During the past decade, Deep Neural Networks (DNNs) proved their value on a large variety of subjects. However despite their high value and public accessibility, the protection of the intellectual property of DNNs is still an issue and an emerging research field. Recent works have successfully extracted fully-connected DNNs using cryptanalytic methods in hard-label settings, proving that it was possible to copy a DNN with high fidelity, i.e., high similitude in the output predictions....

The circulant twin column parity mixer (TCPM) is a type of mixing layer for the round function of cryptographic permutations designed by Hirch et al. at CRYPTO 2023. It has a bitwise differential branch number of 12 and a bitwise linear branch number of 4, which makes it competitive in applications where differential security is required. Hirch et al. gave a concrete instantiation of a permutation using such a mixing layer, named Gaston, and showed the best 3-round differential and linear...

This paper reveals a critical flaw in the design of ARADI, a recently proposed low-latency block cipher by NSA researchers -- Patricia Greene, Mark Motley, and Bryan Weeks. The weakness exploits the specific composition of Toffoli gates in the round function of ARADI's nonlinear layer, and it allows the extension of a given algebraic distinguisher to one extra round without any change in the data complexity. More precisely, we show that the cube-sum values, though depending on the secret key...

Privacy-Preserving Machine Learning is one of the most relevant use cases for Secure Multiparty Computation (MPC). While private training of large neural networks such as VGG-16 or ResNet-50 on state-of-the-art datasets such as Imagenet is still out of reach, given the performance overhead of MPC, private inference is starting to achieve practical runtimes. However, we show that in contrast to plaintext machine learning, the usage of GPU acceleration for both linear and nonlinear neural...

In this work, we take a look at the two recently proposed block ciphers, DEFAULT and BAKSHEESH, both of which are descendent of another block cipher named GIFT. We show that both ciphers can be interpreted within the partial non-linear layer category, thanks to the SBoxes having at least one non-trivial linear structure. We also reevaluate the security claim of DEFAULT.

We present a variant of Function Secret Sharing (FSS) schemes tailored for point, comparison, and interval functions, featuring compact key sizes at the expense of additional comparison. While existing FSS constructions are primarily geared towards $2$-party scenarios, exceptions such as the work by Boyle et al. (Eurocrypt 2015) and Riposte (S&P 2015) have introduced FSS schemes for $p$-party scenarios ($p \geq 3$). This paper aims to achieve the most compact $p$-party FSS key size to date....

As deep learning is being widely adopted across various domains, ensuring the integrity of models has become increasingly crucial. Despite the recent advances in Zero-Knowledge Machine Learning (ZKML) techniques, proving the inference over large ML models is still prohibitive. To enable practical ZKML, model simplification techniques like pruning and quantization should be applied without hesitation. Contrary to conventional belief, recent development in ML space have demonstrated that these...

In recent years, quantum technology has been rapidly developed. As security analyses for symmetric ciphers continue to emerge, many require an evaluation of the resources needed for the quantum circuit implementation of the encryption algorithm. In this regard, we propose the quantum circuit decision problem, which requires us to determine whether there exists a quantum circuit for a given permutation f using M ancilla qubits and no more than K quantum gates within the circuit depth D....

In recent years quantum computing has developed rapidly. The security threat posed by quantum computing to cryptography makes it necessary to better evaluate the resource cost of attacking algorithms, some of which require quantum implementations of the attacked cryptographic building blocks. In this paper we manage to optimize quantum circuits of AES in several aspects. Firstly, based on de Brugière \textit{et al.}'s greedy algorithm, we propose an improved depth-oriented algorithm for...

Consider the task of secure multiparty computation (MPC) among $n$ parties with perfect security and guaranteed output delivery, supporting $t<n/3$ active corruptions. Suppose the arithmetic circuit $C$ to be computed is defined over a finite ring $\mathbb{Z}/q\mathbb{Z}$, for an arbitrary $q\in\mathbb{Z}$. It is known that this type of MPC over such ring is possible, with communication that scales as $O(n|C|)$, assuming that $q$ scales as $\Omega(n)$. However, for constant-size rings...

Differential cryptanalysis is an old and powerful attack against block ciphers. While different techniques have been introduced throughout the years to improve the complexity of this attack, the key recovery phase remains a tedious and error-prone procedure. In this work, we propose a new algorithm and its associated tool that permits, given a distinguisher, to output an efficient key guessing strategy. Our tool can be applied to SPN ciphers whose linear layer consists of a bit-permutation...

In 1994, Langford and Hellman introduced differential-linear (DL) cryptanalysis, with the idea of decomposing the block cipher E into two parts, EU and EL, such that EU exhibits a high-probability differential trail, while EL has a high-correlation linear trail.Combining these trails forms a distinguisher for E, assuming independence between EU and EL. The dependency between the two parts of DL distinguishers remained unaddressed until EUROCRYPT 2019, where Bar-On et al. introduced the DLCT...

In recent years, quantum computers and Shor’s quantum algorithm have been able to effectively solve NP (Non-deterministic Polynomial-time) problems such as prime factorization and discrete logarithm problems, posing a threat to current mainstream asymmetric cryptography, including RSA and Elliptic Curve Cryptography (ECC). As a result, the National Institute of Standards and Technology (NIST) in the United States call for Post-Quantum Cryptography (PQC) methods that include lattice-based...

The linear layer of block ciphers plays an important role in their security. In particular, ciphers designed following the wide-trail strategy use the branch number of the linear layer to derive bounds on the probability of linear and differential trails. At FSE 2014, the LS-design construction was introduced as a simple and regular structure to design bitsliced block ciphers. It considers the internal state as a bit matrix, and applies alternatively an identical S-Box on all the columns,...

Secure Multiparty Computation (MPC) protocols enable secure evaluation of a circuit by several parties, even in the presence of an adversary who maliciously corrupts all but one of the parties. These MPC protocols are constructed using the well-known secret-sharing-based paradigm (SPDZ and SPD$\mathbb{Z}_{2^k}$), where the protocols ensure security against a malicious adversary by computing Message Authentication Code (MAC) tags on the input shares and then evaluating the circuit with these...

Goldwasser-Kalai-Rothblum protocol (GKR) for layered circuits is a sumcheck-based argument of knowledge for layered circuits, running in $\sim 2\mu \ell$ amount of rounds, where $\ell$ is the amount of layers and $\mu$ is the average layer logsize. For a layer $i$ of size $2^{\mu_i}$ the main work consists of running a sumcheck protocol of the form \[\underset{x,y}{\sum} \text{Add}_i(x,y,z)(f(x)+f(y)) + \text{Mul}_i(x,y,z)f(x)f(y)\] over a $2^{2\mu_i}$-dimensional cube, where...

Recent works have revisited blockcipher structures to achieve MPC- and ZKP-friendly designs. In particular, Albrecht et al. (EUROCRYPT 2015) first pioneered using a novel structure SP networks with partial non-linear layers (P-SPNs) and then (ESORICS 2019) repopularized using multi-line generalized Feistel networks (GFNs). In this paper, we persist in exploring symmetric cryptographic constructions that are conducive to the applications such as MPC. In order to study the minimization of...

Recently, as quantum computing technology develops, the importance of quantum resistant cryptography technology is increasing. AIMer is a quantum-resistant cryptographic algorithm that was selected as the first candidate in the electronic signature section of the KpqC Contest, and uses symmetric primitive AIM. In this paper, we propose a high-speed implementation technique of symmetric primitive AIM and evaluate the performance of the implementation. The proposed techniques are two methods,...

Column Parity Mixers, or CPMs in short, are a particular type of linear maps, used as the mixing layer in permutation-based cryptographic primitives like Keccak-f (SHA3) and Xoodoo. Although being successfully applied, not much is known regarding their algebraic properties. They are limited to invertibility of CCPMs, and that the set of invertible CCPMs forms a group. A possible explanation is due to the complexity of describing CPMs in terms of linear algebra. In this paper, we introduce a...

Continuous Group-Key Agreement (CGKA) allows a group of users to maintain a shared key. It is the fundamental cryptographic primitive underlying group messaging schemes and related protocols, most notably TreeKEM, the underlying key agreement protocol of the Messaging Layer Security (MLS) protocol, a standard for group messaging by the IETF. CKGA works in an asynchronous setting where parties only occasionally must come online, and their messages are relayed by an untrusted server. The...

At Asiacrypt 2021, Baksi et al. introduced DEFAULT, the first block cipher designed to resist differential fault attacks (DFA) at the algorithm level, boasting of a 64-bit DFA security. The cipher initially employed a straightforward key schedule, where a single key was XORed in all rounds, and the key schedule was updated by incorporating round-independent keys in a rotating fashion. However, during Eurocrypt 2022, Nageler et al. presented a DFA attack that exposed vulnerabilities in the...

We introduce the QARMAv2 family of tweakable block ciphers. It is a redesign of QARMA (from FSE 2017) to improve its security bounds and allow for longer tweaks, while keeping similar latency and area. The wider tweak input caters to both specific use cases and the design of modes of operation with higher security bounds. This is achieved through new key and tweak schedules, revised S-Box and linear layer choices, and a more comprehensive security analysis. QARMAv2 offers competitive...

We introduce a new type of mixing layer for the round function of cryptographic permutations, called circulant twin column parity mixer (CPM), that is a generalization of the mixing layers in KECCAK-f and XOODOO. While these mixing layers have a bitwise differential branch number of 4 and a computational cost of 2 (bitwise) additions per bit, the circulant twin CPMs we build have a bitwise differential branch number of 12 at the expense of an increase in computational cost: depending on the...

Recent constructions of (tweakable) block ciphers with an embedded cryptographic backdoor relied on the existence of probability-one differentials or perfect (non-)linear approximations over a reduced-round version of the primitive. In this work, we study how the existence of probability-one differentials or perfect linear approximations over two rounds of a substitution-permutation network can be avoided by design. More precisely, we develop criteria on the s-box and the linear layer that...

In this paper, we show an in-place implementation of the ASCON linear layer. An in-place implementation is important in the context of quantum computing, we expect our work will be useful in quantum implementation of ASCON. In order to get the implementation, we first write the ASCON linear layer as a binary matrix; then apply two legacy algorithms (Gauss-Jordan elimination and PLU factorization) as well as our modified version of Xiang et al.'s algorithm/source-code (published in...

We prove that perfectly-secure optimally-resilient secure Multi-Party Computation (MPC) for a circuit with $C$ gates and depth $D$ can be obtained in $O((Cn+n^4 + Dn^2)\log n)$ communication complexity and $O(D)$ expected time. For $D \ll n$ and $C\geq n^3$, this is the first perfectly-secure optimal-resilient MPC protocol with linear communication complexity per gate and constant expected time complexity per layer. Compared to state-of-the-art MPC protocols in the player elimination...

Zero-correlation linear attack is a powerful attack of block ciphers, the lower number of rounds (LNR) which no its distinguisher (named zero-correlation linear approximation, ZCLA) exists reflects the ability of a block cipher against the zero-correlation linear attack. However, due to the large search space, showing there are no ZCLAs exist for a given block cipher under a certain number of rounds is a very hard task. Thus, present works can only prove there no ZCLAs exist in a small...

In symmetric cryptography, block ciphers, stream ciphers and permutations often make use of a round function and many round functions consist of a linear and a non-linear layer. One that is often used is based on the cellular automaton that is denoted by $\chi$ as a Boolean map on bi-infinite sequences, $\mathbb{F}^{\mathbb{Z}}$. It is defined by $\sigma \mapsto \nu$ where each $\nu_i = \sigma_i + (\sigma_{i+1}+1)\sigma_{i+2}$. A map $\chi_n$ is a map that operatos on $n$-bit arrays...

Zero-knowledge proof systems for computational integrity have seen a rise in popularity in the last couple of years. One of the results of this development is the ongoing effort in designing so-called arithmetization-friendly hash functions in order to make these proofs more efficient. One of these new hash functions, Poseidon, is extensively used in this context, also thanks to being one of the first constructions tailored towards this use case. Many of the design principles of Poseidon...

In this paper we, for the first time, study the question under which circumstances decomposing a round function of a Substitution-Permutation Network is possible uniquely. More precisely, we provide necessary and sufficient criteria for the non-linear layer on when a decomposition is unique. Our results in particular imply that, when cryptographically strong S-boxes are used, the decomposition is indeed unique. We then apply our findings to the notion of alignment, pointing out that the...

In many applications, low area and low latency are required for the chip-level implementation of cryptographic primitives. The low-cost implementations of linear layers usually play a crucial role for symmetric ciphers. Some heuristic methods, such as the forward search and the backward search, minimize the number of XOR gates of the linear layer under the minimum latency limitation. For the sake of achieving further optimization for such implementation of the linear layer, we put forward...

The $\mathcal{S}_{leeve}$ construction proposed by Chaum et al. (ACNS'21) introduces an extra security layer for digital wallets by allowing users to generate a "back up key" securely nested inside the secret key of a signature scheme, i.e., ECDSA. The "back up key", which is secret, can be used to issue a "proof of ownership", i.e., only the real owner of this secret key can generate a single proof, which is based on the WOTS+ signature scheme. The authors of $\mathcal{S}_{leeve}$ proposed...

Conventional bit-based division property (CBDP) and bit- based division property using three subsets (BDPT) introduced by Todo et al. at FSE 2016 are the most effective techniques for finding integral characteristics of symmetric ciphers. At ASIACRYPT 2019, Wang et al. proposed the idea of modeling the propagation of BDPT, and recently Liu et al. described a model set method that characterized the BDPT propagation. However, the linear layers of the block ciphers which are analyzed...

FUTURE is a recently proposed, lightweight block cipher. It has an AES-like, SP-based, 10-round encryption function, where, unlike most other lightweight constructions, the diffusion layer is based on an MDS matrix. Despite its relative complexity, it has a remarkable hardware performance due to careful design decisions. In this paper, we conducted a MILP-based analysis of the cipher, where we incorporated exact probabilities rather than just the number of active S-boxes into the model....

Security concerns about a machine learning model used in a prediction-as-a-service include the privacy of the model, the query and the result. Secure inference solutions based on homomorphic encryption (HE) and/or multiparty computation (MPC) have been developed to protect all the sensitive information. One of the most efficient type of solution utilizes HE for linear layers, and MPC for non-linear layers. However, for such hybrid protocols with semi-honest security, an adversary can...

There are many recent results on reverse-engineering (potentially hidden) structure in cryptographic S-boxes. The problem of recovering structure in the other main building block of symmetric cryptographic primitives, namely, the linear layer, has not been paid that much attention so far. To fill this gap, in this work, we develop a systematic approach to decomposing structure in the linear layer of a substitution-permutation network (SPN), covering the case in which the specification of the...

With the advent of Malicious (Peyrin and Wang, Crypto'20), the question of a cipher with an intentional weakness which is only known to its designer has gained its momentum. In their work, the authors discuss how an otherwise secure cipher can be broken by its designer with the help of a secret backdoor (which is not known to the user/attacker). The contribution of Malicious is to propose a cipher-level construction with a backdoor, where it is computationally infeasible to retrieve the...

Secure multi-party computation (MPC) is an essential tool for privacy-preserving machine learning (ML). However, secure training of large-scale ML models currently requires a prohibitively long time to complete. Given that large ML inference and training tasks in the plaintext setting are significantly accelerated by Graphical Processing Units (GPUs), this raises the natural question: can secure MPC leverage GPU acceleration? A few recent works have studied this question in the context of...

The LowMC family of block ciphers was first proposed by Albrecht et al. in [ARS+15], specifically targeting adoption in FHE and MPC applications due to its low multiplicative complexity. The construction operates a 3-bit S-box as the sole non-linear transformation in the algorithm. In contrast, both the linear layer and round key generation are achieved through multiplications of full rank matrices over GF(2). The cipher is instantiable using a diverse set of default configurations, some of...

On CRYPTO2021, Nishanth Chandran, Bhavana Kanukurthi, Sai Lakshmi Bhavana Obattu, and Sruthi Sekar presented a novel secret sharing scheme, called CKO+21 scheme. This scheme makes use of Shamir secret sharing schemes and randomness extractors as its basic components, to generate a multi-layer encapsulation structure. The authors claimed that CKO+21 scheme satisfied “leakage resilience”, that is, the privacy still held under both “not enough revealing” and “appropriate leakage”. More...

We introduce the first proof system for layered arithmetic circuits over an arbitrary ring $R$ that is (possibly) non-commutative and (possibly) infinite, while only requiring black-box access to its arithmetic and a subset $A \subseteq R$. Our construction only requires limited commutativity and regularity properties from $A$, similar to recent work on efficient information theoretic multi-party computation over non-commutative rings by Escudero and Soria-Vazquez (CRYPTO 2021), but...

Continuous group key agreement (CGKA) allows a group of users to maintain a continuously updated shared key in an asynchronous setting where parties only come online sporadically and their messages are relayed by an untrusted server. CGKA captures the basic primitive underlying group messaging schemes. Current solutions including TreeKEM ("Messaging Layer Security'' (MLS) IETF RFC 9420) cannot handle concurrent requests while retaining low communication complexity. The exception being...

A new fundamental 4-round property of AES, called the zero-difference property, was introduced by R{\o}njom, Bardeh and Helleseth at Asiacrypt 2017. Our work characterizes it in a simple way by exploiting the notion of related differences which was introduced and well analyzed by the AES designers. We extend the 4-round property by considering some further properties of related differences over the AES linear layer, generalizing the zero-difference property. This results in a new...

Since the first white-box implementation of AES published twenty years ago, no significant progress has been made in the design of secure implementations against an attacker with full control of the device. Designing white-box implementations of existing block ciphers is a challenging problem, as all proposals have been broken. Only two white-box design strategies have been published this far: the CEJO framework, which can only be applied to ciphers with small S-boxes, and self-equivalence...

The area of multi-party computation (MPC) has recently increased in popularity and number of use cases. At the current state of the art, Ciminion, a Farfalle-like cryptographic function, achieves the best performance in MPC applications involving symmetric primitives. However, it has a critical weakness. Its security highly relies on the independence of its subkeys, which is achieved by using an expensive key schedule. Many MPC use cases involving symmetric pseudo-random functions (PRFs)...

Lightweight cryptography features a small footprint and/or low computational complexity. Low-cost implementations of linear layers usually play an important role in lightweight cryptography. Although it has been shown by Boyar et al. that finding the optimal implementation of a linear layer is a Shortest Linear Program (SLP) problem and NP-hard, there exist a variety of heuristic methods to search for near-optimal solutions. This paper considers the low-latency criteria and focuses on the...

The Keccak sponge function family, designed by Bertoni et al. in 2007, was selected by the U.S. National Institute of Standards and Technology (NIST) in 2012 as the next generation of Secure Hash Algorithm (SHA-3). Due to its theoretical and practical importance, cryptanalysis against SHA-3 has attracted an increasing attention. To the best of our knowledge, the most powerful collision attack on SHA-3 up till now is the linearisation technique proposed by Jian Guo et al. However, that...

Motivated by new applications such as secure Multi-Party Computation (MPC), Fully Homomorphic Encryption (FHE), and Zero-Knowledge proofs (ZK), many MPC-, FHE- and ZK-friendly symmetric-key primitives that minimize the number of multiplications over $\mathbb{F}_p$ for a large prime $p$ have been recently proposed in the literature. This goal is often achieved by instantiating the non-linear layer via power maps $x\mapsto x^d$. In this paper, we start an analysis of new non-linear...

At Indocrypt 2021, Hermelink, Pessl, and Pöppelmann presented a fault attack against Kyber in which a system of linear inequalities over the private key is generated and solved. The attack requires a laser and is, understandably, demonstrated with simulations—not actual equipment. We facilitate and diversify the attack in four ways, thereby admitting cheaper and more forgiving fault-injection setups. Firstly, the attack surface is enlarged: originally, the two input operands of the...

The SM4 block cipher was first released in 2006 as SMS4 used in the Chinese national standard WAPI, and became a Chinese national standard in 2016 and an ISO international standard in 2021. White-box cryptography aims primarily to protect the secret key used in a cryptographic software implementation in the white-box scenario that assumes an attacker to have full access to the execution environment and execution details of an implementation. Since white-box cryptography has many real-life...

We introduce ABBY, an open-source side-channel leakage profiling framework that targets the microarchitectural layer. Existing solutions to characterize the microarchitectural layer are device-specific and require extensive manual effort. The main innovation of ABBY is the collection of data, which can automatically characterize the microarchitecture of a target device and has the additional benefit of being scalable. Using ABBY, we create two sets of data which capture...

The linear layer, which is basically a binary non-singular matrix, is an integral part of cipher construction in a lot of private key ciphers. As a result, optimising the linear layer for device implementation has been an important research direction for about two decades. The Boyar-Peralta's algorithm (SEA'10) is one such common algorithm, which offers significant improvement compared to the straightforward implementation. This algorithm only returns implementation with XOR2 gates, and is...

In this paper we propose FASTA, a stream cipher design optimised for implementation over popular fully homomorphic encryption schemes. A number of symmetric encryption ciphers have been recently proposed for FHE applications, e.g. the block cipher LowMC, and the stream ciphers Rasta (and variants), FLIP and Kreyvium. The main design criterion employed in these ciphers has typically been to minimise the multiplicative complexity of the algorithm. However, other aspects affecting their...

We propose a second-order masking of the AES in hardware that requires an order of magnitude less random bits per encryption compared to previous work. The design and its security analysis are based on recent results by Beyne et al. from Asiacrypt 2020. Applying these results to the AES required overcoming significant engineering challenges by introducing new design techniques. Since the security analysis is based on linear cryptanalysis, the masked cipher needs to have sufficient diffusion...

A $(1,n)$-robust combiner combines $n$ cryptography primitives to construct a new primitive of the same type, and guarantees that if any of the ingredient primitive is secure, then the resulting primitive is secure. In recent two decades, robust combiners for various crypto primitives (e.g. public key encryption, oblivious transfer) have been proposed. Very recently, more works on robust combiners for post-quantum key encapsulation mechanism appear to achieve multi-layer of defence, to...

Differential Fault Analysis (DFA) is a well known cryptanalytic technique that exploits faulty outputs of an encryption device. Despite its popularity and similarity with the classical Differential Analysis (DA), a thorough analysis explaining DFA from a designer's point of view is missing in the literature. To the best of our knowledge, no DFA immune cipher at an algorithmic level has been proposed so far. Furthermore, all known DFA countermeasures somehow depend on the device/protocol or...

Deep learning techniques with neural networks are developing prominently in recent years and have been deployed in numerous applications. Despite their great success, in many scenarios it is important for the users to validate that the inferences are truly computed by legitimate neural networks with high accuracy, which is referred to as the integrity of machine learning predictions. To address this issue, in this paper, we propose zkCNN, a zero knowledge proof scheme for convolutional...

With the introduction of the division trail, the bit-based division property (BDP) has become the most efficient method to search for integral distinguishers. The notation of the division trail allows us to automate the search process by modelling the propagation of the DBP as a set of constraints that can be solved using generic Mixed-integer linear programming (MILP) and SMT/SAT solvers. The current models for the basic operations and Sboxes are efficient and accurate. In contrast, the two...

Block ciphers such as the Advanced Encryption Standard (Rijndael) are used extensively in practice, yet our understanding of their security continues to be highly incomplete. This paper promotes and continues a research program aimed at *proving* the security of block ciphers against important and well-studied classes of attacks. In particular, we initiate the study of (almost) $t$-wise independence of concrete block-cipher construction paradigms such as substitution-permutation networks and...

Rasta and Dasta are two fully homomorphic encryption friendly symmetric-key primitives proposed at CRYPTO 2018 and ToSC 2020, respectively. We point out that the designers of Rasta and Dasta neglected an important property of the $\chi$ operation. Combined with the special structure of Rasta and Dasta, this property directly leads to significantly improved algebraic cryptanalysis. Especially, it enables us to theoretically break 2 out of 3 instances of full Agrasta, which is the aggressive...

Motivated by new applications such as secure Multi-Party Computation (MPC), Fully Homomorphic Encryption (FHE), and Zero-Knowledge proofs (ZK), the need for symmetric encryption schemes that minimize the number of field multiplications in their natural algorithmic description is apparent. This development has brought forward many dedicated symmetric encryption schemes that minimize the number of multiplications in GF(2^n) or GF(p), with p being prime. These novel schemes have lead to new...

CRAFT is a lightweight tweakable Substitution-Permutation-Network (SPN) block cipher optimized for efficient protection of its implementations against Differential Fault Analysis (DFA) attacks. In this paper, we present an equivalent description of CRAFT up to a simple mapping on the plaintext, ciphertext and round tweakeys. We show that the new representation, for a sub-class of keys, leads to a new structure which is a Feistel network, with non-linear operation and key addition only on...

Stealing trained machine learning (ML) models is a new and growing concern due to the model's development cost. Existing work on ML model extraction either applies a mathematical attack or exploits hardware vulnerabilities such as side-channel leakage. This paper shows a new style of attack, for the first time, on ML models running on embedded devices by abusing the scan-chain infrastructure. We illustrate that having course-grained scan-chain access to non-linear layer outputs is sufficient...

This paper studies zero-knowledge SNARKs for NP, where the prover incurs $O(N)$ finite field operations to prove the satisfiability of an $N$-sized R1CS instance. We observe that recent work of Bootle, Chiesa, and Groth (BCG, TCC 20) provides a polynomial commitment scheme that, when combined with the linear-time interactive proof system of Spartan~(CRYPTO 20), yields linear-time IOPs and SNARKs for R1CS. Specifically, for security parameter $\lambda$, and for an $N$-sized R1CS instance over...

Nonlinear diffusion layers are less studied in cryptographic literature, up to now. In 2018, Liu, Rijmen and Leander studied nonlinear non-MDS diffusion layers and mentioned some advantages of them. As they stated, nonlinear diffusion layers could make symmetric ciphers more resistant against statistical and algebraic cryptanalysis. In this paper, with the aid of some special maps over the finite field $\mathbb{F}_{2^n}$, we examine nonlinear MDS mappings and present a family of $4 \times 4$...

We report the homomorphic evaluation of the SM4 symmetric block-cipher based on BGV homomorphic encryption scheme. We implement bootstrapping and non-bootstrapping homomorphic evaluation of the 32-rounds SM4 based on HELib with about 128-bit security level. Our ways refer to and are similar as the AES homomorphic evaluation. The implementation uses packed ciphertexts and bytes in slots. The S-Box evaluation is similar as the AES evaluation method, and the Linear Transform layer uses the...

All academic methods to secure software implementations of block ciphers against adversaries with full control of the device have been broken. Despite the huge progress in the cryptanalysis of these white-box implementations, no recent progress has been made on the design side. Most of the white-box designs follow the CEJO framework, where each round is encoded by composing it with small random permutations. While several generic attacks have been proposed on the CEJO framework, no generic...

We present Poppins, a direct construction of a zero-knowledge argument system for general computation that features an $O_{\lambda}(n)$ time prover and an $O_{\lambda}(1)$ time verifier (after a single $O_{\lambda}(n)$ public setup) for computations of size $n$. Our scheme utilizes a universal linear-size structured reference string (SRS) that allows a single trusted setup to be used across all computation instances of a bounded size. Concretely, for computations of size $n$, our prover's...

CRAFT is a lightweight tweakable block cipher proposed at FSE 2019, which allows countermeasures against Differential Fault Attacks to be integrated into the cipher at the algorithmic level with ease. CRAFT employs a lightweight and involutory S-box and linear layer, such that the encryption function can be turned into decryption at a low cost. Besides, the tweakey schedule algorithm of CRAFT is extremely simple, where four 64-bit round tweakeys are generated and repeatedly used. Due to a...

With the advances of Internet-of-Things (IoT) applications in smart cities and the pervasiveness of network devices with limited resources, lightweight block ciphers have achieved rapid development recently. Due to their relatively simple key schedule, nonlinear invariant attacks have been successfully applied to several families of lightweight block ciphers. This attack relies on the existence of a nonlinear invariant $g:\F_2^n \rightarrow \F_2$ for the round function $F_k$ so that $g(x)...

Subterranean 2.0 is a cipher suite that can be used for hashing, authenticated encryption, MAC computation, etc. It was designed by Daemen, Massolino, Mehrdad, and Rotella, and has been selected as a candidate in the second round of NIST's lightweight cryptography standardization process. Subterranean 2.0 is a duplex-based construction and utilizes a single-round permutation in the duplex. It is the simplicity of the round function that makes it an attractive target of cryptanalysis. In...

The fixslicing implementation strategy was originally introduced as a new representation for the hardware-oriented GIFT block cipher to achieve very efficient software constant-time implementations. In this article, we show that the fundamental idea underlying the fixslicing technique is not of interest only for GIFT, but can be applied to other ciphers as well. Especially, we study the benefits of fixslicing in the case of AES and show that it allows to reduce by 52% the amount of...

This article gives a rigorous mathematical treatment of generalized and closed loop invariants (CLI) which extend the standard notion of (nonlinear) invariants used in the cryptanalysis of block ciphers. Employing the cycle structure of bijective S-box components, we precisely characterize the cardinality of both generalized and CLIs. We demonstrate that for many S-boxes used in practice quadratic invariants (especially useful for mounting practical attacks in cases when the linear...

Modern public key encryption relies on various hardness assumptions for its security. Hardness assumptions may cause security uncertainty, for instance, when a hardness problem is no longer hard or the best solution to a hard problem might not be publicly released. In this paper, we propose a public key encryption scheme Compact-LWE-MQ^{H} to demonstrate the feasibility of constructing public key encryption without relying on hardness assumptions. Instead, its security is based on problems...

A continuous group key agreement (CGKA) protocol allows a long-lived group of parties to agree on a continuous stream of fresh secret key material. The protocol must support constantly changing group membership, make no assumptions about when, if, or for how long members come online, nor rely on any trusted group managers. Due to sessions' long life-time, CGKA protocols must simultaneously ensure both post-compromise security and forward secrecy (PCFS). That is, current key material should...

We consider the theoretically-sound selection of cryptographic parameters, such as the size of algebraic groups or RSA keys, for TLS 1.3 in practice. While prior works gave security proofs for TLS 1.3, their security loss is quadratic in the total number of sessions across all users, which due to the pervasive use of TLS is huge. Therefore, in order to deploy TLS 1.3 in a theoretically-sound way, it would be necessary to compensate this loss with unreasonably large parameters that would be...

The Gimli permutation proposed in CHES 2017 was designed for cross-platform performance. One main strategy to achieve such a goal is to utilize a sparse linear layer (Small-Swap and Big-Swap), which occurs every two rounds. In addition, the round constant addition occurs every four rounds and only one 32-bit word is affected by it. The above two facts have been recently exploited to construct a distinguisher for the full Gimli permutation with time complexity $2^{64}$. By utilizing a new...

The bit-based division property (BDP) is the most effective technique for finding integral characteristics of symmetric ciphers. Recently, automatic search tools have become one of the most popular approaches to evaluating the security of designs against many attacks. Constraint-aided automatic tools for the BDP have been applied to many ciphers with simple linear layers like bit-permutation. Constructing models of complex linear layers accurately and efficiently remains hard. A...

We consider SPN schemes, i.e., schemes whose non-linear layer is defined as the parallel application of $t\ge 1$ independent S-Boxes over $\mathbb{F}_{2^n}$ and whose linear layer is defined by the multiplication with a $(n\cdot t)\times(n\cdot t)$ matrix over $\mathbb{F}_2$. Even if the algebraic representation of a scheme depends on all its components, upper bounds on the growth of the algebraic degree in the literature usually only consider the details of the non-linear layer. Hence a...

Designing cryptographic permutations and block ciphers using a substitution-permutation network (SPN) approach where the nonlinear part does not cover the entire state has recently gained attention due to favorable implementation characteristics in various scenarios. For word-oriented partial SPN (P-SPN) schemes with a fixed linear layer, our goal is to better understand how the details of the linear layer affect the security of the construction. In this paper, we derive conditions that...

The GIFT family of lightweight block ciphers, published at CHES 2017, offers excellent hardware performance figures and has been used, in full or in part, in several candidates of the ongoing NIST lightweight cryptography competition. However, implementation of GIFT in software seems complex and not efficient due to the bit permutation composing its linear layer (a feature shared with PRESENT cipher). In this article, we exhibit a new non-trivial representation of the GIFT family of block...

The HADES design strategy combines the classical SPN construction with the Partial SPN (PSPN) construction, in which at every encryption round, the non-linear layer is applied to only a part of the state. In a HADES design, a middle layer that consists of PSPN rounds is surrounded by outer layers of SPN rounds. The security arguments of HADES with respect to statistical attacks use only the SPN rounds, disregarding the PSPN rounds. This allows the designers to not pose any restriction on the...

In CHES 2017, Jean et al. presented a paper on ``Bit-Sliding'' in which the authors proposed lightweight constructions for SPN based block ciphers like AES, PRESENT, and SKINNY. The main idea behind these constructions was to reduce the length of the datapath to 1 bit and to reformulate the linear layer for these ciphers so that they require fewer scan flip-flops (which have built-in multiplexer functionality and so larger in area as compared to a simple flip-flop). In this paper, we...

Automatic search methods have been widely used for cryptanalysis of block ciphers, especially for the most classic cryptanalysis methods -- differential and linear cryptanalysis. However, the automatic search methods, no matter based on MILP, SMT/SAT or CP techniques, can be inefficient when the search space is too large. In this paper, we improve Matsui's branch-and-bound search algorithm which is known as the first generic algorithm for finding the best differential and linear trails by...

Keyed and unkeyed cryptographic permutations often iterate simple round functions. Substitution-permutation networks (SPNs) are an approach that is popular since the mid 1990s. One of the new directions in the design of these round functions is to reduce the substitution (S-Box) layer from a full one to a partial one, uniformly distributed over all the rounds. LowMC and Zorro are examples of this approach. A relevant freedom in the design space is to allow for a highly non-uniform...

The Gimli permutation was proposed in CHES 2017 and the hash mode Gimli-Hash is now included in the Round 2 candidate Gimli in NIST's Lightweight Cryptography Standardization process. In the Gimli document, the security of the Gimli permutation has been intensively investigated. However, little is known about the security of Gimli-Hash. The designers of Gimli have claimed $2^{128}$ security against all attacks on Gimli-Hash, whose hash is a 256-bit value. Firstly, we present the trivial...

Distinguishers on round-reduced AES have attracted considerable attention in the recent years. While the number of rounds covered in key-recovery attacks did not increase, subspace, yoyo, mixture-differential, and multiple-of-n cryptanalysis advanced the understanding of the properties of the cipher. For substitution-permutation networks, integral attacks are a suitable target for extension since they usually end after a linear layer sums several subcomponents. Based on results by Patarin,...

Smart contracts are self-executing agreements written in program code and are envisioned to be one of the main applications of blockchain technology. While they are supported by prominent cryptocurrencies such as Ethereum, their further adoption is hindered by fundamental scalability challenges. For instance, in Ethereum contract execution suffers from a latency of more than 15 seconds, and the total number of contracts that can be executed per second is very limited. State channel networks...

Recently, the NIST launched a competition for lightweight cryptography and a large number of ciphers are expected to be studied and analyzed under this competition. Apart from the classical security, the candidates are desired to be analyzed against physical attacks. Differential Fault Analysis (DFA) is an invasive physical attack method for recovering key information from cipher implementations. Up to date, almost all the block ciphers have been shown to be vulnerable against DFA, while...

XOR-metrics measure the efficiency of certain arithmetic operations in binary finite fields. We prove some new results about two different XOR-metrics that have been used in the past. In particular, we disprove an existing conjecture about those XOR-metrics. We consider implementations of multiplication with one fixed element in a binary finite field. Here we achieve a complete characterization of all elements whose multiplication matrix can be implemented using exactly 2 XOR-operations....

In this paper, a new framework is developed for proving and adapting the recently proposed multiple-of-8 property and mixture-differential distinguishers. The above properties are formulated as immediate consequences of an equivalence relation on the input pairs, under which the difference at the output of the round function is invariant. This approach provides a further understanding of these newly developed distinguishers. For example, it clearly shows that the branch number of the linear...

Streebog and Kuznyechik are the latest symmetric cryptographic primitives standardized by the Russian GOST. They share the same S-Box, $\pi$, whose design process was not described by its authors. In previous works, Biryukov, Perrin and Udovenko recovered two completely different decompositions of this S-Box. We revisit their results and identify a third decomposition of $\pi$. It is an instance of a fairly small family of permutations operating on $2m$ bits which we call TKlog and which...

In CHES 2017, Moradi et al. presented a paper on ``Bit-Sliding'' in which the authors proposed lightweight constructions for SPN based block ciphers like AES, Present and SKINNY. The main idea behind these constructions was to reduce the length of the datapath to 1 bit and to reformulate the linear layer for these ciphers so that they require fewer scan flip-flops (which have built-in multiplexer functionality and so larger in area as compared to a simple flip-flop). In this paper we take...

Threshold Implementations are well-known as a provably firstorder secure Boolean masking scheme even in the presence of glitches. A precondition for their security proof is a uniform input distribution at each round function, which may require an injection of fresh randomness or an increase in the number of shares. However, it is unclear whether violating the uniformity assumption causes exploitable leakage in practice. Recently, Daemen undertook a theoretical study of lossy mappings to...

This paper investigates the construction of MDS matrices with generalized Feistel structures (GFS). The approach developed by this paper consists in deriving MDS matrices from the product of several sparser ones. This can be seen as a generalization to several matrices of the recursive construction which derives MDS matrices as the powers of a single companion matrix. The first part of this paper gives some theoretical results on the iteration of GFS. In second part, using GFS and...

This work focuses on side-channel resilient design strategies for symmetric-key cryptographic primitives targeting lightweight applications. In light of NIST's lightweight cryptography project, design choices for block ciphers must consider not only security against traditional cryptanalysis, but also side-channel security, while adhering to low area and power requirements. In this paper, we explore design strategies for substitution-permutation network (SPN)-based block ciphers that make...

LowMC is a block cipher family designed in 2015 by Albrecht et al. It is optimized for practical instantiations of multi-party computation, fully homomorphic encryption, and zero-knowledge proofs. LowMC is used in the Picnic signature scheme, submitted to NIST's post-quantum standardization project and is a substantial building block in other novel post-quantum cryptosystems. Many LowMC instances use a relatively recent design strategy (initiated by Gérard et al. at CHES 2013) of applying...

Substitution-Permutation Networks (SPNs) refer to a family of constructions which build a $wn$-bit (tweakable) block cipher from $n$-bit public permutations. Many widely deployed block ciphers are part of this family and rely on very small public permutations. Surprisingly, this structure has seen little theoretical interest when compared with Feistel networks, another high-level structure for block ciphers. This paper extends the work initiated by Dodis et al. in three directions; first,...

We present Chameleon, a novel hybrid (mixed-protocol) framework for secure function evaluation (SFE) which enables two parties to jointly compute a function without disclosing their private inputs. Chameleon combines the best aspects of generic SFE protocols with the ones that are based upon additive secret sharing. In particular, the framework performs linear operations in the ring $\mathbb{Z}_{2^l}$ using additively secret shared values and nonlinear operations using Yao's Garbled Circuits...

Picnic is a practical approach to digital signatures where the security is primarily based on the existence of a one-way function, and the signature size strongly depends on the number of multiplications in the circuit describing that one-way function. The highly parameterizable block cipher family LowMC has the most competitive properties with respect to this metric and is hence a standard choice. In this paper, we study various options for efficient implementations of LowMC...