Ciphertext Security and Signatures
Marloes Venema and Leon Botros
Predicate encryption (PE) is a type of public-key encryption that captures many useful primitives such as attribute-based encryption (ABE). Although much progress has been made to generically achieve security against chosen-plaintext attacks (CPA) efficiently, in practice, we also require security against chosen-ciphertext attacks (CCA). Because achieving CCA-security on a case-by-case basis is a complicated task, several generic conversion methods have been proposed, which typically target different subclasses of PE such as ciphertext-policy ABE. As is common, such conversion methods may sacrifice some efficiency. Notably, for ciphertext-policy ABE, all proposed generic transformations incur a significant decryption overhead. Furthermore, depending on the setting in which PE is used, we may also want to require that messages are signed. To do this, predicate signature schemes can be used. However, such schemes provide a strong notion of privacy for the signer, which may be stronger than necessary for some practical settings at the cost of efficiency. In this work, we propose the notion of predicate extension, which transforms the predicate used in a PE scheme to include one additional attribute, in both the keys and the ciphertexts. Using predicate extension, we can generically obtain CCA-security and signatures from a CPA-secure PE scheme. For the CCA-security transform, we observe that predicate extension implies a two-step approach to achieving CCA-security. This insight broadens the applicability of existing transforms for specific subclasses of PE to cover all PE. We also propose a new transform that incurs slightly less overhead than existing transforms. Furthermore, we show that predicate extension allows us to create a new type of signatures, which we call PE-based signatures. PE-based signatures are weaker than typical predicate signatures in the sense that they do not provide privacy for the signer. Nevertheless, such signatures may be more suitable for some practical settings owing to their efficiency or reduced interactivity. Lastly, to show that predicate extensions may facilitate a more efficient way to achieve CCA-security generically than existing methods, we propose a novel predicate-extension transformation for a large class of pairing-based PE, covered by the pair and predicate encodings frameworks. In particular, this yields the most efficient generic CCA-conversion for ciphertext-policy ABE.
Last updated:  2023-12-22
SnarkFold: Efficient SNARK Proof Aggregation from Split Incrementally Verifiable Computation
Xun Liu, Shang Gao, Tianyu Zheng, and Bin Xiao
The succinct non-interactive argument of knowledge (SNARK) technique is widely used in blockchain systems to replace the costly on-chain computation with the verification of a succinct proof. However, when dealing with multiple proofs, most existing applications require each proof to be independently verified, resulting in a heavy load on nodes and high transaction fees for users. To improve the efficiency of verifying multiple proofs, we introduce SnarkFold, a universal SNARK-proof aggregation scheme based on incrementally verifiable computation (IVC). Unlike previous proof aggregation approaches based on inner product arguments, which have a logarithmic proof size and verification cost, SnarkFold achieves constant verification time and proof size. One core technical advance in SnarkFold, of independent interest, is the ``split IVC'': rather than using one running instance to fold/accumulate the computation, we employ two (or more) running instances of different types in the recursive circuit to avoid transferring into the same structure. This distinguishing feature is particularly well-suited for proof aggregation scenarios, as constructing arithmetic circuits for pairings can be expensive. We further demonstrate how to fold Groth16 proofs with our SnarkFold. With some further optimizations, SnarkFold achieves the highest efficiency among all approaches.
Last updated:  2023-12-22
The Fiat--Shamir Transformation of $(\Gamma_1,\dots,\Gamma_\mu)$-Special-Sound Interactive Proofs
Thomas Attema, Serge Fehr, Michael Klooß, and Nicolas Resch
The Fiat-Shamir transformation is a general principle to turn any public-coin interactive proof into non-interactive one (with security then typically analyzed in the random oracle model). While initially used for 3-round protocols, many recent constructions use it for multi-round protocols. However, in general the soundness error of the Fiat-Shamir transformed protocol degrades exponentially in the number of rounds. On the positive side, it was shown that for the special class of $(k_1,\dots,k_\mu)$-special-sound protocols the loss is actually only linear in the number of random oracle queries, and independent of the number of rounds, which is optimal. A natural next question is whether this positive result extends to the Fiat-Shamir transformation of so-called $(\Gamma_1,\dots,\Gamma_\mu)$-special-sound protocols, a notion recently defined and analyzed in the interactive case, with the aim to capture the most general notion of special-soundness. We show in this work that this is indeed the case. Concretely, we show that the Fiat--Shamir transformation of any $(\Gamma_1,\dots,\Gamma_\mu)$-special-sound interactive proof is knowledge sound under the same condition under which the original interactive proof is knowledge sound. Furthermore, also here the loss is linear in the number of random-oracle queries and independent of the number of rounds. In light of the above, one might suspect that our argument follows as a straightforward combination of the above mentioned prior works. However, this is not the case. The approach used for $(k_1,\dots,k_\mu)$-special-sound protocols, which is based on an extractor that samples without replacement, does not (seem to) generalize; on the other hand, the other approach, which uses an extractor based on sampling with replacement, comes with an additional loss that would blow up in the recursive multi-round analysis.
Last updated:  2024-03-11
Revisiting The Multiple of Property for SKINNY The Exact Computation of the number of right pairs
Hanbeom Shin, Insung Kim, Sunyeop Kim, Seonggyeom Kim, Deukjo Hong, Jaechul Sung, and Seokhie Hong
At EUROCRYPT 2017, Grassi et al. proposed the multiple-of-8 property for 5-round AES, where the number $n$ of right pairs is a multiple of 8. At ToSC 2019, Boura et al. generalized the multiple-of property for a general SPN block cipher and applied it to block cipher SKINNY. In this paper, we present that $n$ is not only a multiple but also a fixed value for SKINNY. Unlike the previous proof of generalization of multiple-of property using equivalence class, we investigate the propagation of the set to compute the exact number $n$. We experimentally verified that presented property holds. We extend this property one round more using the lack of the whitening key on the SKINNY and use this property to construct 6-round distinguisher on SKINNY-64 and SKINNY-128. The probability of success of both distinguisher is almost 1 and the total complexities are $2^{16}$ and $2^{32}$ respectively. We verified that this property only holds for SKINNY, not for AES and MIDORI, and provide the conditions under which it exists for AES-like ciphers.
Last updated:  2023-12-22
Distinguisher and Related-Key Attack on HALFLOOP-96
Jinpeng Liu and Ling Sun
HALFLOOP-96 is a 96-bit tweakable block cipher used in high frequency radio to secure automatic link establishment messages. In this paper, we concentrate on its differential properties in the contexts of conventional, related-tweak, and related-key differential attacks. Using automatic techniques, we determine the minimum number of active S-boxes and the maximum differential probability in each of the three configurations. The resistance of HALFLOOP-96 to differential attacks in the conventional and related-tweak configurations is good, and the longest distinguishers in both configurations consist of five rounds. In contrast, the security of the cipher against differential attacks in the related-key configuration is inadequate. The most effective related-key distinguisher we can find spans eight rounds. The 8-round related-key differential distinguisher is then utilised to initiate a 9-round weak-key attack. With $2^{92.96}$ chosen-plaintexts, 38.77-bit equivalent information about the keys can be recovered. Even though the attack does not pose a significant security threat to HALFLOOP-96, its security margin in the related-key configuration is exceedingly narrow. Therefore, improper use must be avoided in the application.
Last updated:  2023-12-25
Traceable mixnets
Prashant Agrawal, Abhinav Nakarmi, Mahabir Prasad Jhanwar, Subodh Vishnu Sharma, and Subhashis Banerjee
We introduce the notion of traceable mixnets. In a traditional mixnet, multiple mix-servers jointly permute and decrypt a list of ciphertexts to produce a list of plaintexts, along with a proof of correctness, such that the association between individual ciphertexts and plaintexts remains completely hidden. However, in many applications, the privacy-utility tradeoff requires answering some specific queries about this association, without revealing any information beyond the query result. We consider queries of the following types: a) given a ciphertext in the mixnet input list, whether it encrypts one of a given subset of plaintexts in the output list, and b) given a plaintext in the mixnet output list, whether it is a decryption of one of a given subset of ciphertexts in the input list. Traceable mixnets allow the mix-servers to jointly prove answers to the above queries to a querier such that neither the querier nor a threshold number of mix-servers learn any information beyond the query result. Further, if the querier is not corrupted, the corrupted mix-servers do not even learn the query result. We first comprehensively formalise these security properties of traceable mixnets and then propose a construction of traceable mixnets using novel distributed zero-knowledge proofs (ZKPs) of set membership and of a statement we call reverse set membership. Although set membership has been studied in the single-prover setting, the main challenge in our distributed setting lies in making sure that none of the mix-servers learn the association between ciphertexts and plaintexts during the proof. We implement our distributed ZKPs and show that they are faster than state-of-the-art by at least one order of magnitude.
Last updated:  2023-12-21
Upgrading Fuzzy Extractors
Chloe Cachet, Ariel Hamlin, Maryam Rezapour, and Benjamin Fuller
Fuzzy extractors derive stable keys from noisy sources non-interactively (Dodis et al., SIAM Journal of Computing 2008). Since their introduction, research has focused on two tasks: 1) showing security for as many distributions as possible and 2) providing stronger security guarantees including allowing one to enroll the same value multiple times (reusability), security against an active attacker (robustness), and preventing leakage about the enrolled value (privacy). Existing constructions of reusable fuzzy extractors are direct and do not support as many distributions as the best non-reusable constructions. Constructions of robust fuzzy extractors require strong assumptions even in the CRS model. Given the need for progress on the basic fuzzy extractor primitive, it is prudent to seek generic mechanisms to transform a fuzzy extractor into one that is robust, private, and reusable so that it can inherit further improvements. This work asks if one can generically upgrade fuzzy extractors to achieve robustness, privacy, and reusability. We show positive and negative results: we show upgrades for robustness and privacy, but we provide a negative result on reuse. 1. We upgrade (private) fuzzy extractors to be robust under weaker assumptions than previously known in the common reference string model. 2. We show a generic upgrade for a private fuzzy extractor using multi-bit compute and compare (MBCC) obfuscation (Wichs and Zirdelis, FOCS 2017) that requires less entropy than prior work. 3. We show one cannot arbitrarily compose private fuzzy extractors. It is known one cannot reuse an arbitrary fuzzy extractor; each enrollment can leak a constant fraction of the input entropy. We show that one cannot build a reusable private fuzzy extractor by considering other enrollments as auxiliary input. In particular, we show that assuming MBCC obfuscation and collision-resistant hash functions, there does not exist a private fuzzy extractor secure against unpredictable auxiliary inputs strengthening a negative result of Brzuska et al. (Crypto 2014).
Last updated:  2023-12-21
Concrete Time/Memory Trade-Offs in Generalised Stern’s ISD Algorithm
Sreyosi Bhattacharyya and Palash Sarkar
The first contribution of this work is a generalisation of Stern's information set decoding (ISD) algorithm. Stern's algorithm, a variant of Stern's algorithm due to Dumer, as well as a recent generalisation of Stern's algorithm due to Bernstein and Chou are obtained as special cases of our generalisation. Our second contribution is to introduce the notion of a set of effective time/memory trade-off (TMTO) points for any ISD algorithm for given ranges of values of parameters of the algorithm. Such a set succinctly and uniquely captures the entire landscape of TMTO points with only a minor loss in precision. We further describe a method to compute a set of effective TMTO points. As an application, we compute sets of effective TMTO points for the five variants of the Classic McEliece cryptosystem corresponding to the new algorithm as well as for Stern's, Dumer's and Bernstein and Chou's algorithms. The results show that while Dumer's and Bernstein and Chou's algorithms do not provide any interesting TMTO points beyond what is achieved by Stern's algorithm, the new generalisation that we propose provide about twice the number of effective TMTO points that is obtained from Stern's algorithm. Consequences of the obtained TMTO points to the classification of the variants of Classic McEliece in appropriate NIST categories are discussed.
Last updated:  2023-12-21
Applications of Neural Network-Based AI in Cryptography
Abderrahmane Nitaj and Tajjeeddine Rachidi
Artificial intelligence (AI) is a modern technology that allows plenty of advantages in daily life, such as predicting weather, finding directions, classifying images and videos, even automatically generating code, text, and videos. Other essential technologies such as blockchain and cybersecurity also benefit from AI. As a core component used in blockchain and cybersecurity, cryptography can benefit from AI in order to enhance the confidentiality and integrity of cyberspace. In this paper, we review the algorithms underlying four prominent cryptographic cryptosystems, namely the Advanced Encryption Standard, the Rivest--Shamir--Adleman, Learning With Errors, and the Ascon family of cryptographic algorithms for authenticated encryption. Where possible, we pinpoint areas where AI can be used to help improve their security.
Last updated:  2023-12-21
Batch Arguments to NIZKs from One-Way Functions
Eli Bradley, Brent Waters, and David J. Wu
Succinctness and zero-knowledge are two fundamental properties in the study of cryptographic proof systems. Several recent works have formalized the connections between these two notions by showing how to realize non-interactive zero-knowledge (NIZK) arguments from succinct non-interactive arguments. Specifically, Champion and Wu (CRYPTO 2023) as well as Bitansky, Kamath, Paneth, Rothblum, and Vasudevan (ePrint 2023) recently showed how to construct a NIZK argument for NP from a (somewhere-sound) non-interactive batch argument (BARG) and a dual-mode commitment scheme (and in the case of the Champion-Wu construction, a local pseudorandom generator). The main open question is whether a BARG suffices for a NIZK (just assuming one-way functions). In this work, we first show that an adaptively-sound BARG for NP together with an one-way function imply a computational NIZK argument for NP. We then show that the weaker notion of somewhere soundness achieved by existing BARGs from standard algebraic assumptions are also adaptively sound if we assume sub-exponential security. This transformation may also be of independent interest. Taken together, we obtain a NIZK argument for NP from one-way functions and a sub-exponentially-secure somewhere-sound BARG for NP. If we instead assume plain public-key encryption, we show that a standard polynomially-secure somewhere-sound batch argument for NP suffices for the same implication. As a corollary, this means a somewhere-sound BARG can be used to generically upgrade any semantically-secure public-key encryption scheme into one secure against chosen-ciphertext attacks. More broadly, our results demonstrate that constructing non-interactive batch arguments for NP is essentially no easier than constructing NIZK arguments for NP.
Last updated:  2023-12-21
Revocable Quantum Digital Signatures
Tomoyuki Morimae, Alexander Poremba, and Takashi Yamakawa
We study digital signatures with revocation capabilities and show two results. First, we define and construct digital signatures with revocable signing keys from the LWE assumption. In this primitive, the signing key is a quantum state which enables a user to sign many messages and yet, the quantum key is also revocable, i.e., it can be collapsed into a classical certificate which can later be verified. Once the key is successfully revoked, we require that the initial recipient of the key loses the ability to sign. We construct digital signatures with revocable signing keys from a newly introduced primitive which we call two-tier one-shot signatures, which may be of independent interest. This is a variant of one-shot signatures, where the verification of a signature for the message ``0'' is done publicly, whereas the verification for the message ``1'' is done in private. We give a construction of two-tier one-shot signatures from the LWE assumption. As a complementary result, we also construct digital signatures with quantum revocation from group actions, where the quantum signing key is simply ``returned'' and then verified as part of revocation. Second, we define and construct digital signatures with revocable signatures from OWFs. In this primitive, the signer can produce quantum signatures which can later be revoked. Here, the security property requires that, once revocation is successful, the initial recipient of the signature loses the ability to find accepting inputs to the signature verification algorithm. We construct this primitive using a newly introduced two-tier variant of tokenized signatures. For the construction, we show a new lemma which we call the adaptive hardcore bit property for OWFs, which may enable further applications.
Last updated:  2023-12-21
LERNA: Secure Single-Server Aggregation via Key-Homomorphic Masking
Hanjun Li, Huijia Lin, Antigoni Polychroniadou, and Stefano Tessaro
This paper introduces LERNA, a new framework for single-server secure aggregation. Our protocols are tailored to the setting where multiple consecutive aggregation phases are performed with the same set of clients, a fraction of which can drop out in some of the phases. We rely on an initial secret sharing setup among the clients which is generated once-and-for-all, and reused in all following aggregation phases. Compared to prior works [Bonawitz et al. CCS’17, Bell et al. CCS’20], the reusable setup eliminates one round of communication between the server and clients per aggregation—i.e., we need two rounds for semi-honest security (instead of three), and three rounds (instead of four) in the malicious model. Our approach also significantly reduces the server’s computational costs by only requiring the reconstruction of a single secret-shared value (per aggregation). Prior work required reconstructing a secret-shared value for each client involved in the computation. We provide instantiations of LERNA based on both the Decisional Composite Residuosity (DCR) and (Ring) Learning with Rounding ((R)LWR) assumptions respectively and evaluate a version based on the latter assumption. In addition to savings in round-complexity (which result in reduced latency), our experiments show that the server computational costs are reduced by two orders of magnitude in comparison to the state-of-the-art. In settings with a large number of clients, we also reduce the computational costs up to twenty-fold for most clients, while a small set of “heavy clients” is subject to a workload that is still smaller than that of prior work.
Last updated:  2024-01-24
The Splitting Field of $Y^n-2$, Two-Variable NTT and Lattice-Based Cryptography
Wenzhe Yang
The splitting field $F$ of the polynomial $Y^n-2$ is an extension over $\mathbb{Q}$ generated by $\zeta_n=\exp(2 \pi \sqrt{-1} /n)$ and $\sqrt[n]{2}$. In this paper, we lay the foundation for applying the Order-LWE in the integral ring $\mathcal{R}=\mathbb{Z}[\zeta_n, \sqrt[n]{2}]$ to cryptographic uses when $n$ is a power-of-two integer. We explicitly compute the Galois group $\text{Gal}\left(F/\mathbb{Q} \right)$ and the canonical embedding of $F$, based on which we study the properties of the trace pairings of the integral basis $\zeta_n^{k_0} \sqrt[n]{2}^{k_1}$. Then we discuss the security of the Order-LWE in $\mathcal{R}$, and show that it offers the same security level as the RLWE in $\mathbb{Z}[X]/\langle X^{n^2/4} + 1 \rangle$. Moreover, we design a Two-Variable Number Theoretic Transform (2NTT) algorithm for the quotient $\mathcal{R}_p=\mathcal{R}/p\mathcal{R}$, where $p$ is a prime number such that $Y^n \equiv 2 \bmod p$ has $n$ distinct solutions. Compared to the one-variable NTT in $\mathbb{Z}[X]/\langle X^{n^2/4} + 1 \rangle$, a crucial advantage of 2NTT is that it enjoys a quadratic saving of twiddle factors. Hence, we can leverage this quadratic saving to boost the performance of 2NTT in practical implementations. At last, we also look at the applications of the Order-LWE in $\mathcal{R}$. In particular, we construct a new variant of CKKS for $\mathcal{R}$ and study its new properties.
Last updated:  2023-12-20
More efficient comparison protocols for MPC
Wicher Malten, Mehmet Ugurbil, and Miguel de Vega
In 1982, Yao introduced the problem of comparing two private values, thereby launching the study of protocols for secure multi-party computation (MPC). Since then, comparison protocols have undergone extensive study and found widespread applications. We survey state-of-the-art comparison protocols for an arbitrary number of parties, decompose them into smaller primitives and analyse their communication complexity under the usual assumption that the underlying MPC protocol does preprocessing and computes linear operations without communication. We then develop two new comparison protocols and explain why they are faster than similar protocols, including those that are commonly used in practice: they reduce the number of online multiplications, without increasing preprocessing or round complexity. More concretely, online bandwidth is reduced by more than half for the standard comparison protocols whose round complexity is logarithmic in the bit-length, whereas for constant round comparison protocols the reduction is two-thirds.
Last updated:  2024-05-29
Keeping Up with the KEMs: Stronger Security Notions for KEMs and automated analysis of KEM-based protocols
Cas Cremers, Alexander Dax, and Niklas Medinger
Key Encapsulation Mechanisms (KEMs) are a critical building block for hybrid encryption and modern security protocols, notably in the post-quantum setting. Given the asymmetric public key of a recipient, the primitive establishes a shared secret key between sender and recipient. In recent years, a large number of abstract designs and concrete implementations of KEMs have been proposed, e.g., in the context of the NIST process for post-quantum primitives. In this work, we (i) establish stronger security notions for KEMs, and (ii) develop a symbolic analysis method to analyze security protocols that use KEMs. First, we generalize existing security notions for KEMs in the computational setting, introduce several stronger security notions, and prove their relations. Our new properties formalize in which sense outputs of the KEM uniquely determine, i.e., bind, other values. Our new binding properties can be used, e.g., to prove the absence of attacks that were not captured by prior security notions, such as re-encapsulation attacks. Second, we develop a family of fine-grained symbolic models that correspond to our hierarchy of computational security notions, and are suitable for the automated analysis of KEM-based security protocols. We encode our models as a library in the framework of the Tamarin prover. Given a KEM-based protocol, our approach can automatically derive the minimal binding properties required from the KEM; or, if also given a concrete KEM, can analyze if the protocols meets its security goals. In case studies, Tamarin automatically discovers, e.g., that the key exchange protocol proposed in the original Kyber paper requires stronger properties from the KEM than were proven in the paper.
Last updated:  2023-12-20
Multipars: Reduced-Communication MPC over Z2k
Sebastian Hasler, Pascal Reisert, Marc Rivinius, and Ralf Küsters
In recent years, actively secure SPDZ-like protocols for dishonest majority, like SPD$\mathbb Z_{2^k}$, Overdrive2k, and MHz2k, over base rings $\mathbb Z_{2^k}$ have become more and more efficient. In this paper, we present a new actively secure MPC protocol Multipars that outperforms these state-of-the-art protocols over $\mathbb Z_{2^k}$ by more than a factor of 2 in the two-party setup in terms of communication. Multipars is the first actively secure N-party protocol over $\mathbb Z_{2^k}$ that is based on linear homomorphic encryption (LHE) in the offline phase (instead of oblivious transfer or somewhat homomorphic encryption in previous works). The strong performance of Multipars relies on a new adaptive packing for BGV ciphertexts that allows us to reduce the parameter size of the encryption scheme and the overall communication cost. Additionally, we use modulus switching for further size reduction, a new type of enhanced CPA security over $\mathbb Z_{2^k}$, a truncation protocol for Beaver triples, and a new LHE-based offline protocol without sacrificing over $\mathbb Z_{2^k}$. We have implemented Multipars and therewith provide the fastest preprocessing phase over $\mathbb Z_{2^k}$. Our evaluation shows that Multipars offers at least a factor of 8 lower communication costs and up to a factor of 15 faster runtime in the WAN setting compared to the currently best available actively secure MPC implementation over $\mathbb Z_{2^k}$.
Last updated:  2023-12-20
Single-Trace Side-Channel Attacks on CRYSTALS-Dilithium: Myth or Reality?
Ruize Wang, Kalle Ngo, Joel Gärtner, and Elena Dubrova
We present a side-channel attack on CRYSTALS-Dilithium, a post-quantum secure digital signature scheme, with two variants of post-processing. The side-channel attack exploits information leakage in the secret key unpacking procedure of the signing algorithm to recover the coefficients of the polynomials in the secret key vectors ${\bf s}_1$ and ${\bf s}_2$ by profiled deep learning-assisted power analysis. In the first variant, one half of the coefficients of ${\bf s}_1$ and ${\bf s}_2$ is recovered by power analysis and the rest is derived by solving a system of linear equations based on ${\bf t} = {\bf A}{\bf s}_1 + {\bf s}_2$, where ${\bf A}$ and ${\bf t}$ are parts of the public key. This case assumes knowledge of the least significant bits of the vector ${\bf t}$, ${\bf t}_0$. The second variant waives this requirement. However, to succeed, it needs a larger portion of ${\bf s}_1$ to be recovered by power analysis. The remainder of ${\bf s}_1$ is obtained by lattice reduction. Once the full ${\bf s}_1$ is recovered, all the other information necessary for generating valid signatures can be trivially derived from the public key. We evaluate both variants on an ARM Cortex-M4 implementation of Dilithium-2. The profiling stage (trace capture and neural network training) takes less than 10 hours. In the attack assuming that ${\bf t}_0$ is known, the probability of successfully recovering the full vector ${\bf s}_1$ from a single trace captured from a different from profiling device is non-negligible (9%). The success rate approaches 100% if multiple traces are available for the attack. Our results demonstrate the necessity of protecting the secret key of CRYSTALS-Dilithium from single-trace attacks and call for a reassessment of the role of compression of the public key vector ${\bf t}$ in the security of CRYSTALS-Dilithium implementations.
Last updated:  2024-03-16
Toward A Practical Multi-party Private Set Union
Jiahui Gao, Son Nguyen, and Ni Trieu
This paper studies a multi-party private set union (mPSU), a fundamental cryptographic problem that allows multiple parties to compute the union of their respective datasets without revealing any additional information. We propose an efficient mPSU protocol which is secure in the presence of any number of colluding semi-honest participants. Our protocol avoids computationally expensive homomorphic operations or generic multi-party computation, thus providing an efficient solution for mPSU. The crux of our protocol lies in the utilization of new cryptographic tools, namely, Membership Oblivious Transfer (mOT) and Conditional Oblivious Pseudorandom Function (cOPRF). We believe that the mOT and cOPRF may be of independent interest. We implement our mPSU protocol and evaluate their performance. Our protocol shows an improvement of up to $37.82\times$ in term of running time and $389.85\times$ bandwidth cost compared to the existing state-of-the-art protocols.
Last updated:  2023-12-19
Cryptography from Planted Graphs: Security with Logarithmic-Size Messages
Damiano Abram, Amos Beimel, Yuval Ishai, Eyal Kushilevitz, and Varun Narayanan
We study the following broad question about cryptographic primitives: is it possible to achieve security against an arbitrary $\mathsf{poly}(n)$-time adversary with $O(\log n)$-size messages? It is common knowledge that the answer is ``no'' unless information-theoretic security is possible. In this work, we revisit this question by considering the setting of cryptography with public information and computational security. We obtain the following results, assuming variants of well-studied intractability assumptions: 1) A private simultaneous messages (PSM) protocol for every $f:[n]\times[n]\to\{0, 1\}$ requiring $(1+\epsilon)\log n$-bit messages for most functions and $(2+\epsilon)\log n$-bit messages for the remaining ones. We apply this towards non-interactive secure 3-party computation with similar message size in the preprocessing model, improving over previous 2-round protocols. 2) A secret-sharing scheme for any ``forbidden-graph'' access structure on $n$ nodes with $O(\log n)$ share size. 3) On the negative side, we show that computational threshold secret-sharing schemes with public information require share size $\Omega(\log \log n)$. For arbitrary access structures, we show that computational security does not help with 1-bit shares. The above positive results guarantee that any adversary of size $n^{o(\log n)}$ achieves an $n^{-\Omega(1)}$ distinguishing advantage. We show how to make the advantage negligible by slightly increasing the asymptotic message size, still improving over all known constructions. The security of our constructions is based on the conjectured hardness of variants of the planted clique problem, which was extensively studied in the algorithms, statistical inference, and complexity theory communities. Our work provides the first applications of such assumptions improving the efficiency of mainstream cryptographic primitives, gives evidence for the necessity of such assumptions, and suggests new questions in this domain that may be of independent interest.
Last updated:  2023-12-19
Unconditionally Secure Quantum Bit Commitment and Quantum Oblivious Transfer
Ping Wang, Yikang Lei, and Yiting Su
Recently, a novel secure quantum bit commitment (QBC) protocol has been proposed [29]. However, the protocol requires Alice and Bob to share Bell states in advance, making the protocol lacking in practicality. In this paper, we propose two new unconditionally secure quantum bit commitment protocols that do not require pre-shared Bell states based on entangled and non-entangled states, respectively. Their security stems from quantum mechanical properties such as quantum superposition, quantum entanglement, no-cloning theorem, and no-communication theorem. Furthermore, by combining the proposed QBC with Yao's quantum oblivious transfer (QOT) model, we can obtain an unconditionally secure QOT protocol.
Last updated:  2023-12-18
Holepunch: Fast, Secure File Deletion with Crash Consistency
Zachary Ratliff, Wittmann Goh, Abe Wieland, James Mickens, and Ryan Williams
A file system provides secure deletion if, after a file is deleted, an attacker with physical possession of the storage device cannot recover any data from the deleted file. Unfortunately, secure deletion is not provided by commodity file systems. Even file systems which explicitly desire to provide secure deletion are challenged by the subtleties of hardware controllers on modern storage devices; those controllers obscure the mappings between logical blocks and physical blocks, silently duplicate physical blocks, and generally make it hard for host-level software to make reliable assumptions about how file data is kept on the device. State-of-the-art frameworks for secure deletion also have no crash consistency, meaning that an ill-timed power outage or software fault will desynchonize keys and the associated encrypted file data, corrupting the file system. In this paper, we present Holepunch, a new software-level approach for implementing secure deletion. Holepunch treats the storage device as a black box, providing secure deletion via cryptographic erasure. Holepunch uses per-file keys to transparently encrypt outgoing file writes and decrypt incoming file reads, ensuring that all physical data in the storage device is always encrypted. Holepunch uses puncturable pseudorandom functions (PPRFs) to quickly access file keys; upon the deletion of file $f$, Holepunch updates the PPRF so that, even if the PPRF is recovered, the PPRF cannot be used to generate $f$'s key. By using PPRFs instead of the key trees leveraged by prior work, Holepunch reduces both the memory pressure caused by key management and the number of disk IOs needed to access files. Holepunch stores its master key in secure TPM storage, and uses a novel journaling scheme to provide crash consistency between TPM state and on-disk state.
Last updated:  2023-12-21
NOTRY: deniable messaging with retroactive avowal
Faxing Wang, Shaanan Cohney, Riad Wahby, and Joseph Bonneau
Modern secure messaging protocols typically aim to provide deniability. Achieving this requires that convincing cryptographic transcripts can be forged without the involvement of genuine users. In this work, we observe that parties may wish to revoke deniability and avow a conversation after it has taken place. We propose a new protocol called Not-on-the-Record-Yet (NOTRY) which enables users to prove a prior conversation transcript is genuine. As a key building block we propose avowable designated verifier proofs which may be of independent interest. Our implementation incurs roughly 8× communication and computation overhead over the standard Signal protocol during regular operation. We find it is nonetheless deployable in a realistic setting as key exchanges (the source of the overhead) still complete in just over 1ms on a modern computer. The avowal protocol induces only constant computation and communication performance for the communicating parties and scales linearly in the number of messages avowed for the verifier—in the tens of milliseconds per avowal.
Last updated:  2023-12-21
VDOO: A Short, Fast, Post-Quantum Multivariate Digital Signature Scheme
Anindya ganguly, Angshuman Karmakar, and Nitin Saxena
Hard lattice problems are predominant in constructing post-quantum cryptosystems. However, we need to continue developing post-quantum cryptosystems based on other quantum hard problems to prevent a complete collapse of post-quantum cryptography due to a sudden breakthrough in solving hard lattice problems. Solving large multivariate quadratic systems is one such quantum hard problem. Unbalanced Oil-Vinegar is a signature scheme based on the hardness of solving multivariate equations. In this work, we present a post-quantum digital signature algorithm VDOO (Vinegar-Diagonal-Oil-Oil) based on solving multivariate equations. We introduce a new layer called the diagonal layer over the oil-vinegar-based signature scheme Rainbow. This layer helps to improve the security of our scheme without increasing the parameters considerably. Due to this modification, the complexity of the main computational bottleneck of multivariate quadratic systems i.e. the Gaussian elimination reduces significantly. Thus making our scheme one of the fastest multivariate quadratic signature schemes. Further, we show that our carefully chosen parameters can resist all existing state-of-the-art attacks. The signature sizes of our scheme for the National Institute of Standards and Technology's security level of I, III, and V are 96, 226, and 316 bytes, respectively. This is the smallest signature size among all known post-quantum signature schemes of similar security.
Last updated:  2024-04-19
Analyzing the complexity of reference post-quantum software: the case of lattice-based KEMs
Daniel J. Bernstein
Software for various post-quantum KEMs has been submitted by the KEM design teams to the SUPERCOP testing framework. The ref/*.c and ref/*.h files together occupy, e.g., 848 lines for ntruhps4096821, 928 lines for ntruhrss701, 1316 lines for sntrup1277, and 2633 lines for kyber1024. It is easy to see that these numbers overestimate the inherent complexity of software for these KEMs. It is more difficult to systematically measure this complexity. This paper takes these KEMs as case studies and applies consistent rules to streamline the ref software for the KEMs, while still passing SUPERCOP's tests and preserving the decomposition of specified KEM operations into functions. The resulting software occupies 381 lines for ntruhps4096821, 385 lines for ntruhrss701, 472 lines for kyber1024, and 478 lines for sntrup1277. This paper also identifies the external subroutines used in each case, identifies the extent to which code is shared across different parameter sets, quantifies various software complications specific to each KEM, and traces how differences in KEM design goals produced different software complications. As a spinoff, this paper presents a kyber512 key-recovery demo exploiting variations in timings of the Kyber reference code.
Last updated:  2023-12-17
Differential Fault Attack on Ascon Cipher
Amit Jana
This work investigates the security of the Ascon authenticated encryption scheme in the context of fault attacks, with a specific focus on Differential Fault Analysis (DFA). Motivated by the growing significance of lightweight cryptographic solutions, particularly Ascon, we explore potential vulnerabilities in its design using DFA. By employing a novel approach that combines faulty forgery in the decryption query under two distinct fault models, leveraging bit-flip faults in the first phase and bit-set faults in the second, we successfully recover the complete Ascon key. This study sheds light on the impact of key whitening in the final permutation call and discusses potential threats when this safeguard is absent. Additionally, we consider the implications of injecting multiple bit-flip faults at the S-box input, suggesting alternative strategies for compromising the state space. Our findings contribute valuable insights into the gray-box security landscape of Ascon, emphasizing the need for robust defenses to ensure the integrity and resilience of lightweight cryptographic primitives against diverse fault attacks.
Last updated:  2023-12-16
One for All, All for Ascon: Ensemble-based Deep Learning Side-channel Analysis
Azade Rezaeezade, Abraham Basurto-Becerra, Léo Weissbart, and Guilherme Perin
In recent years, deep learning-based side-channel analysis (DLSCA) has become an active research topic within the side-channel analysis community. The well-known challenge of hyperparameter tuning in DLSCA encouraged the community to use methods that reduce the effort required to identify an optimal model. One of the successful methods is ensemble learning. While ensemble methods have demonstrated their effectiveness in DLSCA, particularly with AES-based datasets, their efficacy in analyzing symmetric-key cryptographic primitives with different operational mechanics remains unexplored. Ascon was recently announced as the winner of the NIST lightweight cryptography competition. This will lead to broader use of Ascon and a crucial requirement for thorough side-channel analysis of its implementations. With these two considerations in view, we utilize an ensemble of deep neural networks to attack two implementations of Ascon. Using an ensemble of five multilayer perceptrons or convolutional neural networks, we could find the secret key for the Ascon-protected implementation with less than 3 000 traces. To the best of our knowledge, this is the best currently known result. We can also identify the correct key with less than 100 traces for the unprotected implementation of Ascon, which is on par with the state-of-the-art results.
Last updated:  2023-12-15
Automated Issuance of Post-Quantum Certificates: a New Challenge
Uncategorized
Alexandre Augusto Giron, Frederico Schardong, Lucas Pandolfo Perin, Ricardo Custódio, Victor Valle, and Víctor Mateu
Show abstract
Uncategorized
The Automatic Certificate Management Environment protocol (ACME) has significantly contributed to the widespread use of digital certificates in safeguarding the authenticity and privacy of Internet data. These certificates are required for implementing the Transport Layer Security (TLS) protocol. However, it is well known that the cryptographic algorithms employed in these certificates will become insecure with the emergence of quantum computers. This study assesses the challenges in transitioning ACME to the post-quantum landscape using Post-Quantum Cryptography (PQC). To evaluate the cost of ACME's PQC migration, we create a simulation environment for issuing PQC-only and hybrid digital certificates. Our experiments reveal performance drawbacks associated with the switch to PQC or hybrid solutions. However, considering the high volume of certificates issued daily by organizations like Let's Encrypt, the performance of ACME is of utmost importance. To address this concern, we propose a novel challenge method for ACME. Compared to the widely used HTTP-01 method, our findings indicate an average PQC certificate issuance time that is 4.22 times faster, along with a potential reduction of up to 35% in communication size.
Last updated:  2023-12-15
Camel: E2E Verifiable Instant Runoff Voting without Tallying Authorities
Luke Harrison, Samiran Bag, and Feng Hao
Instant Runoff Voting (IRV) is one example of ranked-choice voting. It provides many known benefits when used in elections, such as minimising vote splitting, ensuring few votes are wasted, and providing resistance to strategic voting. However, the voting and tallying procedures for IRV are much more complicated than those of plurality and are both error-prone and tedious. Many automated systems have been proposed to simplify these procedures in IRV. Some of these also employ cryptographic techniques to protect the secrecy of ballots and enable verification of the tally. Nearly all of these cryptographic systems require a set of trustworthy tallying authorities (TAs) to perform the decryption of votes and/or running of mix servers, which adds significant complexity to the implementation and election management. We address this issue by proposing Camel: an E2E verifiable solution for IRV that requires no TAs. Camel employs a novel representation and a universally verifiable shifting procedure for ballots that facilitate the elimination of candidates as required in an IRV election. We combine these with a homomorphic encryption scheme and zero-knowledge proofs to protect the secrecy of the ballots and enable any party to verify the well-formedness of the ballots and the correctness of the tally in an IRV election. We examine the security of Camel and prove it maintains ballot secrecy by limiting the learned information (namely the tally) against a set of colluding voters.
Last updated:  2023-12-15
When and How to Aggregate Message Authentication Codes on Lossy Channels?
Eric Wagner, Martin Serror, Klaus Wehrle, and Martin Henze
Aggregation of message authentication codes (MACs) is a proven and efficient method to preserve valuable bandwidth in resource-constrained environments: Instead of appending a long authentication tag to each message, the integrity protection of multiple messages is aggregated into a single tag. However, while such aggregation saves bandwidth, a single lost message typically means that authentication information for multiple messages cannot be verified anymore. With the significant increase of bandwidth-constrained lossy communication, as applications shift towards wireless channels, it thus becomes paramount to study the impact of packet loss on the diverse MAC aggregation schemes proposed over the past 15 years to assess when and how to aggregate message authentication. Therefore, we empirically study all relevant MAC aggregation schemes in the context of lossy channels, investigating achievable goodput improvements, the resulting verification delays, processing overhead, and resilience to denial-of-service attacks. Our analysis shows the importance of carefully choosing and configuring MAC aggregation, as selecting and correctly parameterizing the right scheme can, e.g., improve goodput by 39% to 444%, depending on the scenario. However, since no aggregation scheme performs best in all scenarios, we provide guidelines for network operators to select optimal schemes and parameterizations suiting specific network settings.
Last updated:  2023-12-14
FANNG-MPC: Framework for Artificial Neural Networks and Generic MPC
Najwa Aaraj, Abdelrahaman Aly, Tim Güneysu, Chiara Marcolla, Johannes Mono, Rogerio Paludo, Iván Santos-González, Mireia Scholz, Eduardo Soria-Vazquez, Victor Sucasas, and Ajith Suresh
In this work, we introduce FANNG-MPC, a versatile secure multi-party computation framework capable to offer active security for privacy preserving machine learning as a service (MLaaS). Derived from the now deprecated SCALE-MAMBA, FANNG is a data-oriented fork, featuring novel set of libraries and instructions for realizing private neural networks, effectively reviving the popular framework. To the best of our knowledge, FANNG is the first MPC framework to offer actively secure MLaaS in the dishonest majority setting, specifically two parties. FANNG goes beyond SCALE-MAMBA by decoupling offline and online phases and materializing the dealer model in software, enabling a separate set of entities to produce offline material. The framework incorporates database support, a new instruction set for pre-processed material, including garbled circuits and convolutional and matrix multiplication triples. FANNG also implements novel private comparison protocols and an optimized library supporting Neural Network functionality. All our theoretical claims are substantiated by an extensive evaluation using an open-sourced implementation, including the private evaluation of popular neural networks like LeNet and VGG16.
Last updated:  2023-12-19
Regularized PolyKervNets: Optimizing Expressiveness and Efficiency for Private Inference in Deep Neural Networks
Toluwani Aremu
Private computation of nonlinear functions, such as Rectified Linear Units (ReLUs) and max-pooling operations, in deep neural networks (DNNs) poses significant challenges in terms of storage, bandwidth, and time consumption. To address these challenges, there has been a growing interest in utilizing privacy-preserving techniques that leverage polynomial activation functions and kernelized convolutions as alternatives to traditional ReLUs. However, these alternative approaches often suffer from a trade-off between achieving faster private inference (PI) and sacrificing model accuracy. In particular, when applied to much deeper networks, these methods encounter training instabilities, leading to issues like exploding gradients (resulting in NaNs) or suboptimal approximations. In this study, we focus on PolyKervNets, a technique known for offering improved dynamic approximations in smaller networks but still facing instabilities in larger and more complex networks. Our primary objective is to empirically explore optimization-based training recipes to enhance the performance of PolyKervNets in larger networks. By doing so, we aim to potentially eliminate the need for traditional nonlinear activation functions, thereby advancing the state-of-the-art in privacy-preserving deep neural network architectures.
Last updated:  2024-04-26
Sing a song of Simplex
Victor Shoup
We flesh out some details of the recently proposed Simplex atomic broadcast protocol, and modify it so that leaders disperse blocks in a more communication-efficient fashion. The resulting protocol, called DispersedSimplex, maintains the simplicity and excellent -- indeed, optimal -- latency characteristics of the original Simplex protocol. We also present several variations, including a variant that supports "stable leaders", variants that incorporate very recently developed data dissemination techniques that allow us to disperse blocks even more efficiently, and variants that are "signature free". We also suggest a number of practical optimizations and provide concrete performance estimates that take into account not just network latency but also network bandwidth limitations and computational costs. Based on these estimates, we argue that despite its simplicity, DispersedSimplex should, in principle, perform in practice as well as or better than any other state-of-the-art atomic broadcast protocol, at least in terms of common-case throughput and latency.
Last updated:  2024-04-26
Efficient Post-Quantum Secure Deterministic Threshold Wallets from Isogenies
Poulami Das, Andreas Erwig, Michael Meyer, and Patrick Struck
Cryptocurrency networks crucially rely on digital signature schemes, which are used as an authentication mechanism for transactions. Unfortunately, most major cryptocurrencies today, including Bitcoin and Ethereum, employ signature schemes that are susceptible to quantum adversaries, i.e., an adversary with access to a quantum computer can forge signatures and thereby spend coins of honest users. In cryptocurrency networks, signature schemes are typically not executed in isolation, but within a so-called cryptographic wallet. In order to achieve security against quantum adversaries, the signature scheme and the cryptographic wallet must withstand quantum attacks. In this work, we advance the study on post-quantum secure signature and wallet schemes. That is, we provide the first formal model for deterministic threshold wallets and we show a generic post-quantum secure construction from any post-quantum secure threshold signature scheme with rerandomizable keys. We then instantiate our construction from the isogeny-based signature scheme CSI-FiSh and we show that our instantiation significantly improves over prior work.
Last updated:  2023-12-13
Efficient Low-Latency Masking of Ascon without Fresh Randomness
Srinidhi Hari Prasad, Florian Mendel, Martin Schläffer, and Rishub Nagpal
In this work, we present the first low-latency, second-order masked hardware implementation of Ascon that requires no fresh randomness using only $d+1$ shares. Our results significantly outperform any publicly known second-order masked implementations of AES and Ascon in terms of combined area, latency and randomness requirements. Ascon is a family of lightweight authenticated encryption and hashing schemes selected by NIST for standardization. Ascon is tailored for small form factors. It requires less power and energy while attaining the same or even better performance than current NIST standards. We achieve the reduction of latency by rearranging the linear layers of the Ascon permutation in a round-based implementation. We provide an improved technique to achieve implementations without the need for fresh randomness. It is based on the concept of changing of the guards extended to the second-order case. Together with the reduction of latency, we need to consider a large set of additional conditions which we propose to solve using a SAT solver. We have formally verified both, our first- and second-order implementations of Ascon using CocoAlma for the first two rounds. Additionally, we have performed a leakage assessment using t-tests on all 12 rounds of the initial permutation. Finally, we provide a comparison of our second-order masked Ascon implementation with other results.
Last updated:  2023-12-13
Breaking RSA Authentication on Zynq-7000 SoC and Beyond: Identification of Critical Security Flaw in FSBL Software
Prasanna Ravi, Arpan Jati, and Shivam Bhasin
In this report, we perform an in-depth analysis of the RSA authentication feature used in the secure boot procedure of Xilinx Zynq-7000 SoC device. The First Stage Boot Loader (FSBL) is a critical piece of software executed during secure boot, which utilizes the RSA authentication feature to validate all the hardware and software partitions to be mounted on the device. We analyzed the implementation of FSBL (provided by Xilinx) for the Zynq-7000 SoC and identified a critical security flaw, whose exploitation makes it possible to load an unauthenticated application onto the Zynq device, thereby bypassing RSA authentication. We also experimentally validated the presence of the vulnerability through a Proof of Concept (PoC) attack to successfully mount an unauthenticated software application on an RSA authenticated Zynq device. The identified flaw is only present in the FSBL software and thus can be easily fixed through appropriate modification of the FSBL software. Thus, the first contribution of our work is the identification of a critical security flaw in the FSBL software to bypass RSA authentication. Upon bypassing RSA authentication, an attacker can mount any unauthenticated software application on the target device to mount a variety of attacks. Among the several possible attacks, we are interested to perform recovery of the encrypted bitstream in the target boot image of the Zynq-7000 device. To the best of our knowledge, there does not exist any prior work that has reported a practical bitstream recovery attack on the Zynq-7000 device. In the context of bitstream recovery, Ender et al. in 2020 proposed the Starbleed attack that is applicable to standalone Virtex-6 and 7-series Xilinx FPGAs. The design advisory provided by Xilinx as a response to the Starbleed attack claims that the Zynq-7000 SoC is resistant “due to the use of asymmetric and/or symmetric authentication in the boot/configuration process that ensures configuration is authenticated prior to use". Due to the security flaw found in the FSBL, we managed to identify a novel approach to mount the Starbleed attack on the Zynq-7000 device for full bitstream recovery. Thus, as a second contribution of our work, we present the first practical demonstration of the Starbleed attack on the Zynq-7000 SoC. We perform experimental validation of our proposed attacks on the PYNQ-Z1 platform based on the Zynq-7000 SoC.
Last updated:  2023-12-13
Dishonest Majority Multiparty Computation over Matrix Rings
Hongqing Liu, Chaoping Xing, Chen Yuan, and Taoxu Zou
The privacy-preserving machine learning (PPML) has gained growing importance over the last few years. One of the biggest challenges is to improve the efficiency of PPML so that the communication and computation costs of PPML are affordable for large machine learning models such as deep learning. As we know, linear algebra such as matrix multiplication occupies a significant part of the computation in the deep learning such as deep convolutional neural networks (CNN). Thus, it is desirable to propose the MPC protocol specialized for the matrix operations. In this work, we propose a dishonest majority MPC protocol over matrix rings which supports matrix multiplication and addition. Our MPC protocol can be seen as a variant of SPDZ protocol, i.e., the MAC and global key of our protocol are vectors of length $m$ and the secret of our protocol is an $m\times m$ matrix. Compared to the classic SPDZ protocol, our MPC protocol reduces the communication complexity by at least $m$ times. We also show that our MPC protocol is as efficient as [11] which also presented a dishonest majority MPC protocol specialized for matrix operations. The MPC protocol [11] resorts to the homomorphic encryption scheme (BFV scheme) to produce the matrix triples in the preprocessing phase. This implies that their protocol only supports the matrix operations over integer rings or prime fields of large size. On the contrary, we resort to vector oblivious linear evaluations and random vector oblivious linear evaluations to generate correlated randomness in the preprocessing phase. Thus, the matrices of our MPC protocol can be defined over any finite field or integer ring. Due to the small size of our MAC, the communication complexity of our MPC protocol remains almost the same regardless of the size of the field or the ring.
Last updated:  2023-12-13
Non-Interactive Classical Verification of Quantum Depth: A Fine-Grained Characterization
Nai-Hui Chia and Shih-Han Hung
We introduce protocols for classical verification of quantum depth (CVQD). These protocols enable a classical verifier to differentiate between devices of varying quantum circuit depths, even in the presence of classical computation. The goal is to demonstrate that a classical verifier can reject a device with a quantum circuit depth of no more than $d$, even if the prover employs additional polynomial-time classical computation to deceive. Conversely, the verifier accepts a device with a quantum circuit depth of $d'>d$. Previous results for separating hybrid quantum-classical computers with various quantum depths require either quantum access to oracles or interactions between the classical verifier and the quantum prover. However, instantiating oracle separations can significantly increase the quantum depth in general, and interaction challenges the quantum device to keep the qubits coherent while waiting for the verifier's messages. These requirements pose barriers to implementing the protocols on near-term devices. In this work, we present a two-message protocol under the quantum hardness of learning with errors and the random oracle heuristic. An honest prover only needs classical access to the random oracle, and therefore any instantiation of the oracle does not increase the quantum depth. To our knowledge, our protocol is the first non-interactive CVQD, the instantiation of which using concrete hash functions, e.g., SHA-3, does not require additional quantum depth. Our second protocol seeks to explore the minimality of cryptographic assumptions and the tightness of the separations. To accomplish this, we introduce an untrusted quantum machine that shares entanglements with the target machine. Utilizing a robust self-test, our protocol certifies the depth of the target machine with information-theoretic security and nearly optimal separation.
Last updated:  2024-06-07
Failed crypto: Matrices over non-standard arithmetic
Daniel R. L. Brown
A failed hypothesis is reported here. The hope was that large matrices over small non-standard arithmetic are likely to have infeasible division, and furthermore be secure for use in Rabi–Sherman associative cryptography.
Last updated:  2024-05-08
Ratel: MPC-extensions for Smart Contracts
Yunqi Li, Kyle Soska, Zhen Huang, Sylvain Bellemare, Mikerah Quintyne-Collins, Lun Wang, Xiaoyuan Liu, Dawn Song, and Andrew Miller
Enhancing privacy on smart contract-enabled blockchains has garnered much attention in recent research. Zero-knowledge proofs (ZKPs) is one of the most popular approaches, however, they fail to provide full expressiveness and fine-grained privacy. To illustrate this, we underscore an underexplored type of Miner Extractable Value (MEV), called Residual Bids Extractable Value (RBEV). Residual bids highlight the vulnerability where unfulfilled bids inadvertently reveal traders’ unmet demands and prospective trading strategies, thus exposing them to exploitation. ZKP-based approaches failed to ad- dress RBEV as they cannot provide post-execution privacy without some level of information disclosure. Other MEV mitigations like fair-ordering protocols also failed to address RBEV. We introduce Ratel, an innovative framework bridging a multi-party computation (MPC) prototyping framework (MP-SPDZ) and a smart contract language (Solidity), harmonizing the privacy with full expressiveness of MPC with Solidity ’s on-chain programmability. This synergy empowers developers to effortlessly craft privacy-preserving decentralized applications (DApps). We demonstrate Ratel’s efficacy through two distinguished decentralized finance (DeFi) applications: a decentralized exchange and a collateral auction, effectively mitigating the potential RBEV issue. Furthermore, Ratel is equipped with a lightweight crash-reset mechanism, enabling the seamless recovery of transiently benign faulty nodes. To prevent the crash-reset mechanism abused by malicious entities and ward off DoS attacks, we incorporate a cost-utility analysis anchored in the Bayesian approach. Our performance evaluation of the applications developed under the Ratel framework underscores their competency in managing real-world peak-time workloads.
Last updated:  2023-12-12
PARScoin: A Privacy-preserving, Auditable, and Regulation-friendly Stablecoin
Amirreza Sarencheh, Aggelos Kiayias, and Markulf Kohlweiss
Stablecoins are digital assets designed to maintain a consistent value relative to a reference point, serving as a vital component in Blockchain, and Decentralized Finance (DeFi) ecosystem. Typical implementations of stablecoins via smart contracts come with important downsides such as a questionable level of privacy, potentially high fees, and lack of scalability. We put forth a new design, PARScoin, for a Privacy-preserving, Auditable, and Regulation-friendly Stablecoin that mitigates these issues while enabling high performance both in terms of speed of settlement and for scaling to large numbers of users. Our construction is blockchain-agnostic and is analyzed in the Universal Composition (UC) framework, offering a secure and modular approach for its integration into the broader blockchain ecosystem.
Last updated:  2023-12-12
Integral Cryptanalysis Using Algebraic Transition Matrices
Tim Beyne and Michiel Verbauwhede
In this work we introduce algebraic transition matrices as the basis for a new approach to integral cryptanalysis that unifies monomial trails (Hu et al., Asiacrypt 2020) and parity sets (Boura and Canteaut, Crypto 2016). Algebraic transition matrices allow for the computation of the algebraic normal form of a primitive based on the algebraic normal forms of its components by means of well-understood operations from linear algebra. The theory of algebraic transition matrices leads to better insight into the relation between integral properties of $F$ and $F^{−1}$. In addition, we show that the link between invariants and eigenvectors of correlation matrices (Beyne, Asiacrypt 2018) carries over to algebraic transition matrices. Finally, algebraic transition matrices suggest a generalized definition of integral properties that subsumes previous notions such as extended division properties (Lambin, Derbez and Fouque, DCC 2020). On the practical side, a new algorithm is described to search for these generalized properties and applied to Present, resulting in new properties. The algorithm can be instantiated with any existing automated search method for integral cryptanalysis.
Last updated:  2023-12-12
Exploring SIDH-based Signature Parameters
Andrea Basso, Mingjie Chen, Tako Boris Fouotsa, Péter Kutas, Abel Laval, Laurane Marco, and Gustave Tchoffo Saah
Isogeny-based cryptography is an instance of post-quantum cryptography whose fundamental problem consists of finding an isogeny between two (isogenous) elliptic curves $E$ and $E'$. This problem is closely related to that of computing the endomorphism ring of an elliptic curve. Therefore, many isogeny-based protocols require the endomorphism ring of at least one of the curves involved to be unknown. In this paper, we explore the design of isogeny based protocols in a scenario where one assumes that the endomorphism ring of all the curves are public. In particular, we identify digital signatures based on proof of isogeny knowledge from SIDH squares as such a candidate. We explore the design choices for such constructions and propose two variants with practical instantiations. We analyze their security according to three lines, the first consists of attacks based on KLPT with both polynomial and superpolynomial adversary, the second consists of attacks derived from the SIDH attacks and finally we study the zero-knowledge property of the underlying proof of knowledge.
Last updated:  2023-12-13
Oops, I did it again revisited: another look at reusing one-time signatures
Scott Fluhrer
In "Oops, I did it again" - Security of One-Time Signatures under Two-Message Attacks, Bruinderink and Hülsing analyzed the effect of key reuse for several one time signature systems. When they analyzed the Winternitz system, they assumed certain probabilities were independent when they weren't, leading to invalid conclusions. This paper does a more correct characterization of the Winternitz scheme, and while their ultimate conclusion (that key reuse allows for practical forgeries) is correct, the situation is both better and worse than what they concluded.
Last updated:  2024-03-22
Generalized Kotov-Ushakov Attack on Tropical Stickel Protocol Based on Modified Tropical Circulant Matrices
Sulaiman Alhussaini, Craig Collett, and Serge˘ı Sergeev
After the Kotov-Ushakov attack on the tropical implementation of Stickel protocol, various attempts have been made to create a secure variant of such implementation. Some of these attempts used a special class of commuting matrices resembling tropical circulants, and they have been proposed with claims of resilience against the Kotov-Ushakov attack, and even being potential post-quantum candidates. This paper, however, reveals that a form of the Kotov-Ushakov attack remains applicable and, moreover, there is a heuristic implementation of that attack which has a polynomial time complexity and shows an overwhelmingly good success rate.
Last updated:  2024-05-16
Quarantined-TreeKEM: a Continuous Group Key Agreement for MLS, Secure in Presence of Inactive Users
Céline Chevalier, Guirec Lebrun, and Ange Martinelli
The recently standardized secure group messaging protocol “Messaging Layer Security” (MLS) is designed to ensure asynchronous communication within large groups, with an almost-optimal communication cost and the same security level as point-to-point secure messaging protocols such as “Signal”. In particular, the core sub-protocol of MLS, a Continuous Group Key Agreement (CGKA) called TreeKEM, must generate a common group key that respects the fundamental security properties of “post-compromise security” and “forward secrecy” which mitigate the effects of user corruption over time. Most research on CGKAs has focused on how to improve these two security properties. However, post-compromise security and forward secrecy require the active participation of respectively all compromised users and all users within the group. Inactive users – who remain offline for long periods – do not update anymore their encryption keys and therefore represent a vulnerability for the entire group. This issue has already been identified in the MLS standard, but no solution, other than expelling these inactive users after some disconnection time, has been found. We propose here a CGKA protocol based on TreeKEM and fully compatible with the MLS standard, that implements a “quarantine” mechanism for the inactive users in order to mitigate the risk induced by these users during their inactivity period and before they are removed from the group. That mechanism indeed updates the inactive users’ encryption keys on their behalf and secures these keys with a secret sharing scheme. If some of the inactive users eventually reconnect, their quarantine stops and they are able to recover all the messages that were exchanged during their offline period. Our “Quarantined-TreeKEM” protocol thus increases the security of original TreeKEM, with a very limited – and sometimes negative – communication overhead.
Last updated:  2023-12-11
A Transaction-Level Model for Blockchain Privacy
François-Xavier Wicht, Zhipeng Wang, Duc V. Le, and Christian Cachin
Considerable work explores blockchain privacy notions. Yet, it usually employs entirely different models and notations, complicating potential comparisons. In this work, we use the Transaction Directed Acyclic Graph (TDAG) and extend it to capture blockchain privacy notions (PDAG). We give consistent definitions for untraceability and unlinkability. Moreover, we specify conditions on a blockchain system to achieve each aforementioned privacy notion. Thus, we can compare the two most prominent privacy-preserving blockchains -- Monero and Zcash, in terms of privacy guarantees. Finally, we unify linking heuristics from the literature with our graph notation and review a good portion of research on blockchain privacy.
Last updated:  2023-12-11
Middle-Products of Skew Polynomials and Learning with Errors
Cong Ling and Andrew Mendelsohn
We extend the middle product to skew polynomials, which we use to define a skew middle-product Learning with Errors (LWE) variant. We also define a skew polynomial LWE problem, which we connect to Cyclic LWE (CLWE), a variant of LWE in cyclic division algebras. We then reduce a family of skew polynomial LWE problems to skew middle-product LWE, for a family which includes the structures found in CLWE. Finally, we give an encryption scheme and demonstrate its IND-CPA security, assuming the hardness of skew middle-product LWE.
Last updated:  2024-06-04
Conan: Distributed Proofs of Compliance for Anonymous Data Collection
Mingxun Zhou, Elaine Shi, and Giulia Fanti
We consider how to design an anonymous data collection protocol that enforces compliance rules. Imagine that each client contributes multiple data items (e.g., votes, location crumbs, or secret shares of its input) to an anonymous network, which mixes all clients' data items so that the receiver cannot determine which data items belong to the same user. Now, each user must prove to an auditor that the set it contributed satisfies a compliance predicate, without identifying which items it contributed. For example, the auditor may want to ensure that no one voted for the same candidate twice, or that a user's location crumbs are not too far apart in a given time interval. Our main contribution is a novel anonymous, compliant data collection protocol that realizes the above goal. In comparison with naive approaches such as generic multi-party computation or earlier constructions of collaborative zero-knowledge proofs, the most compelling advantage of our approach is that each client's communication and computation overhead do not grow with respect to the number of clients $n$. In this sense, we save a factor of at least $n$ over prior work, which allows our technique to scale to applications with a large number of clients, such as anonymous voting and privacy-preserving federated learning. We first describe our protocol using generic cryptographic primitives that can be realized from standard assumptions. We then suggest a concrete instantiation called {\sc Conan} which we implement and evaluate. In this concrete instantiation, we are willing to employ SNARKs and the random oracle model for better practical efficiency. Notably, in this practical instantiation, each client's additional communication overhead (not counting the overhead of sending its data items over the anonymous network) is only $\widetilde{O}(1)$. We evaluated our technique in various application settings, including secure voting, and secure aggregation protocols for histogram, summation, and vector summation. Our evaluation results show that each client's additional communication overhead is only 2.2KB or 2.6KB, depending on which SNARK implementation we use. Further, each client's computation is only 0.2s - 0.5s for almost all cases, except for the vector summation application where the data items are high-dimensional and each client's computation is 8.5-10.6s.
Last updated:  2023-12-10
Allowing Blockchain Loans with Low Collateral
Tom Azoulay, Uri Carl, and Ori Rottenstreich
Collateral is an item of value serving as security for the repayment of a loan. In blockchain-based loans, cryptocurrencies serve as the collateral. The high volatility of cryptocurrencies implies a serious barrier of entry with a common practice that collateral values equal multiple times the value of the loan. As assets serving as collateral are locked, this requirement prevents many candidates from obtaining loans. In this paper, we aim to make loans more accessible by offering loans with lower collateral, while keeping the risk for lenders bound. We propose a credit score based on data recovered from the blockchain to predict how likely a potential borrower is to repay a loan. Our protocol does not risk the initial amount granted by liquidity providers, but only risks part of the interest yield gained from the borrower by the protocol in the past.
Last updated:  2023-12-10
An Empirical Study of Cross-chain Arbitrage in Decentralized Exchanges
Ori Mazor and Ori Rottenstreich
Blockchain interoperability refers to the ability of blockchains to share information with each other. Decentralized Exchanges (DEXs) are peer-to-peer marketplaces where traders can exchange cryptocurrencies. Several studies have focused on arbitrage analysis within a single blockchain, typically in Ethereum. Recently, we have seen a growing interest in cross-chain technologies to create a more interconnected blockchain network. We present a framework to study cross-chain arbitrage in DEXs. We use this framework to analyze cross-chain arbitrages between two popular DEXs, PancakeSwap and QuickSwap, within a time frame of a month. While PancakeSwap is implemented on a blockchain named BNB Chain, QuickSwap is implemented on a different blockchain named Polygon. The approach of this work is to study the cross-chain arbitrage through an empirical study. We refer to the number of arbitrages, their revenue as well as to their duration. This work lays the basis for understanding cross-chain arbitrage and its potential impact on the blockchain technology.
Last updated:  2024-03-07
PRAC: Round-Efficient 3-Party MPC for Dynamic Data Structures
Sajin Sasy, Adithya Vadapalli, and Ian Goldberg
We present Private Random Access Computations (PRAC), a 3-party Secure Multi-Party Computation (MPC) framework to support random-access data structure algorithms for MPC with efficient communication in terms of rounds and bandwidth. PRAC extends the state-of-the-art DORAM Duoram with a new implementation, more flexibility in how the DORAM memory is shared, and support for Incremental and Wide DPFs. We then use these DPF extensions to achieve algorithmic improvements in three novel oblivious data structure protocols for MPC. PRAC exploits the observation that a secure protocol for an algorithm can gain efficiency if the protocol explicitly reveals information leaked by the algorithm inherently. We first present an optimized binary search protocol that reduces the bandwidth from $O(\lg^2 n)$ to $O(\lg n)$ for obliviously searching over $n$ items. We then present an oblivious heap protocol with rounds reduced from $O(\lg n)$ to $O(\lg \lg n)$ for insertions, and bandwidth reduced from $O(\lg^2 n)$ to $O(\lg n)$ for extractions. Finally, we also present the first oblivious AVL tree protocol for MPC where no party learns the data or the structure of the AVL tree, and can support arbitrary insertions and deletions with $O(\lg n)$ rounds and bandwidth. We experimentally evaluate our protocols with realistic network settings for a wide range of memory sizes to demonstrate their efficiency. For instance, we observe our binary search protocol provides $>27\times$ and $>3\times$ improvements in wall-clock time and bandwidth respectively over other approaches for a memory with $2^{26}$ items; for the same setting our heap's extract-min protocol achieves $>31\times$ speedup in wall-clock time and $>13\times$ reduction in bandwidth.
Last updated:  2023-12-10
Selective Delegation of Attributes in Mercurial Signature Credentials
Colin Putman and Keith M. Martin
Anonymous credential schemes enable service providers to verify information that a credential holder willingly discloses, without needing any further personal data to corroborate that information, and without allowing the user to be tracked from one interaction to the next. Mercurial signatures are a novel class of anonymous credentials which show good promise as a simple and efficient construction without heavy reliance on zero-knowledge proofs. However, they still require significant development in order to achieve the functionality that most existing anonymous credential schemes provide. Encoding multiple attributes of the credential holder in such a way that they can be disclosed selectively with each use of the credential is often seen as a vital feature of anonymous credentials, and is one that mercurial signatures have not yet implemented. In this paper, we show a simple way to encode attributes in a mercurial signature credential and to regulate which attributes a credential holder can issue when delegating their credential to another user. We also extend the security model associated with mercurial signatures to account for the inclusion of attributes, and prove the security of our extension with respect to the original mercurial signature construction.
Last updated:  2023-12-09
The Patching Landscape of Elisabeth-4 and the Mixed Filter Permutator Paradigm
Clément Hoffmann, Pierrick Méaux, and François-Xavier Standaert
Filter permutators are a family of stream cipher designs that are aimed for hybrid homomorphic encryption. While originally operating on bits, they have been generalized to groups at Asiacrypt 2022, and instantiated for evaluation with the TFHE scheme which favors a filter based on (negacyclic) Look Up Tables (LUTs). A recent work of Gilbert et al., to appear at Asiacrypt 2023, exhibited (algebraic) weaknesses in the Elisabeth-4 instance, exploiting the combination of the 4-bit negacyclic LUTs it uses as filter. In this article, we explore the landscape of patches that can be used to restore the security of such designs while maintaining their good properties for hybrid homomorphic encryption. Starting with minimum changes, we observe that just updating the filter function (still with small negacyclic LUTs) is conceptually feasible, and propose the resulting Elisabeth-b4 design with three levels of NLUTs. We then show that a group permutator combining two different functions in the filter can simplify the analysis and improve performances. We specify the Gabriel instance to illustrate this claim. We finally propose to modify the group filter permutator paradigm into a mixed filter permutator, which considers the permutation of the key with elements in a group and a filter outputting elements in a different group. We specify the Margrethe instance as a first example of mixed filter permutator, with key elements in $\mathbb{F}_2$ and output in $\mathbb{Z}_{16}$, that we believe well-suited for recent fully homomorphic encryption schemes that can efficiently evaluate larger (not negacyclic) LUTs.
Last updated:  2024-05-12
Hardness of Range Avoidance and Remote Point for Restricted Circuits via Cryptography
Yilei Chen and Jiatu Li
A recent line of research has introduced a systematic approach to explore the complexity of explicit construction problems through the use of meta problems, namely, the range avoidance problem (abbrev. $\textsf{Avoid}$) and the remote point problem (abbrev. $\textsf{RPP}$). The upper and lower bounds for these meta problems provide a unified perspective on the complexity of specific explicit construction problems that were previously studied independently. An interesting question largely unaddressed by previous works is whether $\textsf{Avoid}$ and $\textsf{RPP}$ are hard for simple circuits such as low-depth circuits. In this paper, we demonstrate, under plausible cryptographic assumptions, that both the range avoidance problem and the remote point problem cannot be efficiently solved by nondeterministic search algorithms, even when the input circuits are as simple as constant-depth circuits. This extends a hardness result established by Ilango, Li, and Williams (STOC '23) against deterministic algorithms employing witness encryption for $\textsf{NP}$, where the inputs to $\textsf{Avoid}$ are general Boolean circuits. Our primary technical contribution is a novel construction of witness encryption inspired by public-key encryption for certain promise language in $\textsf{NP}$ that is unlikely to be $\textsf{NP}$-complete. We introduce a generic approach to transform a public-key encryption scheme with particular properties into a witness encryption scheme for a promise language related to the initial public-key encryption scheme. Based on this translation and variants of standard lattice-based or coding-based PKE schemes, we obtain, under plausible assumption, a provably secure witness encryption scheme for some promise language in $\textsf{NP}\setminus \textsf{coNP}_{/\textsf{poly}}$. Additionally, we show that our constructions of witness encryption are plausibly secure against nondeterministic adversaries under a generalized notion of security in the spirit of Rudich's super-bits (RANDOM '97), which is crucial for demonstrating the hardness of $\textsf{Avoid}$ and $\textsf{RPP}$ against nondeterministic algorithms.
Last updated:  2024-05-11
BOLT: Privacy-Preserving, Accurate and Efficient Inference for Transformers
Qi Pang, Jinhao Zhu, Helen Möllering, Wenting Zheng, and Thomas Schneider
The advent of transformers has brought about significant advancements in traditional machine learning tasks. However, their pervasive deployment has raised concerns about the potential leakage of sensitive information during inference. Existing approaches using secure multiparty computation (MPC) face limitations when applied to transformers due to the extensive model size and resource-intensive matrix-matrix multiplications. In this paper, we present BOLT, a privacy-preserving inference framework for transformer models that supports efficient matrix multiplications and nonlinear computations. Combined with our novel machine learning optimizations, BOLT reduces the communication cost by 10.91x. Our evaluation on diverse datasets demonstrates that BOLT maintains comparable accuracy to floating-point models and achieves 4.8-9.5x faster inference across various network settings compared to the state-of-the-art system.
Last updated:  2023-12-08
Asymptotics of hybrid primal lattice attacks
Daniel J. Bernstein
The literature gives the impression that (1) existing heuristics accurately predict how effective lattice attacks are, (2) non-ternary lattice systems are not vulnerable to hybrid multi-decoding primal attacks, and (3) the asymptotic exponents of attacks against non-ternary systems have stabilized. This paper shows that 1 contradicts 2 and that 1 contradicts 3: the existing heuristics imply that hybrid primal key-recovery attacks are exponentially faster than standard non-hybrid primal key-recovery attacks against the LPR PKE with any constant error width. This is the first report since 2015 of an exponential speedup in heuristic non-quantum primal attacks against non-ternary LPR. Quantitatively, for dimension n, modulus n^{Q_0+o(1)}, and error width w, a surprisingly simple hybrid attack reduces heuristic costs from 2^{(ρ+o(1))n} to 2^{(ρ-ρ H_0+o(1))n}, where z_0=2Q_0/(Q_0+1/2)^2, ρ=z_0 log_4(3/2), and H_0=1/(1+(lg w)/0.057981z_0). This raises the questions of (1) what heuristic exponent is achieved by more sophisticated hybrid attacks and (2) what impact hybrid attacks have upon concrete cryptosystems whose security analyses have ignored hybrid attacks, such as Kyber-512.
Last updated:  2023-12-08
In-depth Correlation Power Analysis Attacks on a Hardware Implementation of CRYSTALS-Dilithium
Huaxin Wang, Yiwen Gao, Yuejun Liu, Qian Zhang, and Yongbin Zhou
During the standardisation process of post-quantum cryptography, NIST encourages research on side-channel analysis for candidate schemes. As the recommended lattice signature scheme, CRYSTALS-Dilithium, when implemented on hardware, has only been subjected to the side-channel attack presented by Steffen et al. in IACR ePrint 2022. This attack is not complete and requires excessive traces. Therefore, we investigate the leakage of an FPGA (Kintex7) implementation of CRYSTALS-Dilithium using the CPA method, where with a minimum of 70000 traces partial private key coefficients can be recovered. As far as we know, this is the first work that applies power leakage to sidechannel attacks on FPGA implementations of CRYSTALS-Dilithium. Furthermore, we optimise the attack by extracting Point-of-Interests using known information due to parallelism (named CPA-PoI) and by iteratively utilising parallel leakages (named CPA-ITR). We experimentally demonstrate that when recovering the same number of key coefficients, the CPA-PoI and CPA-ITR reduce the number of traces used by up to 16.67 percent and 25 percent, respectively, compared to the CPA method. When attacking with the same number of traces, the CPA-PoI method and the CPA-ITR method increase the number of recovered key coefficients by up to 55.17 percent and 93.10 percent, respectively, compared to the CPA method. Our experiments confirm that the FPGA implementation of CRYSTALS-Dilithium is also very vulnerable to side-channel analysis.
Last updated:  2024-05-29
Aegis: A Lightning Fast Privacy-preserving Machine Learning Platform against Malicious Adversaries
Tianpei Lu, Bingsheng Zhang, Lichun Li, and Kui Ren
Privacy-preserving machine learning (PPML) techniques have gained significant popularity in the past years. Those protocols have been widely adopted in many real-world security-sensitive machine learning scenarios, e.g., medical care and finance. In this work, we introduce $\mathsf{Aegis}$~-- a high-performance PPML platform built on top of a maliciously secure 3-PC framework over ring $\mathbb{Z}_{2^\ell}$. In particular, we propose a novel 2-round secure comparison (a.k.a., sign bit extraction) protocol in the preprocessing model. The communication of its semi-honest version is only 25% of the state-of-the-art (SOTA) constant-round semi-honest comparison protocol by Zhou et al. (S&P 2023); communication and round complexity of its malicious version are approximately 25% and 50% of the SOTA (BLAZE) by Patra and Suresh (NDSS 2020), for $\ell=64$. Moreover, the overall communication of our maliciously secure inner product protocol is merely $3\ell$ bits, reducing 50% from the SOTA (Swift) by Koti et al. (USENIX 2021). Finally, the resulting ReLU and MaxPool PPML protocols outperform the SOTA constructions by $4\times$ in the semi-honest setting and $100\times$ in the malicious setting, respectively.
Last updated:  2023-12-21
Fully Parallel, One-Cycle Random Shuffling for Efficient Countermeasure in Post-Quantum Cryptography
Jong-Yeon Park, Dongsoo Lee, Seonggyeom Kim, Wonil lee, Bo Gyeong Kang, and Kouichi Sakurai
Hiding countermeasures are the most widely utilized techniques for thwarting side-channel attacks, and their significance has been further emphasized with the advent of Post Quantum Cryptography (PQC) algorithms, owing to the extensive use of vector operations. Commonly, the Fisher-Yates algorithm is adopted in hiding countermeasures with permuted operation for its security and efficiency in implementation, yet the inherently sequential nature of the algorithm imposes limitations on hardware acceleration. In this work, we propose a novel method named Addition Round Rotation ARR, which can introduce a time-area trade-off with block-based permutation. Our findings indicate that this approach can achieve a permutation complexity level commensurate with or exceeding $2^{128}$ in a single clock cycle while maintaining substantial resistance against second-order analysis. To substantiate the security of our proposed method, we introduce a new validation technique --Identity Verification. This technique allows theoretical validation of the proposed algorithm's security and is consistent with the experimental results. Finally, we introduce an actual hardware design and provide the implementation results on Application-Specific Integrated Circuit (ASIC). The measured performance demonstrates that our proposal fully supports the practical applicability.
Last updated:  2023-12-08
Reverie: an end-to-end accumulation scheme from Cyclefold
Lev Soukhanov
Recent advances in SNARK recursion and incrementally-verifiable computation are vast, but most of the efforts seem to be focused on a particular design goal - proving the result of a large computation known completely in advance. There are other possible applications, requiring different design tradeoffs. Particularly interesting direction is a case with a swarm of collaborating provers, communicating over a peer-to-peer network - which requires to also optimize the amount of data exchanged between the participants of the swarm. One notable such application is Ethereum's consensus, which requires to aggregate millions of signatures of individual validators. In this technical note, we propose an informal notion of an end-to-end IVC scheme, which means that the amount of data that the prover needs exchange with the previous prover to continue the computation is small. We explore the existing design space from this point of view, and suggest an approach to constructing such a scheme by combining the PlonK proof systemwith the recent Cyclefold construction.
Last updated:  2023-12-17
GRandLine: Adaptively Secure DKG and Randomness Beacon with (Almost) Quadratic Communication Complexity
Renas Bacho, Christoph Lenzen, Julian Loss, Simon Ochsenreither, and Dimitrios Papachristoudis
A randomness beacon is a source of continuous and publicly verifiable randomness which is of crucial importance for many applications. Existing works on distributed randomness beacons suffer from at least one of the following drawbacks: (i) security only against a static/non-adaptive adversary, (ii) each epoch takes many rounds of communication, or (iii) computationally expensive tools such as Proof-of-Work (PoW) or Verifiable Delay Functions (VDF). In this paper, we introduce $\mathsf{GRandLine}$, the first adaptively secure randomness beacon protocol that overcomes all these limitations while preserving simplicity and optimal resilience in the synchronous network setting. We achieve our result in two steps. First, we design a novel distributed key generation (DKG) protocol $\mathsf{GRand}$ that runs in $\mathcal{O}(\lambda n^2\log{n})$ bits of communication but, unlike most conventional DKG protocols, outputs both secret and public keys as group elements. Here, $\lambda$ denotes the security parameter. Second, following termination of $\mathsf{GRand}$, parties can use their keys to derive a sequence of randomness beacon values, where each random value costs only a single asynchronous round and $\mathcal{O}(\lambda n^2)$ bits of communication. We implement $\mathsf{GRandLine}$ and evaluate it using a network of up to 64 parties running in geographically distributed AWS instances. Our evaluation shows that $\mathsf{GRandLine}$ can produce about 2 beacon outputs per second in a network of 64 parties. We compare our protocol to the state-of-the-art randomness beacon protocols in the same setting and observe that it vastly outperforms them.
Last updated:  2024-03-22
Reef: Fast Succinct Non-Interactive Zero-Knowledge Regex Proofs
Sebastian Angel, Eleftherios Ioannidis, Elizabeth Margolin, Srinath Setty, and Jess Woods
This paper presents Reef, a system for generating publicly verifiable succinct non-interactive zero-knowledge proofs that a committed document matches or does not match a regular expression. We describe applications such as proving the strength of passwords, the provenance of email despite redactions, the validity of oblivious DNS queries, and the existence of mutations in DNA. Reef supports the Perl Compatible Regular Expression syntax, including wildcards, alternation, ranges, capture groups, Kleene star, negations, and lookarounds. Reef introduces a new type of automata, Skipping Alternating Finite Automata (SAFA), that skips irrelevant parts of a document when producing proofs without undermining soundness, and instantiates SAFA with a lookup argument. Our experimental evaluation confirms that Reef can generate proofs for documents with 32M characters; the proofs are small and cheap to verify (under a second).
Last updated:  2023-12-21
Falcon Takes Off - A Hardware Implementation of the Falcon Signature Scheme
Michael Schmid, Dorian Amiet, Jan Wendler, Paul Zbinden, and Tao Wei
Falcon is one out of three post-quantum signature schemes which have been selected for standardization by NIST in July 2022. To the best of our knowledge, Falcon is the only selected algorithm that does not yet have a publicly reported hardware description that performs signing or key generation. The reason might be that the Falcon signature and key generation algorithms do not fit well in hardware due to the use of floating-point numbers and recursive functions. This publication describes the first hardware implementation for Falcon signing and key generation. To overcome the complexity of the Falcon algorithms, High-Level Synthesis (HLS) was preferred over a hardware description language like Verilog or VHDL. Our HLS code is based on the C reference implementation available at NIST. We describe the required modifications in order to be compliant with HLS, such as rewriting recursive functions into iterative versions. The hardware core at security level 5 requires 45,223 LUTs, 41,370 FFs, 182 DSPs, and 37 BRAMs to calculate one signature in 8.7 ms on a Zynq UltraScale+ FPGA. Security level 5 key generation takes 320.3 ms and requires 100,649 LUTs, 91,029 FFs, 1,215 DSPs, and 69 BRAMs.
Last updated:  2023-12-07
Multi-Signatures for Ad-hoc and Privacy-Preserving Group Signing
Anja Lehmann and Cavit Özbay
Multi-signatures allow to combine individual signatures from different signers on the same message into a short aggregated signature. Newer schemes further allow to aggregate the individual public keys, such that the combined signature gets verified against a short aggregated key. This makes them a versatile alternative to threshold or distributed signatures: the aggregated key can serve as group key, and signatures under that key can only be computed with the help of all signers. What makes multi-signatures even more attractive is their simple key management, as users can re-use the same secret key in several and ad-hoc formed groups. In that context, it will be desirable to not sacrifice privacy as soon as keys get re-used and ensure that users are not linkable across groups. In fact, when multi-signatures with key aggregation were proposed, it was claimed that aggregated keys hide the signers' identities or even the fact that it is a combined key at all. In our work, we show that none of the existing multi-signature schemes provide these privacy guarantees when keys get re-used in multiple groups. This is due to the fact that all known schemes deploy deterministic key aggregation. To overcome this limitation, we propose a new variant of multi-signatures with probabilistic yet verifiable key aggregation. We formally define the desirable privacy and unforgeability properties in the presence of key re-use. This also requires to adapt the unforgeability model to the group setting, and ensure that key-reuse does not weaken the expected guarantees. We present a simple BLS-based scheme that securely realizes our strong privacy and security guarantees. We also formalize and investigate the privacy that is possible by deterministic schemes, and prove that existing schemes provide the advertised privacy features as long as one public key remains secret.
Last updated:  2023-12-07
The statistical nature of leakage in SSE schemes and its role in passive attacks
Marc Damie, Jean-Benoist Leger, Florian Hahn, and Andreas Peter
Encrypted search schemes have been proposed to address growing privacy concerns. However, several leakage-abuse attacks have highlighted the shortcomings of these schemes. The literature remains vague about the consequences of these attacks for real-world applications: are these attacks dangerous in practice? Is it safe to use these schemes? Do we even need countermeasures? This paper introduces a novel mathematical model for attackers' knowledge using statistical estimators. Our model reveals that any attacker's knowledge is inherently noisy, which limits attack effectiveness. This inherent noise can be considered a security guarantee, a natural attack mitigation. Capitalizing on this insight, we develop a risk assessment protocol to guide real-world deployments. Our findings demonstrate that limiting the index size is an efficient leverage to bound attack accuracy. Finally, we employ similar statistical methods to enhance attack analysis methodology. Hence, our work offers a fresh perspective on SSE attacks and provides practitioners and researchers with novel methodological tools.
Last updated:  2024-02-13
Lattice Based Signatures with Additional Functionalities
Swati Rawal, Sahadeo Padhye, and Debiao He
Digital signatures is a cryptographic protocol that can provide the added assurances of identity, status, proof of origin of an electronic document, and can acknowledge informed consent by the signer. Lattice based assumptions have seen a certain rush in recent years to fulfil the desire to expand the hardness assumption beyond factoring or discrete logarithm problem on which digital signatures can rely. In this article, we cover the recent progress made in digital signatures based on lattice assumptions. The article briefly discusses the working of each signature scheme, then investigates the progress made in recent years and compare them with different aspects of security and efficiency. Besides, it provides some future direction which can be helpful in future work in this area.
Last updated:  2023-12-07
Blockchain Governance via Sharp Anonymous Multisignatures
Wonseok Choi, Xiangyu Liu, and Vassilis Zikas
Electronic voting has occupied a large part of the cryptographic protocols literature. The recent reality of blockchains---in particular their need for online governance mechanisms---has put new parameters and requirements to the problem. We identify the key requirements of a blockchain governance mechanism, namely correctness (including eliminative double votes), voter anonymity, and traceability, and investigate mechanisms that can achieve them with minimal interaction and under assumptions that fit the blockchain setting. First, we define a signature-like primitive, which we term sharp anonymous multisignatures (in short, #AMS) that tightly meets the needs of blockchain governance. In a nutshell, #AMSs allow any set of parties to generate a signature, e.g., on a proposal to be voted-upon, which if posted on the blockchain hides the identities of the signers/voters, but reveals their number. This can be seen as a (strict) generalization of threshold ring signatures (TRS). We next turn to constructing such #AMSs and using them in various governance scenarios---e.g., single vs. multiple vote per voter. To this direction, we observe that although the definition of TRS does not imply #AMS, one can compile some of the existing TRS constructions into #AMS. This raises the question: What is the TRS structure that allows such a compilation? To answer the above, we devise templates for TRSs. Our templates encapsulate and abstract the structure that allows for the above compilation---most of the TRS schemes that can be compiled into #AMS are, in fact, instantiations of our template. This abstraction makes our template generic for instantiating TRSs and #AMSs from different cryptographic assumptions (e.g., DDH, LWE, etc). One of our templates is based on chameleon hashing and we explore a framework of lossy chameleon hashes to fully understand its nature. Finally, we turn to how #AMS schemes can be used in our applications. We provide fast (in some cases non-interactive) #AMS-based blockchain governance mechanisms for a wide spectrum of assumptions on the honesty (semi-honest vs malicious) and availability of voters and proposers.
Last updated:  2024-06-07
Cryptanalysis of Lattice-Based Sequentiality Assumptions and Proofs of Sequential Work
Chris Peikert and Yi Tang
This work *completely breaks* the sequentiality assumption (and broad generalizations thereof) underlying the candidate lattice-based proof of sequential work (PoSW) recently proposed by Lai and Malavolta at CRYPTO 2023. In addition, it breaks an essentially identical variant of the PoSW, which differs from the original in only an arbitrary choice that is immaterial to the design and security proof (under the falsified assumption). This suggests that whatever security the original PoSW may have is fragile, and further motivates the search for a construction based on a sound lattice-based assumption. Specifically, for sequentiality parameter $T$ and SIS parameters $n,q,m = n \log q$, the attack on the sequentiality assumption finds a solution of quasipolynomial norm $m^{\lceil \log T \rceil}$ (or norm $O(\sqrt{m})^{\lceil \log T \rceil}$ with high probability) in only *logarithmic* $\tilde{O}_{n,q}(\log T)$ depth; this strongly falsifies the assumption that finding such a solution requires depth *linear* in $T$. (The $\tilde{O}$ notation hides polylogarithmic factors in the variables appearing in its subscript.) Alternatively, the attack finds a solution of polynomial norm $m^{1/\varepsilon}$ in depth $\tilde{O}_{n,q}(T^{\varepsilon})$, for any constant $\varepsilon > 0$. Similarly, the attack on the (slightly modified) PoSW constructs a valid proof in \emph{polylogarithmic} $\tilde{O}_{n,q}(\log^2 T)$ depth, thus strongly falsifying the expectation that doing so requires linear sequential work.
Last updated:  2023-12-06
A Multiparty Commutative Hashing Protocol based on the Discrete Logarithm Problem
Daniel Zentai, Mihail Plesa, and Robin Frot
Let $\mathcal{X}$ and $\mathcal{Y}$ be two sets and suppose that a set of participants $P=\{P_1,P_2,\dots,P_n\}$ would like to calculate the keyed hash value of some message $m\in\mathcal{X}$ known to a single participant in $P$ called the data owner. Also, suppose that each participant $P_i$ knows a secret value $x_i\in\mathcal{X}$. In this paper, we will propose a protocol that enables the participants in this setup to calculate the value $y=H(m,x_1,x_2,\dots ,x_n)$ of a hash function $H:\mathcal{X}^{n+1}\rightarrow\mathcal{Y}$ such that: - The function $H$ is a one-way function. - Participants in $P\backslash\{P_i\}$ cannot obtain $x_i$. - Participants other than the data owner cannot obtain $m$. - The hash value $y=H(m,x_1,x_2,\dots ,x_n)$ remains the same regardless the order of the secret $x_i$ values.
Last updated:  2024-03-27
Predicting performance for post-quantum encrypted-file systems
Daniel J. Bernstein
Public-key cryptography is widely deployed for encrypting stored files. This paper uses microbenchmarks and purchase costs to predict the performance of various post-quantum KEMs in this application. In particular, this paper concludes that Classic McEliece is (1) the most efficient option and (2) easily affordable. As a quantitative example, the estimated five-year per-user cost of mceliece6960119f is 0.00024 dollars if 100000 files are encrypted and stored for an average user during those five years and each file is decrypted twice on average.
Last updated:  2023-12-06
Security Analysis of an Image Encryption Scheme Based on a New Secure Variant of Hill Cipher and 1D Chaotic Maps
George Teseleanu
In 2019, Essaid et al. introduced a chaotic map-based encryption scheme for color images. Their approach employs three improved chaotic maps to dynamically generate the key bytes and matrix required by the cryptosystem. It should be noted that these parameters are dependent on the size of the source image. According to the authors, their method offers adequate security (i.e. $279$ bits) for transmitting color images over unsecured channels. However, we show in this paper that this is not the case. Specifically, we present two cryptanalytic attacks that undermine the security of Essaid et al.'s encryption scheme. In the case of the chosen plaintext attack, we require only two chosen plaintexts to completely break the scheme. The second attack is a a chosen ciphertext attack, which requires two chosen ciphertexts and compared to the first one has a rough complexity of $2^{24}$. The attacks are feasible due to the fact that the key bits and matrix generated by the algorithm remain unaltered for distinct plaintext images.
Last updated:  2024-05-20
Thwarting Last-Minute Voter Coercion
Rosario Giustolisi, Maryam Sheikhi Garjan, and Carsten Schuermann
Counter-strategies are key components of coercion-resistant voting schemes, allowing voters to submit votes that represent their own intentions in an environment controlled by a coercer. By deploying a counter-strategy a voter can prevent the coercer from learning if the voter followed the coercer’s instructions or not. Two effective counter-strategies have been proposed in the literature, one based on fake credentials and another on revoting. While fake-credential schemes assume that voters hide cryptographic keys away from the coercer, revoting schemes assume that voters can revote after being coerced. In this work, we present a new counter-strategy technique that enables flexible vote updating, that is, a revoting approach that provides protection against coercion even if the adversary is able to coerce a voter at the very last minute of the voting phase. We demonstrate that our technique is effective by implementing it in Loki, an Internet-based coercion-resistant voting scheme that allows revoting. We prove that Loki satisfies a game-based definition of coercion-resistance that accounts for flexible vote updating. To the best of our knowledge, we provide the first technique that enables deniable coercion- resistant voting and that can evade last-minute voter coercion.
Last updated:  2023-12-07
The Blockwise Rank Syndrome Learning problem and its applications to cryptography
Nicolas Aragon, Pierre Briaud, Victor Dyseryn, Philippe Gaborit, and Adrien Vinçotte
Recently the notion of blockwise error in a context of rank based cryptography has been introduced by Sont et al. at AsiaCrypt 2023 . This notion of error, very close to the notion sum-rank metric, permits, by decreasing the weight of the decoded error, to greatly improve parameters for the LRPC and RQC cryptographic schemes. A little before the multi-syndromes approach introduced for LRPC and RQC schemes had also allowed to considerably decrease parameters sizes for LRPC and RQC schemes, through in particular the introduction of Augmented Gabidulin codes. In the present paper we show that the two previous approaches (blockwise errors and multi-syndromes) can be combined in a unique approach which leads to very efficient generalized RQC and LRPC schemes. In order to do so, we introduce a new problem, the Blockwise Rank Support Learning problem, which consists of guessing the support of the errors when several syndromes are given in input, with blockwise structured errors. The new schemes we introduce have very interesting features since for 128 bits security they permit to obtain generalized schemes for which the sum of public key and ciphertext is only 1.4 kB for the generalized RQC scheme and 1.7 kB for the generalized LRPC scheme. The new approach proposed in this paper permits to reach a 40 % gain in terms of parameters size when compared to previous results, obtaining even better results in terms of size than for the KYBER scheme whose total sum is 1.5 kB. Besides the description of theses new schemes the paper provides new attacks for the l-RD problem introduced in the paper by Song et al. of AsiaCrypt 2023, in particular these new attacks permit to cryptanalyze all blockwise LRPC parameters they proposed (with an improvement of more than 40bits in the case of structural attacks). We also describe combinatorial attacks and algebraic attacks, for the new Blockwise Rank Support Learning problem we introduce.
Last updated:  2024-06-03
Security Analysis of an Image Encryption Based on the Kronecker Xor Product, the Hill Cipher and the Sigmoid Logistic Map
George Teseleanu
In 2023, Mfungo et al. introduce an image encryption scheme that employs the Kronecker xor product, the Hill cipher and a chaotic map. Their proposal uses the chaotic map to dynamically generate two out of the three secret keys employed by their scheme. Note that both keys are dependent on the size of the original image, while the Hill key is static. Despite the authors' assertion that their proposal offers sufficient security ($149$ bits) for transmitting color images over unsecured channels, we found that this is not accurate. To support our claim, we present a chosen plaintext attack that requires $2$ oracle queries and has a worse case complexity of $\mathcal O(2^{32})$. Note that in this case Mfungo et al.'s scheme has a complexity of $\mathcal O(2^{33})$, and thus our attack is two times faster than an encryption. The reason why this attack is viable is that the two keys remain unchanged for different plaintext images of the same size, while the Hill key remains unaltered for all images.
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