Ascon-128 and Ascon-80pq use 12-round Ascon permutation for initialization and finalization phases and 6-round Ascon permutation for processing associate data and message. In a nonce-misuse setting, we present a new partial-state-recovery conditional-cube attack on Ascon-128 and Ascon-80pq, where 192 bits out of 320-bit state are recovered. For our partial state-recovery attack, its required data complexity, \(D\), is about \(2^{44.8}\) and its required memory complexity, \(M\), is negligible. After a 192-bit partial state is recovered, in a nonce-misuse setting, we can further recover the full 320-bit state with time complexity, \(T=2^{128}\), and then we can recover the secret key with extra data complexity of \(2^{31.5}\), extra time complexity of \(2^{129.5}\), and memory complexity of \(2^{31.5}\). A similar attack of recovering the partial state was independently developed by Baudrin et al. at NIST fifth Lightweight Cryptography workshop. Note that our attack does not violate the NIST LWC security requirements on Ascon-128 and Ascon-80pq as well as the designers' claims.

In this paper, we provide several improvements over the existing differential-linear attacks on ChaCha. ChaCha is a stream cipher which has $20$ rounds. At CRYPTO $2020$, Beierle et al. observed a differential in the $3.5$-th round if the right pairs are chosen. They produced an improved attack using this, but showed that to achieve a right pair, we need $2^5$ iterations on average. In this direction, we provide a technique to find the right pairs with the help of listing. Also, we provide a strategical improvement in PNB construction, modification of complexity calculation and an alternative attack method using two input-output pairs. Using these, we improve the time complexity, reducing it to $2^{221.95}$ from $2^{230.86}$ reported by Beierle et al. for $256$ bit version of ChaCha. Also, after a decade, we improve existing complexity (Shi et al: ICISC 2012) for a $6$-round of $128$ bit version of ChaCha by more than 11 million times and produce the first-ever attack on 6.5-round ChaCha$128$ with time complexity $2^{123.04}.$

In this article, we propose GIFT-COFB, an Authenticated Encryption with Associated Data (AEAD) scheme, based on the GIFT lightweight block cipher and the COFB lightweight AEAD operating mode. We explain how these two primitives can fit together and the various design adjustments possible for performance and security improvements. We show that our design provides excellent performances in all constrained scenarios, hardware or software, while being based on a provably-secure mode and a well analysed block cipher.

The Hill cipher is a classical poly-alphabetical cipher based on matrices. Although known plaintext attacks for the Hill cipher have been known for almost a century, feasible ciphertext only attacks have been developed only about ten years ago and for small matrix dimensions. In this paper we extend the ciphertext only attacks for the Hill cipher in two ways. First, we present two attacks for the affine version of the Hill cipher. Secondly, we show that the presented attacks can be extended to several modes of operations. We also provide the reader with several experimental results and show how the message's language can influence the presented attacks.

This paper proposes a new block cipher called HARPOCRATES, which is different from traditional SPN, Feistel, or ARX designs. The new design structure that we use is called the substitution convolution network. The novelty of the approach lies in that the substitution function does not use fixed S-boxes. Instead, it uses a key-driven lookup table storing a permutation of all 8-bit values. If the lookup table is sufficiently randomly shuffled, the round sub-operations achieve good confusion and diffusion to the cipher. While designing the cipher, the security, cost, and performances are balanced, keeping the requirements of encryption of data-at-rest in mind. The round sub-operations are massively parallelizable and designed such that a single active bit may make the entire state (an 8 × 16 binary matrix) active in one round. We analyze the security of the cipher against linear, differential, and impossible differential cryptanalysis. The cipher’s resistance against many other attacks like algebraic attacks, structural attacks, and weak keys are also shown. We implemented the cipher in software and hardware; found that the software implementation of the cipher results in better throughput than many well-known ciphers. Although HARPOCRATES is appropriate for the encryption of data-at-rest, it is also well-suited in data-in-transit environments.

ARX algorithms are a class of symmetric-key algorithms constructed by Addition, Rotation, and XOR. To evaluate the resistance of an ARX cipher against differential and impossible-differential cryptanalysis, the recent automated methods employ constraint satisfaction solvers to search for optimal characteristics or impossible differentials. The main difficulty in formulating this search is finding the differential models of the non-linear operations. While an efficient bit-vector differential model was obtained for the modular addition with two variable inputs, no differential model for the modular addition by a constant has been proposed so far, preventing ARX ciphers including this operation from being evaluated with automated methods. In this paper, we present the first bit-vector differential model for the $n$-bit modular addition by a constant input. Our model contains $O(\log_2(n))$ basic bit-vector constraints and describes the binary logarithm of the differential probability. We describe an SMT-based automated method that includes our model to search for differential characteristics of ARX ciphers including constant additions. We also introduce a new automated method for obtaining impossible differentials where we do not search over a small pre-defined set of differences, such as low-weight differences, but let the SMT solver search through the space of differences. Moreover, we implement both methods in our open-source tool \texttt{ArxPy} to find characteristics and impossible differentials of ARX ciphers with constant additions in a fully automated way. As some examples, we provide related-key impossible differentials and differential characteristics of TEA, XTEA, HIGHT, LEA, SHACAL-1, and SHACAL-2, which achieve better results compared to previous works.

In this article we perform a general study on the criterion of weightwise nonlinearity for the functions which are weightwise perfectly balanced (WPB). First, we investigate the minimal value this criterion can take over WPB functions, deriving theoretic bounds, and exhibiting the first values. We emphasize the link between this minimum and weightwise affine functions, and we prove that for $n\ge 8$ no $n$-variable WPB function can have this property. Then, we focus on the distribution and the maximum of this criterion over the set of WPB functions. We provide theoretic bounds on the latter and algorithms to either compute or estimate the former, together with the results of our experimental studies for $n$ up to $8$. Finally, we present two new constructions of WPB functions obtained by modifying the support of linear functions for each set of fixed Hamming weight. This provides a large corpus of WPB function with proven weightwise nonlinearity, and we compare the weightwise nonlinearity of these constructions to the average value, and to the parameters of former constructions in $8$ and $16$ variables.

ARX algorithms are a class of symmetric-key algorithms constructed by Addition, Rotation, and XOR, which achieve the best software performances in low-end microcontrollers. To evaluate the resistance of an ARX cipher against differential cryptanalysis and its variants, the recent automated methods employ constraint satisfaction solvers, such as SMT solvers, to search for optimal characteristics. The main difficulty to formulate this search as a constraint satisfaction problem is obtaining the differential models of the non-linear operations, that is, the constraints describing the differential probability of each non-linear operation of the cipher. While an efficient bit-vector differential model was obtained for the modular addition with two variable inputs, no differential model for the modular addition by a constant has been proposed so far, preventing ARX ciphers including this operation from being evaluated with automated methods. In this paper, we present the first bit-vector differential model for the n-bit modular addition by a constant input. Our model contains O(log_2(n)) basic bit-vector constraints and describes the binary logarithm of the differential probability. We also represent an SMT-based automated method to look for differential characteristics of ARX, including constant additions, and we provide an open-source tool ArxPy to find ARX differential characteristics in a fully automated way. To provide some examples, we have searched for related-key differential characteristics of TEA, XTEA, HIGHT, and LEA, obtaining better results than previous works. Our differential model and our automated tool allow cipher designers to select the best constant inputs for modular additions and cryptanalysts to evaluate the resistance of ARX ciphers against differential attacks.

In ICISC-05, and in the ePrint $2010/287$, Patarin claimed a lower bound on the number of $2q$ tuples of $n$-bit strings $(P_1, \ldots, P_{2q}) \in (\{0,1\}^{n})^{2q}$ satisfying $P_{2i - 1} \oplus P_{2i} = \lambda_i$ for $1 \leq i \leq q$ such that $P_1, P_2, \ldots$, $P_{2q}$ are distinct and $\lambda_i \in \{0,1\}^n \setminus \{0^n\}$. This result is known as {\em Mirror theory} and widely used in cryptography. It stands as a powerful tool to provide a high-security guarantee for many block cipher-(or even ideal permutation-) based designs. In particular, Mirror theory has a direct application in the security of XOR of block ciphers. Unfortunately, the proof of Mirror theory contains some unverifiable gaps and several mistakes. This paper provides a simple and verifiable proof of Mirror theory.

We present a diffusion block (DB), which is extraordinarily fast. After one round, it reaches complete diffusion, which means only 16 memory reads and 15 XOR operations. It uses only the most common operations available in any microprocessor. The diffusion and speed are based on a large key, about 64 kB for encryption and 34 kB for decryption, expanded from the classical key size of 128, 256, or more bits. The basic block length is 128 bits and could be expanded to 192, 256, or more. DB uses the same core idea as uses AES, DES, and others, which has been studied for more than 50 years by many cryptanalysts.

Differential attack is a basic cryptanalysis method for block ciphers that exploits the high probability relations between the input and output differences. The existing work in quantum differential cryptanalysis of block ciphers focuses on resource estimation to recover the last round subkeys on the basis of existing relations constructed on classical computers. To find such relations using quantum computer, we propose a method to search the high probability differential and impossible differential characteristics using quantum computer. The method explores all possible input and output difference pairs simultaneously using superposition of qubits. The proposed method is used to design the quantum circuit to search the differential characteristics for a toy cipher smallGIFT. The branch-and-bound based method is used to validate differential and impossible differential characteristics obtained using proposed method.

A tweakable enciphering scheme (TES) is a length preserving (tweakable) encryption scheme that provides (tweakable) strong pseudorandom permutation security on arbitrarily long messages. TES is traditionally built using block ciphers and the security of the mode depends on the strong pseudorandom permutation security of the underlying block cipher. In this paper, we construct TESs using public random permutations. Public random permutations are being considered as a replacement of block cipher in several cryptographic schemes including AEs, MACs, etc. However, to our knowledge, a systematic study of constructing TES using public random permutations is missing. In this paper, we give a generic construction of a TES which uses a public random permutation, a length expanding public permutation based PRF and a hash function which is both almost xor universal and almost regular. Further, we propose a concrete length expanding public permutation based PRF construction. We also propose a single keyed TES using a public random permutation and an AXU and almost regular hash function.

In the last couple of years, a new wave of results appeared, proposing and exploiting new properties of round-reduced AES. In this paper we survey and combine some of these results (namely, the multiple-of-n property and the mixture differential cryptanalysis) in a systematic way in order to answer more general questions regarding the probability distribution of encrypted diagonal sets. This allows to analyze this special set of inputs, and report on new properties regarding the probability distribution of the number of different pairs of corresponding ciphertexts are equal in certain anti-diagonal(s) after 5 rounds. An immediate corollary of the multiple-of-8 property is that the variance of such a distribution can be shown to be higher than for a random permutation. Surprisingly, also the mean of the distribution is significantly different from random, something which cannot be explained by the multiple-of-8 property. We propose a theoretical explanation of this, by assuming an APN-like assumption on the S-Box which closely resembles the AES-Sbox. By combining the multiple-of-8 property, the mixture differential approach, and the results just mentioned about the mean and the variance, we are finally able to formulate the probability distribution of the diagonal set after 5-round AES as a sum of independent binomial distributions.

Public permutations have been established as important primitives for the purpose of designing cryptographic schemes. While many such schemes for authentication and encryption have been proposed in the past decade, the birthday bound in terms of the primitive's block length $n$ has been mostly accepted as the standard security goal. Thus, remarkably little research has been conducted yet on permutation-based modes with higher security guarantees. At CRYPTO'19, Chen et al. showed two constructions with higher security based on the sum of two public permutations. Their work has sparked increased interest in this direction by the community. However, since their proposals were domain-preserving, the question of encryption schemes with beyond-birthday-bound security was left open. This work tries to address this gap by proposing $\textsf{CENCPP}^*$, a nonce-based encryption scheme from public permutations. Our proposal is a variant of Iwata's block-cipher-based mode \textsf{CENC} that we adapt for public permutations, thereby generalizing Chen et al.'s Sum-of-Even-Mansour construction to a mode with variable output lengths. Like \textsf{CENC}, our proposal enjoys a comfortable rate-security trade-off that needs $w + 1$ calls to the primitive for $w$ primitive outputs. We show a tight security level for up to $O(2^{2n/3}/w^2)$ primitive calls. While the term of $w \geq 1$ can be arbitrary, two independent keys suffice. Beyond our proposal of $\textsf{CENCPP}^*$ in a generic setting with $w + 1$ independent permutations, we show that only $\log_2(w + 1)$ bits of the input for domain separation suffice to obtain a single-permutation variant with a security level of up to $O(2^{2n/3}/w^4)$ queries.

Double-block Hash-then-Sum (DbHtS) MACs are a class of MACs achieve beyond-birthday-bound (BBB) security, including SUM-ECBC, PMAC_Plus, 3kf9 and LightMAC_Plus etc. Recently, Shen et al. (Crypto 2021) proposed a security framework for two-key DbHtS MACs in the multi-user setting, stating that when the underlying blockcipher is ideal and the universal hash function is regular and almost universal, the two-key DbHtS MACs achieve 2n/3-bit security. Unfortunately, the regular and universal properties can not guarantee the BBB security of two-key DbHtS MACs. We propose three counter-examples which are proved to be 2n/3-bit secure in the multi-user setting by the framework, but can be broken with probability 1 using only O(2^{n/2}) queries even in the single-user setting. We also point out the miscalculation in their proof leading to such a flaw. However, we haven’t found attacks against 2k-SUM-ECBC, 2k-PMAC_Plus and 2k-LightMAC_Plus proved 2n/3-bit security in their paper.

In 2002, Chow et al. initiated the formal study of white-box cryptography and introduced the CEJO framework. Since then, various white-box designs based on their framework have been proposed, all of them broken. Ranea and Preneel proposed a different method in 2020, called self-equivalence encodings and analyzed its security for AES. In this paper, we apply this method to generate the first academic white-box Speck implementations using self-equivalence encodings. Although we focus on Speck in this work, our design could easily be adapted to protect other add-rotate-xor (ARX) ciphers. Then, we analyze the security of our implementation against key-recovery attacks. We propose an algebraic attack to fully recover the master key and external encodings from a white-box Speck implementation, with limited effort required. While this result shows that the linear and affine self-equivalences of self-equivalence encodings are insecure, we hope that this negative result will spur additional research in higher-degree self-equivalence encodings for white-box cryptography. Finally, we created an open-source Python project implementing our design, publicly available at https://github.com/jvdsn/white-box-speck. We give an overview of five strategies to generate output code, which can be used to improve the performance of the white-box implementation. We compare these strategies and determine how to generate the most performant white-box Speck code. Furthermore, this project could be employed to test and compare the efficiency of attacks on white-box implementations using self-equivalence encodings.

We proposed three general frameworks F1,F2, and F3 for n-to-n-bit PRFs with one, two parallel, and two serial public permutation calls respectively, where every permutation is preceded and followed by any bitwise linear mappings. We analyze them in the Q2 model where attackers have quantum-query access to PRFs and permutations. Our results show F1 is not secure with O(n) quantum queries while its PRFs achieve n/2-bit security in the classical setting, and F2,F3 are not secure with O(2^{n/2}n) quantum queries while their PRFs, such as SoEM, PDMMAC, and pEDM, achieve 2n/3-bit security in the classical setting. Besides, we attack three general instantiations XopEM, EDMEM, and EDMDEM of F2,F3, which derive from replacing the two PRPs in Xop, EDM, and EDMD with two independent EM constructions, and concrete PRF instantiations DS-SoEM, PDMMAC, and pEDM, SoKAC21 of F2,F3, with at most O(2^{n/2}n) quantum queries.

At EUROCRYPT~2021, Beierle et al. presented the first public analysis of the GPRS ciphers GEA-1 and GEA-2. They showed that although GEA-1 uses a 64-bit session key, it can be recovered with the knowledge of only 65 bits of keystream in time $2^{40}$ using $44$ GiB of memory. The attack exploits a weakness in the initialization process of the cipher that was presumably hidden intentionally by the designers to reduce its security. While no such weakness was found for GEA-2, the authors presented an attack on this cipher with time complexity of about $2^{45}$. The main practical obstacle is the required knowledge of 12800 bits of keystream used to encrypt a full GPRS frame. Variants of the attack are applicable (but more expensive) when given less consecutive keystream bits, or when the available keystream is fragmented (it contains no long consecutive block). In this paper, we improve and complement the previous analysis of GEA-1 and GEA-2. For GEA-1, we devise an attack in which the memory complexity is reduced by a factor of about $2^{13} = 8192$ from $44$ GiB to about 4 MiB, while the time complexity remains $2^{40}$. Our implementation recovers the GEA-1 session key in average time of 2.5~hours on a modern laptop. For GEA-2, we describe two attacks that complement the analysis of Beierle et al. The first attack obtains a linear tradeoff between the number of consecutive keystream bits available to the attacker (denoted by $\ell$) and the time complexity. It improves upon the previous attack in the range of (roughly) $\ell \leq 7000$. Specifically, for $\ell = 1100$ the complexity of our attack is about $2^{54}$, while the previous one is not faster than the $2^{64}$ brute force complexity. In case the available keystream is fragmented, our second attack reduces the memory complexity of the previous attack by a factor of $512$ from 32 GiB to 64 MiB with no time complexity penalty. Our attacks are based on new combinations of stream cipher cryptanalytic techniques and algorithmic techniques used in other contexts (such as solving the $k$-XOR problem).

Double-block Hash-then-Sum (DbHtS) MACs are a class of MACs that aim for achieving beyond-birthday-bound security, including SUM-ECBC, PMAC\_Plus, 3kf9 and LightMAC_Plus. Recently Datta et al. (FSE'19), and then Kim et al. (Eurocrypt'20) prove that DbHtS constructions are secure beyond the birthday bound in the single-user setting. However, by a generic reduction, their results degrade to (or even worse than) the birthday bound in the multi-user setting. In this work, we revisit the security of DbHtS MACs in the multi-user setting. We propose a generic framework to prove beyond-birthday-bound security for DbHtS constructions. We demonstrate the usability of this framework with applications to key-reduced variants of DbHtS MACs, including 2k-SUM-ECBC, 2k-PMAC_Plus and 2k-LightMAC_Plus. Our results show that the security of these constructions will not degrade as the number of users grows. On the other hand, our results also indicate that these constructions are secure beyond the birthday bound in both single-user and multi-user setting without additional domain separation, which is used in the prior work to simplify the analysis. Moreover, we find a critical flaw in 2kf9, which is proved to be secure beyond the birthday bound by Datta et al. (FSE'19). We can successfully forge a tag with probability 1 without making any queries. We go further to show attacks with birthday-bound complexity on several variants of 2kf9.

We study the provable security claims of two NIST Lightweight Cryptography (LwC) finalists, GIFT-COFB and Photon-Beetle, and present several attacks whose complexities contradict their claimed bounds in their final round specification documents. For GIFT-COFB, we show an attack using $q_e$ encryption queries and no decryption query to break privacy (IND-CPA). The success probability is $O(q_e/2^{n/2})$ for $n$-bit block while the claimed bound contains $O(q^2_e/2^{n})$. This positively solves an open question posed in~[Khairallah, ePrint~2021/648 (also accepted at FSE~2022)]. For Photon-Beetle, we show an attack using $q_e$ encryption queries (using a small number of input blocks) followed by a single decryption query and no primitive query to break authenticity (INT-CTXT). The success probability is $O(q^2_e/2^{b})$ for a $b$-bit block permutation, and it is significantly larger than what the claimed bound tells, which is independent of the number of encryption queries. We also show a simple tag guessing attack that violates the INT-CTXT bound when the rate $r=32$. Then, we analyze other (improved/modified) bounds of Photon-Beetle shown in the subsequent papers~[Chakraborty et al., ToSC 2020(2) and Chakraborty et al., ePrint~2019/1475]. As a side result of our security analysis of Photon-Beetle, we point out that a simple and efficient forgery attack is possible in the related-key setting. We emphasize that our results do not contradict the claimed ``bit security'' in the LwC specification documents for any of the schemes that we studied. That is, we do not negate the claims that GIFT-COFB is $(n/2 - \log n)$-bit secure for $n=128$, and Photon-Beetle is $(b/2 - \log b/2)$-bit secure for $b=256$ and $r=128$, where $r$ is a rate. We also note that the security against related-key attacks is not included in the security requirements of NIST LwC, and is not claimed by the designers.

At ASIACRYPT 2021, Liu et al. pointed out a weakness of the Rasta-like ciphers neglected by the designers. The main strategy is to construct exploitable equations of the $n$-bit $\chi$ operation denoted by $\chi_n$. However, these equations are all obtained by first studying $\chi_n$ for small $n$. In this note, we demonstrate that if the explicit formula of the inverse of $\chi_n$ denoted by $\chi_n^{-1}$ is known, all these exploitable equations would have been quite obvious and the weakness of the Rasta-like ciphers could have been avoided at the design phase. However, the explicit formula of $\chi_n^{-1}$ seems to be not well-known and the most relevant work was published by Biryukov et al. at ASIACRYPT 2014. In this work, we give a very simple formula of $\chi_n^{-1}$ that can be written down in only one line and we prove its correctness in a rigorous way. Based on its formula, the formula of exploitable equations for Rasta-like ciphers can be easily derived and therefore more exploitable equations are found.

Fault attacks are among the well-studied topics in the area of cryptography. These attacks constitute a powerful tool to recover the secret key used in the encryption process. Fault attacks work by forcing a device to work under non-ideal environmental conditions (such as high temperature) or external disturbances (such as glitch in the power supply) while performing a cryptographic operation. The recent trend shows that the amount of research in this direction; which ranges from attacking a particular primitive, proposing a fault countermeasure, to attacking countermeasures; has grown up substantially and going to stay as an active research interest for a foreseeable future. Hence, it becomes apparent to have a comprehensive yet compact study of the (major) works. This work, which covers a wide spectrum in the present day research on fault attacks that fall under the purview of the symmetric key cryptography, aims at fulfilling the absence of an up-to-date survey. We present mostly all aspects of the topic in a way which is not only understandable for a non-expert reader, but also helpful for an expert as a reference.

This paper considers a problem of identifying matching attacks against Romulus-M, one of the ten finalists of NIST Lightweight Cryptography standardization project. Romulus-M is provably secure, i.e., there is a theorem statement showing the upper bound on the success probability of attacking the scheme as a function of adversaries' resources. If there exists an attack that matches the provable security bound, then this implies that the attack is optimal, and that the bound is tight in the sense that it cannot be improved. We show that the security bounds of Romulus-M are tight for a large class of parameters by presenting concrete matching attacks.

We introduce a generalization of substitution permutation networks using quasigroups. Then, we prove that for quasigroups isotopic with a group $\mathbb{G}$, the complexity of mounting a differential attack against our generalization is the same as attacking a substitution permutation network based on $\mathbb{G}$. Although the result is negative, we believe that the design can be instructional for teaching students that failure is a natural part of research. Also, we hope to prevent others from making the same mistake by showing where such a path leads.

Constant blinding is an efficient countermeasure against just-in-time (JIT) spraying attacks. Unfortunately, this mitigation mechanism is not always implemented correctly. One such example is the constant blinding mechanism found in the Adobe Flash Player. Instead of choosing a strong mainstream pseudo-random number generator (PRNG), the Flash Player designers chose to implement a proprietary one. This led to the discovery of a vulnerability that can be exploited to recover the initial seed used by the PRNG and thus, to bypass the constant blinding mechanism. Using this vulnerability as a starting point, we show that no matter the parameters used by the previously mentioned PRNG it still remains a weak construction. A consequence of this study is an improvement of the seed recovering mechanism from previously known complexity of $\mathcal O(2^{21})$ to one of $\mathcal O(2^{11})$.

eSTREAM brought to the attention of the cryptographic community a number of stream ciphers including Grain v0 and its revised version Grain v1. The latter was selected as a finalist of the competition's hardware-based portfolio. The Grain family includes two more instantiations, namely Grain 128 and Grain 128a. The scope our paper is to provide an insight on how to obtain secure configurations of the Grain family of stream ciphers. We propose different variants for Grain and analyze their security with respect to slide attacks. More precisely, as various attacks against initialization algorithms of Grain were discussed in the literature, we study the security impact of various parameters which may influence the LFSR's initialization scheme.

At CRYPTO'19, A. Gohr proposed neural distinguishers for the lightweight block cipher Speck32/64, achieving better results than the state-of-the-art at that point. However, the motivation for using that particular architecture was not very clear, leading us to investigate whether a smaller and/or better performing neural distinguisher exists. This paper studies the depth-10 and depth-1 neural distinguishers proposed by Gohr with the aim of finding out whether smaller or better-performing distinguishers for Speck32/64 exist. We first evaluate whether we can find smaller neural networks that match the accuracy of the proposed distinguishers. We answer this question in affirmative with the depth-1 distinguisher successfully pruned, resulting in a network that remained within one percentage point of the unpruned network's performance. Having found a smaller network that achieves the same performance, we examine if its performance can be improved as well. We also study whether processing the input before giving it to the pruned depth-1 network would improve its performance. To this end, convolutional autoencoders were found that managed to reconstruct the ciphertext pairs successfully, and their trained encoders were used as a preprocessor before training the pruned depth-1 network. We found that, even though the autoencoders achieve a perfect reconstruction, the pruned network did not have the necessary complexity anymore to extract useful information from the preprocessed input, motivating us to look at the feature importance to get more insights. To achieve this, we used LIME, with results showing that a stronger explainer is needed to assess it correctly.

Profiling side-channel analysis allows evaluators to estimate the worst-case security of a target. When security evaluations relax the assumptions about the adversary's knowledge, profiling models may easily be sub-optimal due to the inability to extract the most informative points of interest from the side-channel measurements. When used for profiling attacks, deep neural networks can learn strong models without feature selection with the drawback of expensive hyperparameter tuning. Unfortunately, due to very large search spaces, one usually finds very different model behaviors, and a widespread situation is to face overfitting with typically poor generalization capacity. Usually, overfitting or poor generalization would be mitigated by adding more measurements to the profiling phase to reduce estimation errors. This paper provides a detailed analysis of different deep learning model behaviors and shows that adding more profiling traces as a single solution does not necessarily help improve generalization. In fact, we recognize the main problem to be the sub-optimal selection of hyperparameters, which is then difficult to resolve by simply adding more measurements. Instead, we propose to use small hyperparameter tweaks or regularization as techniques to resolve the problem.

Authenticated encryption (AE) is a symmetric-key encryption function that provides confidentiality and authenticity of a message. One of the evaluation criteria for AE is state size, which is memory size needed for encryption. State size is especially important when cryptosystem is implemented in constrained devices, while trivial reduction by using a small primitive is not generally acceptable as it leads to a degraded security. In these days, the state size of AE has been very actively studied and a number of small-state AE schemes have been proposed, but they are inherently serial. It would be a natural question if we come up with a parallelizable AE with a smaller state size than the state-of-the-art. In this paper, we study the seminal OCB mode for parallelizable AE and propose a method to reduce its state size without losing the bit security of it. More precisely, while (the most small-state variant of) OCB has $3n$-bit state, by carefully treating the checksum that is halved, we can achieve $2.5n$-bit state, while keeping the $n/2$-bit security as original. We also propose an inverse-free variant of it based on OTR. While the original OTR has $4n$-bit state, ours has $3.5n$-bit state. To our knowledge these numbers are the smallest ones achieved by the blockcipher modes for parallel AE and inverse-free parallel AE.

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 efficient evaluation over common FHE libraries are often overlooked, compromising their real-world performance. Whilst FASTA may also be considered as a variant of Rasta, it has its parameters and linear layer especially chosen to allow efficient implementation over the BGV scheme, particularly as implemented in the HElib library. This results in a speedup by a factor of 25 compared to the most efficient publicly available implementation of Rasta. FASTA’s target is BGV, as implemented in HElib. However the design ideas introduced in the cipher could also be potentially employed to achieve improvements in the homomorphic evaluation in other popular FHE schemes/libraries. We do consider such alternatives in this paper (e.g. BFV and BGVrns, as implemented in SEAL and PALISADE), but argue that, unlike BGV in HElib, it is more challenging to make use of their parallelism in a Rasta-like stream cipher design.

At CRYPTO 2019, Chen et al. have shown a beyond the birthday bound secure $n$-bit to $n$-bit PRF based on public random permutations. Followed by the work, Dutta and Nandi have proposed a beyond the birthday bound secure nonce based MAC $\textsf{nEHtM}_p$ based on public random permutation. In particular, the authors have shown that $\textsf{nEHtM}_p$ achieves tight $2n/3$-bit security ({\em with respect to the state size of the permutation}) in the single-user setting, and their proven bound gracefully degrades with the repetition of the nonces. However, we have pointed out that their security proof is not complete (albeit it does not invalidate their security claim). In this paper, we propose a minor variant of $\textsf{nEHtM}_p$ construction, called $\textsf{nEHtM}^*_p$ and show that it achieves a tight $2n/3$ bit security in the multi-user setting. Moreover, the security bound of our construction also degrades gracefully with the repetition of nonces. Finally, we have instantiated our construction with the PolyHash function to realize a concrete beyond the birthday bound secure public permutation-based MAC, $\textsf{nEHtM}_p^+$ in the multi-user setting.

In recent years, oblivious pseudorandom functions (OPRFs) have become a ubiquitous primitive used in cryptographic protocols and privacy-preserving technologies. The growing interest in OPRFs, both theoretical and applied, has produced a vast number of different constructions and functionality variations. In this paper, we provide a systematic overview of how to build and use OPRFs. We first categorize existing OPRFs into essentially four families based on their underlying PRF (Naor-Reingold, Dodis-Yampolskiy, Hashed Diffie-Hellman, and generic constructions). This categorization allows us to give a unified presentation of all oblivious evaluation methods in the literature, and to understand which properties OPRFs can (or cannot) have. We further demonstrate the theoretical and practical power of OPRFs by visualizing them in the landscape of cryptographic primitives, and by providing a comprehensive overview of how OPRFs are leveraged for improving the privacy of internet users. Our work systematizes 15 years of research on OPRFs and provides inspiration for new OPRF constructions and applications thereof.

SKINNY-AEAD is one of the second-round candidates of the Lightweight Cryptography Standardization project held by NIST. SKINNY-AEAD M1 is the primary member of six SKINNY-AEAD schemes, while SKINNY-AEAD M3 is another member with a small tag. In the design document, only security analyses of their underlying primitive SKINNY-128-384 are provided. Besides, there are no valid third-party analyses on SKINNY-AEAD M1/M3 according to our knowledge. Therefore, this paper focuses on constructing the first third-party security analyses on them under a nonce-respecting scenario. By taking the encryption mode of SKINNY-AEAD into consideration and exploiting several properties of SKINNY, we can deduce some necessary constraints on the input and tweakey differences of related-tweakey impossible differential distinguishers. Under these constraints, we can find distinguishers suitable for mounting powerful tweakey recovery attacks. With the help of the automatic searching algorithms based on STP, we find some 14-round distinguishers. Based on one of these distinguishers, we mount a 20-round and an 18-round tweakey recovery attack on SKINNY-AEAD M1/M3. To the best of our knowledge, all these attacks are the best ones so far.

RSA cryptography is an asymmetric communication protocol, and it is facing diverse issues. Recent research works suggest that RSA security has already broken. On the contrary, AES is the most used symmetric-key cryptography protocol, and it is also facing issues. Literature search suggests that there is an issue of cryptanalysis attacks. A shared secret key requires for AES cryptography. The most famous key exchange protocol is Diffie-Hellman; however, it has an issue of the number field sieve discrete log algorithm attacks. Moreover, recent research suggested that Diffie-Hellman is less secure than widely perceived. Moreover, there is another issue of Logjam attack that allows man-in-middle attack in Diffie-Hellman. Thus, we combine RSA, AES, and Diffie-Hellman algorithm to provide security on the key exchange protocol, called privateDH. Our key objective is to provide security to the Diffie-Hellman Algorithm. Therefore, privateDH does not share the data publicly with the intended party. Instead, privateDH encrypts all shareable data in the time of key exchange by encrypting using the AES algorithm. privateDH uses the RSA algorithm and retrieves the public key to avoid a man-in-the-middle attack. Thus, we demonstrate how to provide security to the Diffie-Hellman algorithm to defeat various kinds of attacks.

In order to provide benefits in the areas of fully homomorphic encryption (FHE), multi-party computation (MPC), post-quantum signature schemes, or efficient masked implementations for side-channel resistance, reducing the number of multiplications has become a quite popular trend for the symmetric cryptographic primitive designs. With an aggressive design strategy exploiting the extremely simple and low-degree S-box and low number of rounds, Pyjamask, the fundamental block cipher of the AEAD with the same name, has the smallest number of AND gates per bit among all the existing block ciphers (except LowMC or Rasta which work on unconventional plaintext/key sizes). Thus, although the AEAD Pyjamask stuck at the second round of the NIST lightweight cryptography standardization process, the block cipher Pyjamask itself still attracts a lot of attention. Not very unexpectedly, the low degree and the low number of rounds are the biggest weakness of Pyjamask. At FSE 2020, Dobraunig et al. successfully mounted an algebraic and higher-order differential attack on full Pyjamask-96, one member of the Pyjamask block cipher family. However, the drawback of this attack is that it has to use the full codebook, which makes the attack less appealing. In this paper, we take integral attacks as our weapon, which are also sensitive to the low degree. Based on a new 11-round integral distinguisher found by state-of-the-art detection techniques, and combined with the relationship between round keys that reduces the involved keys, we give the key recovery attack on the full Pyjamask-96 without the full codebook for the first time. Further, the algebraic and higher-order differential technique does not work for Pyjamask-128, the other member of the Pyjamask block cipher family. To better understand the security margin of Pyjamask-128, we present the first third-party cryptanalysis on Pyjamask-128 up to 11 out of 14 rounds.

The Even-Mansour cipher is a simple method for constructing a (keyed) pseudorandom permutation $E$ from a public random permutation $P:\{0,1\}^n \rightarrow \{0,1\}^n$. It is a core ingredient in a wide array of symmetric-key constructions, including several lightweight cryptosystems presently under consideration for standardization by NIST. It is secure against classical attacks, with optimal attacks requiring $q_E$ queries to $E$ and $q_P$ queries to $P$ such that $q_E \cdot q_P \approx 2^n$. If the attacker is given *quantum* access to both $E$ and $P$, however, the cipher is completely insecure, with attacks using $q_E, q_P = O(n)$ queries known. In any plausible real-world setting, however, a quantum attacker would have only *classical* access to the keyed permutation $E$ implemented by honest parties, while retaining quantum access to $P$. Attacks in this setting with $q_E \cdot q_P^2 \approx 2^n$ are known, showing that security degrades as compared to the purely classical case, but leaving open the question as to whether the Even-Mansour cipher can still be proven secure in this natural ``post-quantum'' setting. We resolve this question, showing that any attack in that setting requires $q_E \cdot q^2_P + q_P \cdot q_E^2 \approx 2^n$. Our results apply to both the two-key and single-key variants of Even-Mansour. Along the way, we establish several generalizations of results from prior work on quantum-query lower bounds that may be of independent interest.

A well-established PRP-to-PRF conversion design is truncation: one evaluates an $n$-bit pseudorandom permutation on a certain input, and truncates the result to $a$ bits. The construction is known to achieve tight $2^{n-a/2}$ security. Truncation has gained popularity due to its appearance in the GCM-SIV key derivation function (ACM CCS 2015). This key derivation function makes four evaluations of AES, truncates the outputs to $n/2$ bits, and concatenates these to get a $2n$-bit subkey. In this work, we demonstrate that truncation is wasteful. In more detail, we present the Summation-Truncation Hybrid (STH). At a high level, the construction consists of two parallel evaluations of truncation, where the truncated $(n-a)$-bit chunks are not discarded but rather summed together and appended to the output. We prove that STH achieves a similar security level as truncation, and thus that the $n-a$ bits of extra output is rendered for free. In the application of GCM-SIV, the current key derivation can be used to output $3n$ bits of random material, or it can be reduced to three primitive evaluations. Both changes come with no security loss.

One oft-endeavored security property for cryptographic hash functions is collision resistance: it should be computationally infeasible to find distinct inputs $x,x'$ such that $H(x) = H(x')$, where $H$ is the hash function. Unruh (EUROCRYPT 2016) proposed collapseability as its quantum equivalent. The Merkle-Damgård and sponge hashing modes have recently been proven to be collapseable under the assumption that the underlying primitive is collapseable. These modes are inherently sequential. In this work, we investigate collapseability of tree hashing. We first consider fixed length tree hashing modes, and derive conditions under which their collapseability can be reduced to the collapseability of the underlying compression function. Then, we extend the result to two methods for achieving variable length hashing: tree hashing with domain separation between message and chaining value, and tree hashing with length encoding at the end of the tree. The proofs are performed using the collapseability composability framework of Fehr (TCC 2018), that allows us to discard of deeply technical quantum details and to focus on proper composition of the tree hashes from their compression function.

We present two tweakable wide block cipher modes from doubly-extendable cryptographic keyed (deck) functions and a keyed hash function: double-decker and docked-double-decker. Double-decker is a direct generalization of Farfalle-WBC of Bertoni et al. (ToSC 2017(4)), and is a four-round Feistel network on two arbitrarily large branches, where the middle two rounds call deck functions and the first and last rounds call the keyed hash function. Docked-double-decker is a variant of double-decker where the bulk of the input to the deck functions is moved to the keyed hash functions. We prove that the distinguishing advantage of the resulting wide block ciphers is simply two times the sum of the pseudorandom function distinguishing advantage of the deck function and the blinded keyed hashing distinguishing advantage of the keyed hash functions. We demonstrate that blinded keyed hashing is more general than the conventional notion of XOR-universality, and that it allows us to instantiate our constructions with keyed hash functions that have a very strong claim on bkh security but not necessarily on XOR-universality, such as Xoofffie (ePrint 2018/767). The bounds of double-decker and docked-double-decker are moreover reduced tweak-dependent, informally meaning that collisions on the keyed hash function for different tweaks only have a limited impact. We describe two use cases that can exploit this property opportunistically to get stronger security than what would be achieved with prior solutions: SSD encryption, where each sector can only be written to a limited number of times, and incremental tweaks, where one includes the state of the system in the variable-length tweak and appends new data incrementally.

GIFT-64 is a 64-bit block cipher with a 128-bit key that is more lightweight than PRESENT. This paper provides a detailed analysis of GIFT-64 against differential and linear attacks. Our work complements automatic search methods for the best differential and linear characteristics with a careful manual analysis. This hybrid approach leads to new insights. In the differential setting, we theoretically explain the existence of differential characteristics with two active S-boxes per round and derive some novel properties of these characteristics. Furthermore, we prove that all optimal differential characteristics of GIFT-64 covering more than seven rounds must activate two S-boxes per round. We can construct all optimal characteristics by hand. In parallel to the work in the differential setting, we conduct a similar analysis in the linear setting. However, unlike the clear view in differential setting, the optimal linear characteristics of GIFT-64 must have at least one round activating only one S-box. Moreover, with the assistance of automatic searching methods, we identify 24 GIFT-64 variants achieving better resistance against differential attack while maintaining a similar security level against a linear attack. Since the new variants strengthen GIFT-64 against statistical cryptanalysis, we claim that the number of rounds could be reduced from 28 to 26 for the variants. This observation enables us to create a cipher with lower energy consumption than GIFT-64. Similarly to the case in GIFT-64, we do not claim any related-key security for the round-reduced variant as this is not relevant for most applications.

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 natural question arises: (how) do the details of the linear layer influence the growth of the algebraic degree? We show that the linear layer plays a crucial role in the growth of the algebraic degree and present a new upper bound on the algebraic degree in SP-networks. As main results, we prove that in the case of low-degree round functions with large S-Boxes: $\textit{(a)}$ an initial exponential growth of the algebraic degree can be followed by a linear growth until the maximum algebraic degree is reached; $\textit{(b)}$ the rate of the linear growth is proportional to the degree of the linear layer over $\mathbb{F}_{2^n}^t$. Besides providing a theoretical insight, our analysis is particularly relevant for assessing the security of cryptographic permutations designed to be competitive in applications like MPC, FHE, SNARKs, and STARKs, including permutations based on the Hades design strategy. We have verified our findings on small-scale instances and we have compared them against the currently best results in the literature, showing a substantial improvement of upper bounds on the algebraic degree in case of low-degree round functions with large S-Boxes.

Mixed integer linear programming (MILP) based tools are used to estimate the strength of block ciphers against the cryptanalytic attacks. The existing tools use partial difference distribution table (p-DDT) approach to optimize the probability of differential characteristics for large (≥8-bit) S-box based ciphers. We propose to use the full difference distribution table (DDT) with the probability of each possible propagation for MILP modeling of large S-boxes. This requires more than 16 variables to represent the linear inequalities of each propagation and corresponding probabilities. The existing tools (viz. Logic Friday) cannot handle the linear inequalities in more than 16 variables. In this paper, we present a new tool (namely MILES) to minimize the linear inequalities in more than 16 variables. This tool reduces the number of inequalities by minimizing the truth table corresponding to the DDT of S-box. We use our tool to minimize the linear inequalities for 8-bit S-boxes (AES and SKINNY) and get better results than existing tools. We show the application of MILES on 8-bit S-box based lightweight block cipher PIPO. There are 20621 inequalities in 23 variables corresponding to the possible propagations in DDT and these are minimized to 6035 inequalities using MILES. MILP model based on these linear inequalities is used to optimizethe probability of differential characteristics for round-reduced PIPO. MILP model based on these inequalities is used to optimize the probability of differential and impossible differential characteristics for PIPO-64/128 reduced to 9 and 4 rounds respectively. We present an iterative 2-round related-key differential characteristic with the probability of 2^{-4} and that is used to construct a full round related-key differential distinguisher with the probability of 2^{-24}. We present a major collision in PIPO-64/128 which produces the same ciphertext (C) by encrypting the plaintext (P) under two different keys.

BORON is a 64-bit lightweight block cipher based on the substitution-permutation network that supports an 80-bit (BORON-80) and 128-bit (BORON-128) secret key. In this paper, we revisit the use of differential cryptanalysis on BORON in the single-key model. Using an SAT/SMT approach, we look for differentials that consist of multiple differential characteristics with the same input and output differences. Each characteristic that conforms to a given differential improves its overall probability. We also implemented the same search using Matsui's algorithm for verification and performance comparison purposes. We identified high-probability differentials which were then used in key recovery attacks against BORON-80/128. We first show that the previous differential cryptanalysis attack against 9-round of BORON was at most an 8.5 round attack due to the omission of the final block XOR layer. Then, we used 8-round differentials with a probability of $2^{-58.156}$ and $2^{-62.415}$ in key recovery attacks against 9 and 10 rounds of BORON-80 and BORON-128 with time/data/memory complexities of {$2^{63.63}/2^{62}/2^{55}$ and $2^{100.28}/2^{64}/2^{71}$} respectively. Our key recovery framework provides a more accurate estimate of the attack complexity as compared to previous work. The attacks proposed in this paper are the best differential attacks against BORON-80/128 in the single-key model to date.

The differential uniformity, the boomerang uniformity, and the extended Walsh spectrum etc are important parameters to evaluate the security of S(substitution)-box. In this paper, we introduce efficient formulas to compute these cryptographic parameters of permutation polynomials of the form $x^rh(x^{(q-1)/d})$ over a finite field of $q=2^n$ elements, where $r$ is a positive integer and $d$ is a positive divisor of $q-1$. The computational cost of those formulas is proportional to $d$. We investigate differentially 4-uniform permutation polynomials of the form $x^rh(x^{(q-1)/3})$ and compute the boomerang spectrum and the extended Walsh spectrum of them using the suggested formulas when $4\le n\le 10$ is even, where $d=3$ is the smallest nontrivial $d$ for even $n$. We also investigate the differential uniformity of some permutation polynomials introduced in some recent papers for the case $d=2^{n/2}+1$

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 heuristic search of lightweight implementation for linear layers. Most of the prior approach iteratively combines the inputs (of linear layers) to reach the output, which can be regarded as the forward search. To better adapt the low-latency criteria, we propose a new framework of backward search that attempts to iteratively split every output (into an XORing of two bits) until all inputs appear. By bounding the time of splitting, the new framework can find a sub-optimal solution with a minimized depth of circuits. We apply our new search algorithm to linear layers of block ciphers and find many low-latency candidates for implementations. Notably, for AES Mixcolumns, we provide an implementation with 103 XOR gates with a depth of 3, which is among the best hardware implementations of the AES linear layer. Besides, we obtain better implementations in XOR gates for 54.3% of 4256 Maximum Distance Separable (MDS) matrices proposed by Li et al. at FSE 2019. We also achieve an involutory MDS matrix (in M4(GL(8, F_2))) whose implementation uses the lowest number (i.e., 86, saving 2 from the state-of-the-art result) of XORs with the minimum depth.

With the advancement of the quantum computing technologies, a large body of research work is dedicated to revisit the security claims for ciphers being used. An adversary with access to a quantum computer can employ certain new attacks which would not be possible in the current pre-quantum era. In particular, the Grover's search algorithm is a generic attack against symmetric key cryptographic primitives, that can reduce the search complexity to square root. To apply the Grover's search algorithm, one needs to implement the target cipher as a quantum circuit. Although relatively recent, this field of research has attracted serious attention from the research community, as several ciphers (like AES, GIFT, SPECK, SIMON etc.) are being implemented as quantum circuits. In this work, we target the lightweight block cipher RECTANGLE and the Authenticated Encryption with Associated Data (AEAD) KNOT which is based on RECTANGLE; and implement those in the ProjectQ library (an open-source quantum compatible library designed by researchers from ETH Zurich). AEADs are considerably more complex to implement than a typical block/stream cipher, and ours is among the first works to do this.

Neural aided cryptanalysis is a challenging topic, in which the neural distinguisher (N D) is a core module. In this paper, we propose a new N D considering multiple ciphertext pairs simultaneously. Besides, multiple ciphertext pairs are constructed from different keys. The motivation is that the distinguishing accuracy can be improved by exploiting features derived from multiple ciphertext pairs. To verify this motivation, we have applied this new N D to five different ciphers. Experiments show that taking multiple ciphertext pairs as input indeed brings accuracy improvement. Then, we prove that our new N D applies to two different neural aided key recovery attacks. Moreover, the accuracy improvement is helpful for reducing the data complexity of the neural aided statistic attack. The code is available at https://github.com/AI-Lab-Y/ND_mc.

When generating quartets for the rectangle attacks on ciphers with linear key-schedule, we find the right quartets which may suggest key candidates have to satisfy some nonlinear relations. However, some quartets generated always violate these relations, so that they will never suggest any key candidates. Inspired by previous rectangle frameworks, we find that guessing certain key cells before generating quartets may reduce the number of invalid quartets. However, guessing a lot of key cells at once may lose the benefit from the early abort technique, which may lead to a higher overall complexity. To get better tradeoff, we build a new rectangle framework on ciphers with linear key-schedule with the purpose of reducing overall complexity or attacking more rounds. In the tradeoff model, there are many parameters affecting the overall complexity, especially for the choices of the number and positions of key guessing cells before generating quartets. To identify optimal parameters, we build a uniform automatic tool on SKINNY as an example, which includes the optimal rectangle distinguishers for key-recovery phase, the number and positions of guessing key cells before generating quartets, the size of key counters to build that affecting the exhaustive search step, etc. Based on the automatic tool, we identify a 32-round key-recovery attack on SKINNY-128-384 in the related-key setting, which extends the best previous attack by 2 rounds. For other versions with n-2n or n-3n, we also achieve one more round than before. In addition, using the previous rectangle distinguishers, we achieve better attacks on round-reduced ForkSkinny, Deoxys-BC-384 and GIFT-64. At last, we discuss the conversion of our rectangle framework from related-key setting into single-key setting and give new single-key rectangle attack on 10-round Serpent.

COFB is a lightweight Authenticated Encryption with Associated Data (AEAD) mode based on block ciphers. It was proposed in CHES 2017 and is the basis for GIFT-COFB, a finalist in the NIST lightweight standardization project. It comes with provable security results that guarantee its security up to the birthday bound in the nonce-respecting model. However, the designers offer multiple versions of the analysis with different details and the implications of attacks against the scheme are not discussed deeply. In this article, we look at a group of possible forgery and privacy attacks against COFB. We show that the security for both forgery and privacy is bounded by the number of forgery attempts. We show the existence of forgery and privacy attacks with success probability $q_d/2^{n/2}$, given $q_d$ forgery attempts. In particular, we show an attack with $2^{n/2}$ attempts using only a single known-plaintext encryption query against COFB. While these attacks do not contradict the claims made by the designers of GIFT-COFB, they show its limitations in terms of the number of forgery attempts. They also show that, while COFB generates a 128-bit tag, it behaves in a very similar manner to an AEAD scheme with 64-bit tag. As a result of independent interest, our analysis provides a contradiction to the main theorem of {\it Journal of Cryptology volume 33, pages 703–741 (2020)}, which includes an improved security proof of COFB compared to the CHES 2017 version. Finally, we discuss the term $nq_d/2^{n/2}$ that appears in the security proof of GIFT-COFB and CHES 2017, showing why there is a security gap between the provable results and the attacks. We emphasize that the results in this article do not threaten the security of GIFT-COFB in the scope of the NIST lightweight cryptography requirements or the claims made by the designers in the specification document of the design.

In this work, we present a hardware implementation of the lightweight Authenticated Encryption with Associated Data (AEAD) SpoC-128. Designed by AlTawy, Gong, He, Jha, Mandal, Nandi and Rohit; SpoC-128 was submitted to the Lightweight Cryptography (LWC) competition being organised by the National Institute of Standards and Technology (NIST) of the United States Department of Commerce. Our implementation follows the Application Programming Interface (API) specified by the cryptographic engineering research group in the George Mason University (GMU). The source codes are available over the public internet as an open-source project.

Motivated by modern cryptographic use cases such as multi-party computation (MPC), homomorphic encryption (HE), and zero-knowledge (ZK) protocols, several symmetric schemes that are efficient in these scenarios have recently been proposed in the literature. Some of these schemes are instantiated with low-degree nonlinear functions, for example low-degree power maps (e.g., MiMC, HadesMiMC, Poseidon) or the Toffoli gate (e.g., Ciminion). Others (e.g., Rescue, Vision, Grendel) are instead instantiated via high-degree functions which are easy to evaluate in the target application. A recent example for the latter case is the hash function Grendel, whose nonlinear layer is constructed using the Legendre symbol. In this paper, we analyze high-degree functions such as the Legendre symbol or the modulo-2 operation as building blocks for the nonlinear layer of a cryptographic scheme over (F_p)^n. Our focus regards the security analysis rather than the efficiency in the mentioned use cases. For this purpose, we present several new invertible functions that make use of the Legendre symbol or of the modulo-2 operation. Even though these functions often provide strong statistical properties and ensure a high degree after a few rounds, the main problem regards their small number of possible outputs, that is, only three for the Legendre symbol and only two for the modulo-2 operation. By fixing them, it is possible to reduce the overall degree of the function significantly. We exploit this behavior by describing the first preimage attack on full Grendel, and we verify it in practice.

In ToSC 2021(2), Sun et al. implemented an automatic search with the Boolean satisfiability problem (SAT) method on GIFT-128 and identified a 19-round linear approximation with the expected linear potential being $2^{-117.43}$, which is utilised to launch a 24-round attack on the cipher. In this addendum, we discover a new 19-round linear approximation with a lower expected linear potential. However, in the attack, one more round can be appended after the distinguisher. As a result, we improve the previous optimal linear attack by one round and put forward a 25-round linear attack. Given that the optimal differential attack on GIFT-128, for now, covers 27-round, the resistances of the cipher against differential and linear attacks still have a 2-round gap.

Bent functions are optimal combinatorial objects and have been studied over the last four decades. Secondary construction plays a central role in constructing bent functions since it may generate bent functions outside the primary classes of bent functions. In this study, we improve a theoretical framework of the secondary construction of bent functions in terms of the composition of Boolean functions. Based on this framework, we propose several constructions of bent functions through the composition of a balanced Boolean function and dually isomorphic (DI) bent functions defined herein. In addition, we present a construction of self-dual bent functions.

Related-key attacks (RKA) are powerful cryptanalytic attacks, where the adversary can tamper with the secret key of a cryptographic scheme. Since their invention, RKA security has been an important design goal in cryptography, and various works aim at designing cryptographic primitives that offer protection against related-key attacks. At EUROCRYPT'03, Bellare and Kohno introduced the first formal treatment of related-key attacks focusing on pseudorandom functions and permutations. This was later extended to cover other primitives such as signatures and public key encryption schemes, but until now, a comprehensive formal security analysis of authenticated encryption schemes with associated data (AEAD) in the RKA setting has been missing. The main contribution of our work is to close this gap for the relevant class of nonce-based AEAD schemes. To this end, we revisit the common approach to construct AEAD from encryption and message authentication. We extend the traditional security notion of AEAD to the RKA setting and consider an adversary that can tamper with the key $K_e$ and $K_m$ of the underlying encryption and MAC, respectively. We study two security models. In our weak setting, we require that tampering will change both $K_e$ and $K_m$, while in our strong setting, tampering can be arbitrary, i.e., only one key might be affected. We then study the security of the standard composition methods by analysing the nonce-based AEAD schemes N1 (Encrypt-and-MAC), N2 (Encrypt-then-MAC), and N3 (MAC-then-Encrypt) due to Namprempre, Rogaway, and Shrimpton (EUROCRYPT'03). We show that these schemes are weakly RKA secure, while they can be broken under a strong related-key attack. Finally, based on the N3 construction, we give a novel AEAD scheme that achieves our stronger notion.

In 2009, Dinur and Shamir proposed the cube attack, an algebraic cryptanalysis technique that only requires black box access to a target cipher. Since then, this attack has received both many criticisms and endorsements from crypto community; this work aims at revising and collecting the many attacks that have been proposed starting from it. We categorise all of these attacks in five classes; for each class, we provide a brief summary description along with the state-of-the-art references and the most recent cryptanalysis results. Furthermore, we extend and refine the new notation we proposed in 2021 and we use it to provide a consistent definition for each attack family. Finally, in the appendix, we provide an in-depth description of the kite attack framework, a cipher independent tool we firstly proposed in 2018 that implements the kite attack on GPUs. To prove its effectiveness, we use Mickey2.0 as a use case, showing how to embed it in the framework.

Firstly, we improve the evaluation theory of differential propagation for modular additions and XORs, respectively. By introducing the concept of $additive$ $sums$ and using signed differences, we can add more information of value propagation to XOR differential propagation to calculate the probabilities of differential characteristics more precisely. Based on our theory, we propose the first modeling method to describe the general ARX differential propagation, which is not based on the Markov cipher assumption. Secondly, we propose an automatic search tool for differential characteristics with more precise probabilities in ARX ciphers. We find that some differential characteristics that used to be valid become impossible, and some probabilities that used to be underestimated increase. In applications, for CHAM-64/128 (one of the underlying block ciphers in COMET, one of 32 second-round candidates in NIST’s lightweight cryptography standardization process), we find that there is no valid $39$-round differential characteristic with a probability of $2^{-63}$ computed using previous methods, and we correct the probabilities to $2^{-64}$ and $2^{-64}$ instead of $2^{-65}$ and $2^{-65}$ computed using previous methods for two 39-round differential characteristics starting from the $1$-st round, respectively; however, if we search for differential characteristics starting from the $5$-th round, the two differential characteristics are invalid, which means that the round constants can affect the security of ARX ciphers against differential cryptanalysis; for Alzette with $c = \tt{0xb7e15162}$ (one of the S-boxes in SPARKLE, one of 10 finalists in NIST’s lightweight cryptography standardization process), we correct the probabilities to $0$ and $2^{-22}$ instead of $2^{-23}$ and $2^{-23}$ computed using previous methods for two 4-round differential characteristics, respectively; for XTEA, we correct the probabilities to $0$ and $2^{-49}$ instead of $2^{-58}$ and $2^{-56}$ computed using previous methods for two 10-round differential characteristics, respectively. Moreover, for Alzette with $c = \tt{0xb7e15162}$, XTEA, the $\tt{quarterround}$ function of Salsa20, and the round function of Chaskey, we find some invalid DCs that Leurent’s ARX Toolkit cannot detect. Thirdly, we propose a SAT-based automatic search tool for impossible differential characteristics in ARX ciphers. We find some distinguishers ignored by previous methods. In applications, for CHAM-64/128, we find five $20$-round and nineteen $19$-round impossible differential characteristics starting from the $3$-rd round for the first time. However, if we search for impossible differential characteristics starting from the $1$-st round, we cannot find any $20$-round impossible differential characteristic, which means that the round constants can affect the security of ARX ciphers against impossible differential cryptanalysis. Moreover, we find more impossible differential characteristics for 18-round, 16-round, 14-round, and 12-round CHAM-64/128, respectively. According to our results, the differential (resp. impossible differential) attack constructed by the previous methods of placing a DC (resp. an ID) anywhere in a block cipher may be invalid.

This paper proposes functional cryptanalysis, a flexible and versatile approach to analyse symmetric-key primitives with two primary features. Firstly, it is a generalization of multiple attacks including (but not limited to) differential, rotational and rotational-xor cryptanalysis. Secondly, it is a theoretical framework that unifies all of the aforementioned cryptanalysis techniques and at the same time opens up possibilities for the development of new cryptanalytic approaches. The main idea of functional cryptanalysis is the usage of binary relations in the form of functions, hence the name functional, instead of binary operations like in a classical settings of "differential"-like cryptanalysis. We establish the theoretical foundations of functional cryptanalysis from standard terminologies. This work also presents an interpretation of functional cryptanalysis from the point of view of commutative algebra. In particular, we exhibit an algorithm to compute the functional probability (hence differential, rotational, and rotational-xor probability) using Grobner bases. We demonstrate the applicability of functional cryptanalysis against reduced-round Xoodoo and compare it against the best differential. To avoid dealing with invalid differential trails, we propose a method to construct a valid differential trail using Satisfiability Modulo Theory (SMT). To the best of our knowledge, this is the first time the SMT model is used to construct a valid differential while previous approaches rely on Mixed-Integer Linear Programming (MILP) model. Lastly, we remark that the use of non-translation functionals shares analogous advantages and limitations with the use of nonlinear approximations in linear cryptanalysis.

Security of the many keyed hash-based cryptographic constructions (such as HMAC) depends on the fact that the underlying compression function $g(H,M)$ is a pseudorandom function (PRF). This paper presents key-recovery algorithms for 7 rounds (of 12) of Streebog compression function. Two cases were considered, as a secret key can be used: the previous state $H$ or the message block $M$. The proposed methods implicitly show that Streebog compression function has a large security margin as PRF in the above-mentioned secret-key settings.

In this paper, a method for searching correlations between the binary stream of Linear Feedback Shift Register (LFSR) and the keystream of SNOW-V and SNOW-Vi is presented based on the technique of approximation to composite functions. With the aid of the linear relationship between the four taps of LFSR input into Finite State Machine (FSM) at three consecutive clocks, we present an automatic search model based on the SAT/SMT technique and search out a series of linear approximation trails with high correlation. By exhausting the intermediate masks, we find a binary linear approximation with a correlation $-2^{-47.76}$. Using such approximation, we propose a correlation attack on SNOW-V with an expected time complexity $2^{246.53}$, a memory complexity $2^{238.77}$ and $2^{237.5}$ keystream words generated by the same key and Initial Vector (IV). For SNOW-Vi, we provide a binary linear approximation with the same correlation and mount a correlation attack with the same complexity as that of SNOW-V. To the best of our knowledge, this is the first known attack on full SNOW-V and SNOW-Vi, which is better than the exhaustive key search with respect to time complexity. The results indicate that neither SNOW-V nor SNOW-Vi can guarantee the 256-bit security level if we ignore the design constraint that the maximum length of keystream for a single pair of key and IV is less than $2^{64}$.

Industry 4.0 is all about doing things in a concurrent, secure, and fine-grained manner. IoT edge-sensors and their associated data play a predominant role in today's industry ecosystem. Breaching data or forging source devices after injecting advanced persistent threats (APT) damages the industry owners' money and loss of operators' lives. The existing challenges include APT injection attacks targeting vulnerable edge devices, insecure data transportation, trust inconsistencies among stakeholders, incompliant data storing mechanisms, etc. Edge-servers often suffer because of their lightweight computation capacity to stamp out unauthorized data or instructions, which in essence, makes them exposed to attackers. When attackers target edge servers while transporting data using traditional PKI-rendered trusts, consortium blockchain (CBC) offers proven techniques to transfer and maintain those sensitive data securely. With the recent improvement of edge machine learning, edge devices can filter malicious data at their end which largely motivates us to institute a Blockchain and AI aligned APT detection system. The unique contributions of the paper include efficient APT detection at the edge and transparent recording of the detection history in an immutable blockchain ledger. In line with that, the certificateless data transfer mechanism boost trust among collaborators and ensure an economical and sustainable mechanism after eliminating existing certificate authority. Finally, the edge-compliant storage technique facilitates efficient predictive maintenance. The respective experimental outcomes reveal that the proposed technique outperforms the other competing systems and models.

We determine the exact AND-gate cost of checking if $a\leq x < b$, where $a$ and $b$ are constant integers. Perhaps surprisingly, we find that the cost of interval checking never exceeds that of a single comparison and, in some cases, it is even lower.

In this paper we propose the linear hull construction for block ciphers with quadratic Maiorana-McFarland structure round functions. The search for linear trails with high squared correlations from our Maiorana-McFarland structure based constructive linear cryptanalysis is linear algebraic. Hence from this linear algebraic essence, the space of all linear trails has the structure such that good linear hulls can be constructed. Then for the Simon2n and its variants, we prove the lower bound $\frac{1}{2^n}$ on the potential of the linear hull with the fixed input and output masks at arbitrary long rounds, under independent assumptions. We argue that for Simon2n the potential of the realistic linear hull of the Simon2n with the linear key-schedule should be bigger than $\frac{1}{2^{2n}}$.\\ On the other hand we prove that the expected differential probability (EDP) is at least $\frac{1}{2^n}$ under the independence assumptions. It is argued that the lower bound of EDP of Simon2n of realistic differential trails is bigger than $\frac{1}{2^{2n}}$. It seems that at least theoretically the Simon2n is insecure for the key-recovery attack based on our new constructed linear hulls and key-recovery attack based on our constructed differential trails.\\

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 half the state. Consequently, it reveals a class of weak keys for which CRAFT is less resistant against differential and linear cryptanalyses. As a result, we present one weak-key single-tweak differential attack on 23 rounds (with time complexity of $2^{94}$ encryptions and data complexity of $2^{74}$ chosen plaintext/tweak/ciphertext tuples and works for $2^{112}$ weak keys) and one weak-key related-tweak attack on 26 rounds of the cipher (with time complexity of $2^{105}$ encryptions and data complexity $2^{73}$ chosen plaintext/tweak/ciphertext tuples and works for $2^{108}$ weak keys). Note that these attacks do not break the security claim of the CRAFT block cipher.

Despite intensive research on Boolean functions for cryptography for over thirty years, there are very few known general constructions allowing to satisfy all the necessary criteria for ensuring the resistance against all the main known attacks on the stream ciphers using them. In this paper, we investigate the general construction of Boolean functions $f$ from vectorial functions, in which the support of $f$ equals the image set of an injective vectorial function $F$, that we call a parameterization of $f$. Any Boolean function whose Hamming weight is a power of 2, and in particular, every balanced Boolean function, can be obtained this way. We study five illustrations of this general construction. The three first correspond to known classes of functions (Maiorana-McFarland, majority functions and balanced functions in odd numbers of variables with optimal algebraic immunity). The two last correspond to new classes of Boolean functions: - sums of indicators of disjoint graphs of $(k,n-k$)-functions, - functions parameterized by highly nonlinear injective vectorial $(n-1,n)$-functions derived from functions due to Beelen and Leander. We study the cryptographic parameters (corresponding to the main criteria) of balanced Boolean functions, according to those of their parameterizations: the algebraic degree of $f$, that we relate to the algebraic degrees of $F$ and of its graph indicator, the nonlinearity of $f$, that we relate by a bound to the nonlinearity of $F$, and the algebraic immunity (AI), whose optimality is related to a natural question in linear algebra, and which may be handled (in two ways) by means of the graph indicator of $F$. We show how the algebraic degree and the nonlinearity of the parameterized function can be controlled. We revisit each of the five classes for each criterion. We show that the fourth class is very promising, thanks to a lower bound on the nonlinearity by means of the nonlinearity of the chosen $(k,n-k$)-functions. Its sub-class made of the sums of indicators of affine functions, for which we prove an upper bound on the nonlinearity, seems also interesting. The fifth class includes functions with optimal algebraic degree, good nonlinearity and good AI. We leave for future works the determination of simple effective sufficient conditions on $F$ ensuring that $f$ has a good AI, the completion of the study of the fourth class, the mathematical study of the AI and fast algebraic immunity of the functions in the fifth class, and the introduction and study of a class of parameterized functions having good parameters and whose output is fast to compute.

We improve upon the security of (tweakable) correlation-robust hash functions, which are essential components of garbling schemes and oblivious-transfer extension schemes. We in particular focus on constructions from permutations, and improve upon the work by Guo et al. (IEEE S&P '20) in terms of security and efficiency. We present a tweakable one-call construction which matches the security of the most secure two-call construction -- the resulting security bound takes form O((p+q)q/2^n), where q is the number of construction evaluations and p is the number of direct adversarial queries to the underlying n-bit permutation, which is modeled as random. Moreover, we present a new two-call construction with much better security degradation -- in particular, for applications of interest, where only a constant number of evaluations per tweak are made, the security degrades as O((sqrt(q)p+q^2)/2^n). Our security proof relies on on the sum-capture theorems (Babai ’02; Steinberger ’12, Cogliati and Seurin ’18), as well as on new balls-into-bins combinatorial lemmas for limited independence ball-throws. Of independent interest, we also provide a self-contained concrete security treatment of oblivious transfer extension.

Block ciphers are prevalent in various security protocols used daily such as TLS, OpenPGP, and SSH. Their primary purpose is the protection of user data, both in transit and at rest. One of the de facto methods to evaluate block cipher security is differential cryptanalysis. Differential cryptanalysis observes the propagation of input patterns (input differences) through the cipher to produce output patterns (output differences). This probabilistic propagation is known as a differential; the identification of which is a measure of a block cipher’s security margins. This paper introduces an optimized GPU-based branch-and-bound framework for differential search. We optimize search efficiency by parallelizing all branch-and-bound operations, completing the entire search on the GPU without communicating with the CPU. The meet-in-the-middle (MITM) approach is also adopted for further performance gains. We analyze the financial and computational costs of the proposed framework using Google Cloud VM to showcase its practicality. When optimized for performance, we can attain up to 90x speedup while saving up to 47% of the running cost as compared to a single CPU core. When optimized for cost, the proposed framework can save up to 83% of financial costs while retaining a speedup of up to 40x. As a proof of concept, the proposed framework was then applied on 128-bit TRIFLE-BC, 64-bit PRESENT, and 64-bit GIFT. Notably, we identified the best differentials for PRESENT (16 rounds) and 64-bit GIFT (13 rounds) to date, with estimated probabilities of $2^{-61.7964}$ and $2^{-60.66}$ respectively. Although the differential results for TRIFLE-BC were incremental, the proposed framework was able to construct differentials for 43 rounds that consisted of approximately 5.8x more individual trails than previous work, making it one of the most efficient approaches for larger block ciphers.

This paper revisits the multi-user (mu) security of symmetric encryption, from the perspective of delivering an analysis of the AES-GCM-SIV AEAD scheme. Our end result shows that its mu security is comparable to that achieved in the single-user setting. In particular, even when instantiated with short keys (e.g., 128 bits), the security of AES-GCM-SIV is not impacted by the collisions of two user keys, as long as each individual nonce is not re-used by too many users. Our bounds also improve existing analyses in the single-user setting, in particular when messages of variable lengths are encrypted. We also validate security against a general class of key-derivation methods, including one that halves the complexity of the final proposal. As an intermediate step, we consider mu security in a setting where the data processed by every user is bounded, and where user keys are generated according to arbitrary, possibly correlated distributions. This viewpoint generalizes the currently adopted one in mu security, and can be used to analyze re-keying practices.

In this paper, we study quantum key-recovery attacks on block ciphers. While it is well known that a quantum adversary can generically speed up an exhaustive search of the key, much less is known on how to use specific vulnerabilities of the cipher to accelerate this procedure. In this context, we show how to convert classical boomerang and mixing boomerang attacks into efficient quantum key-recovery attacks. In some cases, we can even obtain a quadratic speedup, the same as simple differential attacks. We apply this technique to a 5-round attack on SAFER++.

The topic of this contribution is the cryptanalytic use of spurious keys, i.e. non-target keys returned by exhaustive key search. We show that the counting of spurious keys allows the construction of distinguishing attacks against block ciphers that are generically expected to start working at (marginally) lower computational cost than is required to find the target key by exhaustive search. We further show that if a brute force distinguisher does return a strong distinguishing signal, fairly generic optimizations to random key sampling will in many circumstances render the cost of detecting the signal massively lower than the cost of exhaustive search. We then use our techniques to quantitatively characterize various non-Markov properties of round-reduced Speck32/64. We fully compute, for the first time, the ciphertext pair distribution of 3-round Speck32/64 with one input difference $\Delta$ without any approximations and show that it differs markedly from Markov model predictions; we design a perfect distinguisher for the output distribution induced by the same input difference for 5-round Speck32/64 that is efficient enough to process millions of samples on an ordinary PC in a few days; we design a generic two-block known-plaintext distinguisher against Speck32/64 and show that it achieves 58 percent accuracy against 5-round Speck, equivalent e.g. to a linear distinguisher with $\approx 50$ percent bias. Turning our attention back to differential cryptanalysis, we show that our known-plaintext distinguisher automatically handles the 5-round output distribution induced by input difference $\Delta$ as well as the perfect differential distinguisher, but that no significant additional signal is obtained from knowing the plaintexts. We then apply the known-plaintext brute force distinguisher to 7-round Speck32/64 with fixed input difference $\Delta$, finding that it achieves essentially the same distinguishing advantage as state-of-the-art techniques (neural networks with key averaging). We also show that our techniques can precisely characterize non-Markov properties in longer differential trails for Speck32/64.

The concept of lightweight cryptography has gained in popularity recently, also due to various competitions and standardization efforts specifically targeting more efficient algorithms, which are also easier to implement. One of the important properties of lightweight constructions is the area of a hardware implementation, or in other words, the size of the implementation in a particular environment. Reducing the area usually has multiple advantages like decreased production cost or lower power consumption. In this paper, we focus on MAC functions and on ASIC implementations in hardware, and our goal is to minimize the area requirements in this setting. For this purpose, we design a new MAC scheme based on the well-known Pelican MAC function. However, in an effort to reduce the size of the implementation, we make use of smaller internal permutations. While this certainly leads to a higher internal collision probability, effectively reducing the allowed data, we show that the full security is still maintained with respect to other attacks, in particular forgery and key recovery attacks. This is useful in scenarios which do not require large amounts of data. Our detailed estimates, comparisons, and concrete benchmark results show that our new MAC scheme has the lowest area requirements and offers competitive performance. Indeed, we observe an area advantage of up to 30% in our estimated comparisons, and an advantage of around 13% compared to the closest competitor in a concrete implementation.

In this work, we show how weak key forgeries against polynomial hash based Authenticated Encryption (AE) schemes, such as AES-GCM, can be leveraged to launch partitioning oracle attacks. Partitioning oracle attacks were recently introduced by Len et al. (Usenix'21) as a new class of decryption error oracle which, conceptually, takes a ciphertext as input and outputs whether or not the decryption key belongs to some known subset of keys. Partitioning oracle attacks allow an adversary to query multiple keys simultaneously, leading to practical attacks against low entropy keys (e.g. those derived from passwords). Weak key forgeries were given a systematic treatment in the work of Procter and Cid (FSE'13), who showed how to construct MAC forgeries that effectively test whether the decryption key is in some (arbitrary) set of target keys. Consequently, it would appear that weak key forgeries naturally lend themselves to constructing partition oracles; we show that this is indeed the case, and discuss some practical applications of such an attack. Our attack applies in settings where AE schemes are used with static session keys, and has the particular advantage that an attacker has full control over the underlying plaintexts, allowing any format checks on underlying plaintexts to be met -- including those designed to mitigate against partitioning oracle attacks. Prior work demonstrated that key commitment is an important security property of AE schemes, in particular settings. Our results suggest that resistance to weak key forgeries should be considered a related design goal. Lastly, our results reinforce the message that weak passwords should never be used to derive encryption keys.

We consider the problem of finding low-weight multiples of polynomials over binary fields, which arises in stream cipher cryptanalysis or in finite field arithmetic. We first devise memory-efficient algorithms based on the recent advances in techniques for solving the knapsack problem. Then, we tune our algorithms using the celebrated Parallel Collision Search (PCS) method to decrease the time cost at the expense of a slight increase in space. Both our memory-efficient and time-memory trade-off algorithms improve substantially the state-of-the-art. The gain is for instance remarkable for large weights; a situation which occurs when the available keystream is small, e.g. the Bluetooth keystream.

This paper presents distinguishing and key recovery attacks on the reduced-round SNOW-V and SNOW-Vi, which are stream ciphers proposed for standard encryption schemes for the 5G mobile communication system. First, we construct a Mixed-Integer Linear Programming (MILP) model to search for integral characteristics using the division property, and find the best integral distinguisher in the 3-, 4-, 5-round SNOW-V, and 5-round SNOW-Vi with time complexities of \(2^{8}\), \(2^{16}\), \(2^{48}\), and \(2^{16}\), respectively. Next, we construct a bit-level MILP model to efficiently search for differential characteristics, and find the best differential characteristics in the 3- and 4-round versions. These characteristics lead to the 3-round differential distinguishers for SNOW-V and SNOW-Vi with time complexities of \(2^{17}\) and \(2^{12}\) and the 4-round differential distinguishers for SNOW-V and SNOW-Vi with time complexities of \(2^{97}\) and \(2^{39}\), respectively. Then, we consider single-bit and dual-bit differential cryptanalysis, which is inspired by the existing study on Salsa and ChaCha. By carefully choosing the IV values and differences, we can construct practical bit-wise differential distinguishers for the 4-round SNOW-V, 4-, and 5-round SNOW-Vi with time complexities of \(2^{4.466}\), \(2^{1.000}\), and \(2^{14.670}\), respectively. Finally, we improve the existing differential attack based on probabilistic neutral bits, which is also inspired by the existing study on Salsa and ChaCha. As a result, we present the best key recovery attack on the 4-round SNOW-V and SNOW-Vi with time complexities of \(2^{153.97}\) and \(2^{233.99}\) and data complexities of \(2^{26.96}\) and \(2^{19.19}\), respectively. Consequently, we significantly improve the existing best attacks in the initialization phase by the designers.

This work investigates a generic way of combining two very effective and well-studied cryptanalytic tools, proposed almost 18 years apart, namely the boomerang attack introduced by Wagner in FSE 1999 and the yoyo attack by Ronjom et. al. in Asiacrypt 2017. In doing so, the s-box switch and ladder switch techniques are leveraged to embed a yoyo trail inside a boomerang trail. As an immediate application, a 6-round key recovery attack on AES-128 is mounted with time complexity of $2^{78}$. A 10-round key recovery attack on recently introduced AES-based tweakable block cipher Pholkos is also furnished to demonstrate the applicability of the new technique on AES-like constructions. The results on AES are experimentally verified by applying and implementing them on a small scale variant of AES. We provide arguments that draw a relation between the proposed strategy with the retracing boomerang attack devised in Eurocrypt 2020. To the best of our knowledge, this is the first attempt to merge the yoyo and boomerang techniques to analyze SPN ciphers and warrants further attention as it has the potential of becoming an important cryptanalysis tool.

This paper considers the capability of 4-round Keccak-224/256/384/512 against the cryptanlysis involved by the quantum algorithm. In order to effectively find the corresponding rotational number for the rotational counterpart of preimage, we first establish a probabilistic algorithm based on the Grover search to guess a possible rotational number by using the fixed relations of bits pairs in some coordinates. This is committed to achieving that each iteration of searching the rotational counterparts contains only one run of 4-round Keccak variant applied for the verification, which can reduce the attack complexity in the quantum setting. Based on finding the rotational number under an acceptable randomness, we construct two attack models to focus on the recovery of preimage. In the first model, the Grover’s algorithm serves as finding out a rotational counterpart of the preimage. Through 64 attempts of checking the correct rotational number, the desired preimage can be obtained. In the second model, we abstract the finding of rotational counterparts into searching vertexes on a hypercube, and then, the SKW quantum algorithm is used to deal with the finding of the vertexes acted as rotational counterparts. Compared to the recent works in classical setting, we greatly reduce the attack complexity of preimage recovery. Furthermore, the first attack model is superior to the generic quantum preimage attack for 4-round Keccak-224/256/384/512, and the second model has slightly lower attack effect but more practicality on the 4-round Keccak-512/384, that is, the model is exponentially easier to implement in quantum circuit than both our first attack model and the generic quantum preimage attack.

The generation of pseudorandom binary sequences is of a great importance in numerous applications stretching from simulation and gambling to cryptography. Pseudorandom bit generators (PRBGs) can be split into two classes depending on their claimed security. The first includes PRBGs that are provably secure (such as the Blum-Blum-Shub one). Security of the second class rests on heuristic arguments. Sadly, PRBG from the first class are inherently inefficient and some PRBG are insecure against quantum attacks. While, their siblings from the second class are very efficient, but security relies on their resistance against known cryptographic attacks. This work presents a construction of PRBG from the asymmetric numeral system (ANS) compression algorithm. We define a family of PRBGs for $2^R$ ANS states and prove that it is indistinguishable from a truly random one for a big enough $R$. To make our construction efficient, we investigate PRBG built for smaller $R=7,8,9$ and show how to remove local correlations from output stream. We permute output bits using rotation and Keccak transformations and show that permuted bits pass all NIST tests. Our PRBG design is provably secure (for a large enough $R$) and heuristically secure (for a smaller $R$). Besides, we claim that our PRBG is secure against quantum adversaries.

In this paper, we formulate a new framework of cryptanalysis called rotational-linear attack on ARX ciphers. We firstly build an efficient distinguisher for the cipher $ E$ consisted of the rotational attack and the linear attack together with some intermediate variables. Then a key recovery technique is introduced with which we can recover some bits of the last whitening key in the related-key scenario. To decrease data complexity of our attack, we also apply a new method, called bit flipping, in the rotational cryptanalysis for the first time and the effective partitioning technique to the key-recovery part. Applying the new framework of attack to the MAC algorithm Chaskey, we build a full-round distinguisher over it. Besides, we have recovered $21$ bits of information of the key in the related-key scenario, for keys belonging to a large weak-key class based on 6-round distinguisher. The data complexity is $2^{38.8}$ and the time complexity is $2^{46.8}$. Before our work, the rotational distinguisher can only be used to reveal key information by checking weak-key conditions. This is the first time it is applied in a last-rounds key-recovery attack. We build a 17-round rotational-linear distinguisher for ChaCha permutation as an improvement compared to single rotational cryptanalysis over it.

In this note, we prove the conjecture posed by Keller and Rosemarin at Eurocrypt 2021 on the nullity of a matrix polynomial of a block matrix with Hadamard type blocks over commutative rings of characteristic 2. Therefore, it confirms the conjectural optimal bound on the dimension of invariant subspace of the Starkad cipher using the HADES design strategy. We also give characterizations of the algebraic structure formed by Hadamard matrices over commutative rings.

With the proposal of Picnic3, it has become interesting to investigate the security of LowMC with a full S-box layer. To significantly improve the efficiency of the Picnic signature, the designers of Picnic3 recommended to use the 4-round LowMC as the underlying block cipher, which has been shown to be insecure with 2 chosen plaintexts by Liu-Isobe-Meier. However, the attack scenario is very different and constrained in Picnic as the attacker is only allowed to know one single plaintext-ciphertext pair under the same key for LowMC. Recently, Banik et al. proposed guess-and-determine attacks on reduced LowMC in the Picnic setting. A major finding in their attacks is that the 3-bit S-box of LowMC can be linearized by guessing a quadratic equation. Notably, the attack on 2-round LowMC with a full S-box layer can be achieved with time complexity $2^{2m}$ where $m$ is the number of S-boxes in each round. As $k=3m$, their attacks can not reach 3 rounds where $k$ is the length of the key in bits. Although Banik et al. have improved the attacks with the meet-in-the-middle strategies, its memory complexity is rather high, which is $m\times 2^m$ bits of memory. In this note, we aim at low-memory key-recovery attacks as it is more fair to compare it with a pure exhaustive search. Specifically, we will describe improved algebraic attacks on 2-round LowMC by expressing the 3-bit S-box as 14 linearly independent quadratic boolean equations, which is inspired by the unsuccessful algebraic attacks on AES. As a result, the algebraic attacks on 2-round LowMC with key sizes of 129/192/255 bits can be improved by a factor of $2^{4}/2^{6.3}/2^{7.6}$, respectively. It seems that our attacks imply the attacks on 3-round LowMC. However, by taking the cost of gaussian elimination into account, the derived attacks on 3-round LowMC with key sizes of 192 and 255 bits are only about $2^{2.3}$ and $2^{3.7}$ times faster than the brute force. Our techniques are further applied to the instances with a partial S-box layer and significantly improve previous attacks with negligible memory complexity.

In this paper, we revisit the difference enumeration technique for LowMC and develop new algebraic techniques to achieve efficient key-recovery attacks. In the original difference enumeration attack framework, an inevitable step is to precompute and store a set of intermediate state differences for efficient checking via the binary search. Our first observation is that Bar-On et al.'s general algebraic technique developed for SPNs with partial nonlinear layers can be utilized to fulfill the same task, which can make the memory complexity negligible as there is no need to store a huge set of state differences any more. Benefiting from this technique, we could significantly improve the attacks on LowMC when the block size is much larger than the key size and even break LowMC with such a kind of parameter. On the other hand, with our new key-recovery technique, we could significantly improve the time to retrieve the full key if given only a single pair of input and output messages together with the difference trail that they take, which was stated as an interesting question by Rechberger et al. at ToSC 2018. Combining both techniques, with only 2 chosen plaintexts, we could break 4 rounds of LowMC adopting a full S-Box layer with block size of 129, 192 and 255 bits, respectively, which are the 3 recommended parameters for Picnic3, an alternative third-round candidate in NIST's Post-Quantum Cryptography competition. We have to emphasize that our attacks do not indicate that Picnic3 is broken as the Picnic use-case is very different and an attacker cannot even freely choose 2 plaintexts to encrypt for a concrete LowMC instance. However, such parameters are deemed as secure in the latest LowMC. Moreover, much more rounds of seven instances of the backdoor cipher LowMC-M as proposed by Peyrin and Wang in CRYPTO 2020 can be broken without finding the backdoor by making full use of the allowed $2^{64}$ data. The above mentioned attacks are all achieved with negligible memory.

The main goal of traceable cryptography is to protect against unauthorized redistribution of cryptographic functionalities. Such schemes provide a way to embed identities (i.e., a "mark") within cryptographic objects (e.g., decryption keys in an encryption scheme, signing keys in a signature scheme). In turn, the tracing guarantee ensures that any "pirate device" that successfully replicates the underlying functionality can be successfully traced to the set of identities used to build the device. In this work, we study traceable pseudorandom functions (PRFs). As PRFs are the workhorses of symmetric cryptography, traceable PRFs are useful for augmenting symmetric cryptographic primitives with strong traceable security guarantees. However, existing constructions of traceable PRFs either rely on strong notions like indistinguishability obfuscation or satisfy weak security guarantees like single-key security (i.e., tracing only works against adversaries that possess a single marked key). In this work, we show how to use fingerprinting codes to upgrade a single-key traceable PRF into a fully collusion resistant traceable PRF, where security holds regardless of how many keys the adversary possesses. We additionally introduce a stronger notion of security where tracing security holds even against active adversaries that have oracle access to the tracing algorithm. In conjunction with known constructions of single-key traceable PRFs, we obtain the first fully collusion resistant traceable PRF from standard lattice assumptions. Our traceable PRFs directly imply new lattice-based secret-key traitor tracing schemes that are CCA-secure and where tracing security holds against active adversaries that have access to the tracing oracle.

Side-channel attacks are a serious problem in the implementation of cryptosystems. Masking is an effective countermeasure to this problem and it has been actively studied for implementations of block ciphers. An obstacle to efficient masked implementation is the complexity of an evaluation of multiplication, which is quadratic in the order of masking. A natural approach to this problem is to explore ways to reduce the number of multiplications required to compute an S-box. Algebraic decomposition is another interesting approach proposed by Carlet et al. in 2015, which gives a way to represent an S-box as composition of polynomials with low algebraic degrees. In this paper, for the algebraic decomposition, we propose to use a special type of low-algebraic-degree polynomials, which we call generalized multiplication (GM) polynomials. The masking scheme for multiplication can be applied to GM polynomials, which is more efficient than the masking scheme for general low-algebraic-degree polynomials. Our performance evaluation based on some experimental results shows the effectiveness of masked implementation using the proposed decomposition compared to masked implementation using the decomposition of Carlet et al.

We consider the problem of constructing an unconditionally secure cipher for the case when the key length is less than the length of the encrypted message. (Unconditional security means that a computationally unbounded adversary cannot obtain information about the encrypted message without the key.) In this article, we propose data compression and randomization techniques combined with entropically-secure encryption. The resulting cipher can be used for encryption in such a way that the key length does not depend on the entropy or the length of the encrypted message; instead, it is determined by the required security level.

We introduce distance-comparison-preserving symmetric encryption (DCPE), a new type of property-preserving encryption (PPE) that preserves relative distance between plaintext vectors. DCPE is naturally suited for nearest-neighbor search on encrypted data. To achieve meaningful security, we divert from prior work on PPE and ask for approximate correctness, which is natural given the prevalence of approximate nearest neighbor (ANN) search. We conduct a thorough study of what security approximate DCPE can provide and how to construct it. Based on a relation we prove between approximate DCP and approximate distance-preserving functions, we design our core approximate DCPE scheme we call Scale-And-Perturb ($\mathsf{SAP}$). The encryption algorithm of $\mathsf{SAP}$ processes data on-the-fly. To boost security, we also introduce two preprocessing techniques: (1) normalizing the plaintext distribution, and (2) shuffling, wherein the component-wise encrypted dataset is randomly permuted. We prove (under suitable restrictions) that $\mathsf{SAP}$ achieves an indistinguishability-based security notion we call Real-or-Replaced ($\mathsf{RoR}$). In particular, our $\mathsf{RoR}$ result implies that our scheme prevents membership inference attacks by Yeom et al. (CSF 2018). Moreover, we show for i.i.d. multivariate normal plaintexts, we get security against approximate frequency-finding attacks, the main line of attacks against property-preserving encryption. This follows from a one-wayness $(\mathsf{OW})$ analysis. Finally, carefully combining our $\mathsf{OW}$ and $\mathsf{RoR}$ results, we are able characterize bit-security of $\mathsf{SAP}$. Our overall findings are that our scheme not only has superior bit-security to OPE but resists specific attacks that even ideal order-revealing encryption (Boneh et al., EUROCRYPT 2015) does not. This suggests it could be sufficient for certain ANN applications, a subject on which we encourage further study.

We push a little further the study of two characterizations of almost perfect nonlinear (APN) functions introduced in our recent monograph. We state open problems about them, and we revisit in their perspective a well-known result from Dobbertin on APN exponents. This leads us to new results about APN power functions and more general APN polynomials with coefficients in a subfield F_{2^k} , which ease the research of such functions and of differentially uniform functions, and simplifies the related proofs by avoiding tedious calculations. In a second part, we give slightly simpler proofs than in the same monograph, of two known results on Boolean functions, one of which deserves to be better known but needed clarification, and the other needed correction.

A large proportion of modern symmetric cryptographic building blocks are designed using the Substitution-Permutation Networks (SPNs), or more generally, Shannon's confusion-diffusion paradigm. To justify its theoretical soundness, Dodis et al. (EUROCRYPT 2016) recently introduced the theoretical model of confusion-diffusion networks, which may be viewed as keyless SPNs using random permutations as S-boxes and combinatorial primitives as permutation layers, and established provable security in the plain indifferentiability framework of Maurer, Renner, and Holenstein (TCC 2004). We extend this work and consider Non-Linear Confusion-Diffusion Networks (NLCDNs), i.e., networks using non-linear permutation layers, in weaker indifferentiability settings. As the main result, we prove that 3-round NLCDNs achieve the notion of sequential indifferentiability of Mandal et al. (TCC 2012). We also exhibit an attack against 2-round NLCDNs, which shows the tightness of our positive result on 3 rounds. It implies correlation intractability of 3-round NLCDNs, a notion strongly related to known-key security of block ciphers and secure hash functions. Our results provide additional insights on understanding the complexity for known-key security, as well as using confusion-diffusion paradigm for designing cryptographic hash functions.

Today's data-intensive applications increasingly suffer from significant performance bottlenecks due to the limited memory bandwidth of the classical von Neumann architecture. Near-Data Processing (NDP) has been proposed to perform computation near memory or data storage to reduce data movement for improving performance and energy consumption. However, the untrusted NDP processing units (PUs) bring in new threats to workloads that are private and sensitive, such as private database queries and private machine learning inferences. Meanwhile, most existing secure hardware designs do not consider off-chip components trustworthy. Once data leaving the processor, they must be protected, e.g., via block cipher encryption. Unfortunately, current encryption schemes do not support computation over encrypted data stored in memory or storage, hindering the adoption of NDP techniques for sensitive workloads. In this paper, we propose SecNDP, a lightweight encryption and verification scheme for untrusted NDP devices to perform computation over ciphertext and verify the correctness of linear operations. Our encryption scheme leverages arithmetic secret sharing in secure Multi-Party Computation (MPC) to support operations over ciphertext, and uses counter-mode encryption to reduce the decryption latency. The security of the scheme is formally proven. Compared with a non-NDP baseline, secure computation with SecNDP significantly reduces the memory bandwidth usage while providing security guarantees. We evaluate SecNDP for two workloads of distinct memory access patterns. In the setting of eight NDP units, we show a speedup up to 7.46x and energy savings of 18% over an unprotected non-NDP baseline, approaching the performance gain attained by native NDP without protection.Furthermore, SecNDP does not require any security assumption on NDP to hold, thus, using the same threat model as existing secure processors. SecNDP can be implemented without changing the NDP protocols and their inherent hardware design.

Pseudorandom functions are traditionally built upon block ciphers, but with the trend of permutation based cryptography, it is a natural question to investigate the design of pseudorandom functions from random permutations. We present a generic study of how to build beyond birthday bound secure pseudorandom functions from public random permutations. We first show that a pseudorandom function based on a single permutation call cannot be secure beyond the $2^{n/2}$ birthday bound, where n is the state size of the function. We next consider the Sum of Even-Mansour (SoEM) construction, that instantiates the sum of permutations with the Even-Mansour construction. We prove that SoEM achieves tight $2n/3$-bit security if it is constructed from two independent permutations and two randomly drawn keys. We also demonstrate a birthday bound attack if either the permutations or the keys are identical. Finally, we present the Sum of Key Alternating Ciphers (SoKAC) construction, a translation of Encrypted Davies-Meyer Dual to a public permutation based setting, and show that SoKAC achieves tight $2n/3$-bit security even when a single key is used.

In December 2020, David Oranchak, Jarl Van Eycke, and Sam Blake solved a 51-year old mystery: the Zodiac cipher of 340 symbols. Blake (2021) explains their solution. The correctness of their solution has not been seriously doubted, and here we give a further argument in its favor: the unicity distance of the cipher's system is at most 152.

A substantial effort has been devoted to proving optimal bounds for the security of key-alternating ciphers with independent sub-keys in the random permutation model (e.g., Chen and Steinberger, EUROCRYPT '14; Hoang and Tessaro, CRYPTO '16). While common in the study of multi-round constructions, the assumption that sub-keys are truly independent is not realistic, as these are generally highly correlated and generated from shorter keys. In this paper, we show the existence of non-trivial distributions of limited independence for which a t-round key-alternating cipher achieves optimal security. Our work is a natural continuation of the work of Chen et al. (CRYPTO '14) which considered the case of t = 2 when all-subkeys are identical. Here, we show that key-alternating ciphers remain secure for a large class of (t-1)-wise and (t-2)-wise independent distribution of sub-keys. Our proofs proceed by generalizations of the so-called Sum-Capture Theorem, which we prove using Fourier-analytic techniques.

SNOW-V is a stream cipher recently designed for 5G communication system. In this paper, we propose two efficient algorithms to evaluate the precise correlation of SNOW-V's two main nonlinear components with linear hull effects fully considered. Based on these algorithms, we could efficiently and extensively search much more linear masks than before. The ideas of these algorithms can be generalized to other similar nonlinear components in symmetric cipher. We apply our algorithms to full SNOW-V to search different types of linear approximations with high correlations. Our results depict more linear approximations with higher correlations than those proposed for full SNOW-V and SNOW-$\text{V}_{\boxplus_{32},\boxplus_8}$ recently. The best linear approximation we found has absolute correlation $2^{-47.567}$. There are at least 8, 135 and 1092 linear approximations with absolute correlation greater than $2^{-47.851}$, $2^{-49}$ and $2^{-50}$ respectively, which would derive a fast correlation attack with time/memory/data complexities $2^{240.86}$, $2^{240.37}$ and $2^{236.87}$. It is better than all the previous results of fast correlation attack against full SNOW-V. Moreover, we propose some properties for linear trails with 3 active S-boxes, which give a theoretical explanation that automatic search method lacks of. Our work provides a more comprehensive description for the linear approximation properties of full SNOW-V.

The k-xor or Generalized Birthday Problem aims at finding, given k lists of bit-strings, a k-tuple among them XORing to 0. If the lists are unbounded, the best classical (exponential) time complexity has withstood since Wagner's CRYPTO 2002 paper. If the lists are bounded (of the same size) and such that there is a single solution, the dissection algorithms of Dinur et al. (CRYPTO 2012) improve the memory usage over a simple meet-in-the-middle. In this paper, we study quantum algorithms for the k-xor problem. With unbounded lists and quantum access, we improve previous work by Grassi et al. (ASIACRYPT 2018) for almost all k. Next, we extend our study to lists of any size and with classical access only. We define a set of ``merging trees'' which represent the best known strategies for quantum and classical merging in k-xor algorithms, and prove that our method is optimal among these. Our complexities are confirmed by a Mixed Integer Linear Program that computes the best strategy for a given k-xor problem. All our algorithms apply also when considering modular additions instead of bitwise xors. This framework enables us to give new improved quantum k-xor algorithms for all k and list sizes. Applications include the subset-sum problem, LPN with limited memory and the multiple-encryption problem.

Authenticated encryption (AE) is used in a wide variety of applications, potentially in settings for which it was not originally designed. Recent research tries to understand what happens when AE is not used as prescribed by its designers. A question given relatively little attention is whether an AE scheme guarantees ``key commitment'': ciphertext should only decrypt to a valid plaintext under the key used to generate the ciphertext. Generally, AE schemes do not guarantee key commitment as it is not part of AE's design goal. Nevertheless, one would not expect this seemingly obscure property to have much impact on the security of actual products. In reality, however, products do rely on key commitment. We discuss three recent applications where missing key commitment is exploitable in practice. We provide proof-of-concept attacks via a tool that constructs AES-GCM ciphertext which can be decrypted to two plaintexts valid under a wide variety of file formats, such as PDF, Windows executables, and DICOM. Finally we discuss two solutions to add key commitment to AE schemes which have not been analyzed in the literature: a generic approach that adds an explicit key commitment scheme to the AE scheme, and a simple fix which works for AE schemes like AES-GCM and ChaCha20Poly1305, but requires separate analysis for each scheme.

In CRYPTO'16, Cogliati and Seurin proposed a block cipher based nonce based MAC, called {\em Encrypted Wegman-Carter with Davies-Meyer} (\textsf{EWCDM}), that gives $2n/3$ bit MAC security in the nonce respecting setting and $n/2$ bit security in the nonce misuse setting, where $n$ is the block size of the underlying block cipher. However, this construction requires two independent block cipher keys. In CRYPTO'18, Datta et al. came up with a single-keyed block cipher based nonce based MAC, called {\em Decrypted Wegman-Carter with Davies-Meyer} (\textsf{DWCDM}), that also provides $2n/3$ bit MAC security in the nonce respecting setting and $n/2$ bit security in the nonce misuse setting. However, the drawback of \textsf{DWCDM} is that it takes only $2n/3$ bit nonce. In fact, authors have shown that \textsf{DWCDM} cannot achieve beyond the birthday bound security with $n$ bit nonces. In this paper, we prove that \textsf{DWCDM} with $3n/4$ bit nonces provides MAC security up to $O(2^{3n/4})$ MAC queries against all nonce respecting adversaries. We also improve the MAC bound of \textsf{EWCDM} from $2n/3$ bit to $3n/4$ bit. The backbone of these two results is a refined treatment of extended mirror theory that systematically estimates the number of solutions to a system of bivariate affine equations and non-equations, which we apply on the security proofs of the constructions to achieve $3n/4$ bit security.

The goal of this paper is to investigate linear approximations of random functions and permutations. Our motivation is twofold. First, before the distinguishability of a practical cipher from an ideal one can be analysed, the cryptanalyst must have an accurate understanding of the statistical behaviour of the ideal cipher. Secondly, this issue has been neglected both in old and in more recent studies, particularly when multiple linear approximations are being used simultaneously. Traditional models have been based on the average behaviour and simplified using other assumptions such as independence of the linear approximations. Multidimensional cryptanalysis was introduced to avoid making artificial assumptions about statistical independence of linear approximations. On the other hand, it has the drawback of including many trivial approximations that do not contribute to the attack but just cause a waste of time and memory. We show for the first time in this paper that the trivial approximations reduce the degree of freedom of the related χ² distribution. Previously, the affine linear cryptanalysis was proposed to allow removing trivial approximations and, at the same time, admitting a solid statistical model. In this paper, we identify another type of multidimensional linear approximation, called Davies-Meyer approximation, which has similar advantages, and present full statistical models for both the affine and the Davies-Meyer type of multidimensional linear approximations. The new models given in this paper are realistic, accurate and easy to use. They are backed up by standard statistical tools such as Pearson’s χ² test and finite population correction and demonstrated to work accurately using practical examples.

Integral cryptanalysis is a powerful tool for attacking symmetric primitives, and division property is a state-of-the-art framework for finding integral distinguishers. This work describes new theoretical and practical insights into traditional bit-based division property. We focus on analyzing and exploiting monotonicity/convexity of division property and its relation to the graph indicator. In particular, our investigation leads to a new compact representation of propagation, which allows CNF/MILP modeling for larger S-Boxes, such as 16-bit Super-Sboxes of lightweight block ciphers or even 32-bit random S-boxes. This solves the challenge posed by Derbez and Fouque (ToSC 2020), who questioned the possibility of SAT/SMT/MILP modeling of 16-bit Super-Sboxes. As a proof-of-concept, we model the Super-Sboxes of the 8-round LED by CNF formulas, which was not feasible by any previous approach. Our analysis is further supported by an elegant algorithmic framework. We describe simple algorithms for computing division property of a set of $n$-bit vectors in time $O(n2^n)$, reducing such sets to minimal/maximal elements in time $O(n2^n)$, computing division property propagation table of an $n\times m$-bit S-box and its compact representation in time $O((n+m)2^{n+m})$. In addition, we develop an advanced algorithm tailored to "heavy" bijections, allowing to model, for example, a randomly generated 32-bit S-box.

This paper proposes the use of Legendre symbols as component gates in the design of ciphers tailored for use in cryptographic proof systems. Legendre symbols correspond to high-degree maps, but can be evaluated much faster. As a result, a cipher that uses Legendre symbols can offer the same security as one that uses high-degree maps but without incurring the penalty of a comparatively slow evaluation time. After discussing the design considerations induced by the use of Legendre symbol gates, we present a concrete design that follows this strategy, along with an elaborate security analysis thereof. This cipher is called Grendel.

We revisit designing AND-RX block ciphers, that is, the designs assembled with the most fundamental binary operations---AND, Rotation and XOR operations and do not rely on existing units. Likely, the most popular representative is the NSA cipher \texttt{SIMON}, which remains one of the most efficient designs, but suffers from difficulty in security evaluation. As our main contribution, we propose \texttt{SAND}, a new family of lightweight AND-RX block ciphers. To overcome the difficulty regarding security evaluation, \texttt{SAND} follows a novel design approach, the core idea of which is to restrain the AND-RX operations to be within nibbles. By this, \texttt{SAND} admits an equivalent representation based on a $4\times8$ \textit{synthetic S-box} ($SSb$). This enables the use of classical S-box-based security evaluation approaches. Consequently, for all versions of \texttt{SAND}, (a) we evaluated security bounds with respect to differential and linear attacks, and in both single-key and related-key scenarios; (b) we also evaluated security against impossible differential and zero-correlation linear attacks. This better understanding of the security enables the use of a relatively simple key schedule, which makes the ASIC round-based hardware implementation of \texttt{SAND} to be one of the state-of-art Feistel lightweight ciphers. As to software performance, due to the natural bitslice structure, \texttt{SAND} reaches the same level of performance as \texttt{SIMON} and is among the most software-efficient block ciphers.

At ToSC 2021, Rohit \textit{et al.} presented the first distinguishing and key recovery attacks on 7 rounds Ascon without violating the designer's security claims of nonce-respecting setting and data limit of $2^{64}$ blocks per key. So far, these are the best attacks on 7 rounds Ascon. However, the distinguishers require (impractical) $2^{60}$ data while the data complexity of key recovery attacks exactly equals $2^{64}$. Whether there are any practical distinguishers and key recovery attacks (with data less than $2^{64}$) on 7 rounds Ascon is still an open problem. In this work, we give positive answers to these questions by providing a comprehensive security analysis of Ascon in the weak key setting. Our first major result is the 7-round cube distinguishers with complexities $2^{46}$ and $2^{33}$ which work for $2^{82}$ and $2^{63}$ keys, respectively. Notably, we show that such weak keys exist for any choice (out of 64) of 46 and 33 specifically chosen nonce variables. In addition, we improve the data complexities of existing distinguishers for 5, 6 and 7 rounds by a factor of $2^{8}, 2^{16}$ and $2^{27}$, respectively. Our second contribution is a new theoretical framework for weak keys of Ascon which is solely based on the algebraic degree. Based on our construction, we identify $2^{127.99}$, $2^{127.97}$ and $2^{116.34}$ weak keys (out of $2^{128}$) for 5, 6 and 7 rounds, respectively. Next, we present two key recovery attacks on 7 rounds with different attack complexities. The best attack can recover the secret key with $2^{63}$ data, $2^{69}$ bits of memory and $2^{115.2}$ time. Our attacks are far from threatening the security of full 12 rounds Ascon, but we expect that they provide new insights into Ascon's security.

The use of deep learning techniques to perform side-channel analysis attracted the attention of many researchers as they obtained good performances with them. Unfortunately, the understanding of the neural networks used to perform side-channel attacks is not very advanced yet. In this paper, we propose to contribute to this direction by studying the impact of some particular deep learning techniques for tackling side-channel attack problems. More precisely, we propose to focus on three existing techniques: batch normalization, dropout and weight decay, not yet used in side-channel context. By combining adequately these techniques for our problem, we show that it is possible to improve the attack performance, i.e. the number of traces needed to recover the secret, by more than 55%. Additionally, they allow us to have a gain of more than 34% in terms of training time. We also show that an architecture trained with such techniques is able to perform attacks efficiently even in the context of desynchronized traces.