FUTURE is a recently proposed, lightweight block cipher. It has an AES-like, SP-based, 10-round encryption function, where, unlike most other lightweight constructions, the diffusion layer is based on an MDS matrix. Despite its relative complexity, it has a remarkable hardware performance due to careful design decisions. In this paper, we conducted a MILP-based analysis of the cipher, where we incorporated exact probabilities rather than just the number of active S-boxes into the model. Through the MILP analysis, we were able to find differential and linear distinguishers for up to 5 rounds of FUTURE, extending the known distinguishers of the cipher by one round.

The related-key statistical saturation (RKSS) attack is a cryptanalysis method proposed by Li et al. at FSE 2019. It can be seen as the extension of previous statistical saturation attacks under the related-key setting. The attack takes advantage of a set of plaintexts with some bits fixed, while the other bits take all possible values, and considers the relation between the value distributions of a part of the ciphertext bits generated under related keys. Usually, RKSS distinguishers exploit the property that the value distribution stays invariant under the modification of the key. However, this property can only be deterministically verified if the plaintexts cover all possible values of a selection of bits. In this paper, we propose the probabilistic RKSS cryptanalysis which avoids iterating over all non-fixed plaintext bits by applying a statistical method on top of the original RKSS distinguisher. Compared to the RKSS attack, this newly proposed attack has a significantly lower data complexity and has the potential of attacking more rounds. As an illustration, for reduced-round Piccolo, we obtain the best key recovery attacks (considering both pre- and post-whitening keys) on both versions in terms of the number of rounds. Note that these attacks do not threaten the full-round security of Piccolo.

We apply Siegenthaler's construction, along with several techniques, to classify all $(n-4)$-resilient Boolean functions with $n$ variables, for all values of $n \geq 4$, up to extended variable-permutation equivalence. We show that, up to this equivalence, there are only 761 functions for any $n$ larger than or equal to 10, and for smaller values of $n$, i.e., for $n$ increasing from 4 to 9, there are 58, 256, 578, 720, 754, and 760 functions, respectively. Furthermore, we classify all 1-resilient 6-variable Boolean functions and show that there are 1035596784 such functions up to extended variable-permutation equivalence.

In this paper, we focus on constructing an automatic search model that greatly improves efficiency with little loss of accuracy and obtains some better results in the construction of integral distinguishers for block ciphers. First, we define a new notion named BDPT Trail, which divides BDPT propagation into three parts: the division trail for K, division trail for L, and Key-Xor operation. Secondly, we improve the insufficiency of the previous methods of calculating division trails and propose an effective algorithm that can obtain more valid division trails for L of the S-box operation. Third, we propose a new algorithm that models each Key-Xor operation based on the MILP technique for the first time. Based on this, we can accurately characterize the Key-Xor operation by solving these MILP models. After that, by selecting the appropriate initial BDPT and stopping rules, we construct an automatic search model. As a result, our automatic search model is applied to search for integral distinguishers for some block ciphers. For GIFT-64, we find a 11-round integral distinguisher, which is one more round than the previous best results. For Rectangle, we find a better $10$-round integral distinguisher with 9 balanced bits, which has eight more bits than the previous best results. For Simon64, we can find more balanced bits than the previous longest distinguishers.

The most crucial but time-consuming task for differential cryptanalysis is to find a differential with a high probability. To tackle this task, we propose a new SAT-based automatic search framework to efficiently figure out a differential with the highest probability under a specified condition. As the previous SAT methods (e.g., the Sun et al’s method proposed at ToSC 2021(1)) focused on accelerating the search for an optimal single differential characteristic, these are not optimized for evaluating a clustering effect to obtain a tighter differential probability of differentials. In contrast, our framework takes advantage of a method to solve incremental SAT problems in parallel using a multi-threading technique, and consequently, it offers the following advantages compared with the previous methods: (1) speedy identification of a differential with the highest probability under the specified conditions; (2) efficient construction of the truncated differential with the highest probability from the obtained multiple differentials; and (3) applicability to a wide class of symmetric-key primitives. To demonstrate the effectiveness of our framework, we apply it to the block cipher PRINCE and the tweakable block cipher QARMA. We successfully figure out the tight differential bounds for all variants of PRINCE and QARMA within the practical time, thereby identifying the longest distinguisher for all the variants, which improves existing ones by one to four more rounds. Besides, we uncover notable differences between PRINCE and QARMA in the behavior of differential, especially for the clustering effect. We believe that our findings shed light on new structural properties of these important primitives. In the context of key recovery attacks, our framework allows us to derive the key-recovery-friendly truncated differentials for all variants of QARMA. Consequently, we report key recovery attacks based on (truncated) differential cryptanalysis on QARMA for the first time and show these key recovery attacks are competitive with existing other attacks.

In this paper we propose the first efficient quantum version of key-recovery attacks on block ciphers based on impossible differentials, which was left as an open problem in previous work. These attacks work in two phases. First, a large number of differential pairs are collected, by solving a limited birthday problem with the attacked block cipher considered as a black box. Second, these pairs are filtered with respect to partial key candidates. We show how to translate the pair filtering step into a quantum procedure, and provide a complete analysis of its complexity. If the path of the attack can be properly reoptimized, this procedure can reach a significant speedup with respect to classical attacks. We provide two applications on SKINNY-128-256 and AES-192/256. These results do not threaten the security of these ciphers but allow us to better understand their (post-quantum) security margin.

Shadow is a lightweight block cipher proposed at IEEE IoT journal 2021. Shadow’s main design principle is adopting a variant 4- branch Feistel structure in order to provide a fast diffusion rate. We define such a structure as Shadow structure and prove that it is al- most identical to the Generalized Feistel Network, which invalidates the design principle. Moreover, we give a structural distinguisher that can distinguish Shadow structure from random permutation with only two plaintext/ciphertext pairs. By exploiting the key schedule, the distin- guisher can be extended to key recovery attack with only one plain- text/ciphertext pair. Furthermore, by considering Shadow’s round func- tion, only certain forms of monomials can appear in the ciphertext, re- sulting in an integral distinguisher of four plaintext/ciphertext pairs. Even more, the algebraic degree does not increase more than 12 for Shadow-32 and 20 for Shadow-64 regardless of rounds used. Our results show that Shadow is highly vulnerable to algebraic attacks, and that algebraic attacks should be carefully considered when designing ciphers with AND, rotation, and XOR operations.

In this paper, we analyze the security of authenticated encryption modes OTR (Minematsu, Eurocrypt 2014) and OPP (Granger, Jovanovic, Mennink, and Neves, Eurocrypt 2016) in a setting where an adversary is allowed to make encryption queries in quantum superposition. Starting with OTR -- or more technically, AES-OTR, a third-round CAESAR candidate -- we extend prior quantum attacks on the mode's unforgeability in the literature to provide the first attacks breaking confidentiality, i.e., IND-qCPA security, of AES-OTR in different settings depending on how the associated data is processed. On a technical level, one of our IND-qCPA attacks involves querying the quantum encryption oracle on a superposition of data with unequal length; to the best of our knowledge, such an attack has never been modelled before in the (post-)quantum cryptographic literature, and we hence believe our technique is of independent interest. Coming to OPP, we present the first key-recovery attack against the scheme which uses only a single quantum encryption query.

This paper specifies a new arithmetization-oriented hash function called Tip5. It uses the SHARK design strategy with low-degree power maps in combination with lookup tables, and is tailored to the field with $p=2^{64}-2^{32}+1$ elements. The context motivating this design is the recursive verification of STARKs. This context imposes particular design constraints, and therefore the hash function's arithmetization is discussed at length.

A transciphering framework converts a symmetric ciphertext into a homomorphic ciphertext on the server-side, reducing computational and communication overload on the client-side. In Asiacrypt 2021, Cho et al. proposed the RtF framework that supports approximate computation. In this paper, we propose a family of noisy ciphers, dubbed Rubato, with a novel design strategy of introducing noise to a symmetric cipher of a low algebraic degree. With this strategy, the multiplicative complexity of the cipher is significantly reduced, compared to existing HE-friendly ciphers, without degrading the overall security. More precisely, given a moderate block size (16 to 64), Rubato enjoys a low multiplicative depth (2 to 5) and a small number of multiplications per encrypted word (2.1 to 6.25) at the cost of slightly larger ciphertext expansion (1.26 to 1.31). The security of Rubato is supported by comprehensive analysis including symmetric and LWE cryptanalysis. Compared to HERA within the RtF framework, client-side and server-side throughput is improved by 22.9% and 32.2%, respectively, at the cost of only 1.6% larger ciphertext expansion.

Column Parity Mixers, or CPMs in short, are a particular type of linear maps, used as the mixing layer in permutation-based cryptographic primitives like Keccak-f (SHA3) and Xoodoo. Although being successfully applied, not much is known regarding their algebraic properties. They are limited to invertibility of CCPMs, and that the set of invertible CCPMs forms a group. A possible explanation is due to the complexity of describing CPMs in terms of linear algebra. In this paper, we introduce a new approach to studying CPMs using module theory from commutative algebra. We show that many interesting algebraic properties can be deduced using this approach, and that known results regarding CPMs turn out to be trivial consequences of module theoretic concepts. We also show how this approach can be used to study the linear layer of Xoodoo, and other linear maps with a similar structure which we call DCD-compositions. Using this approach, we prove that every DCD-composition where the underlying vector space with the same dimension as that of Xoodoo has a low order. This provides a solid mathematical explanation for the low order of the linear layer of Xoodoo, which equals 32. We design a DCD-composition using this module theoretic approach, but with a higher order using a different dimension.

We provide a new definitional framework capturing the multi-user security of encryption schemes and pseudorandom functions in the face of adversaries that can adaptively compromise users' keys. We provide a sequence of results establishing the security of practical symmetric encryption schemes under adaptive compromise in the random oracle or ideal cipher model. The bulk of analysis complexity for adaptive compromise security is relegated to the analysis of lower-level primitives such as pseudorandom functions. We apply our framework to give proofs of security for the BurnBox system for privacy in the face of border searches and the in-use searchable symmetric encryption scheme due to Cash et al. In both cases, prior analyses had bugs that our framework helps avoid.

We investigate the concept of $\mathcal{S}_0$-equivalent class, $n$-variable Boolean functions up to the addition of a symmetric function null in $0_n$ and $1_n$, as a tool to study weightwise perfectly balanced functions. On the one hand we show that weightwise properties, such as being weightwise perfectly balanced, the weightwise nonlinearity and weightwise algebraic immunity, are invariants of these classes. On the other hand we analyze the variation of global parameters inside the same class, showing for example that there is always a function with high degree, algebraic immunity, or nonlinearity in the $\mathcal{S}_0$-equivalent class of a function. Finally, we discuss how these results extend to other equivalence relations and their applications in cryptography.

This paper analyses the security of the so-called Milenage construction, developed by ETSI SAGE, when it is based on a non-one-to-one pseudo-random function (PRF) rather than a one-to-one pseudo-random permutation (PRP). It is shown that Milenage based on an $n$-bit random function and producing $t$ $n$-bit outputs, is indistinguishable from a random $tn$-bit function up to $q = O(2^{n/2}/t)$ queries. We also extend the existing security proof for PRP-based Milenage due to Gilbert by generalising the model and incorporating the Milenage message authentication function in the proof.

As the first generic method for finding the optimal differential and linear characteristics, Matsui's branch and bound search algorithm has played an important role in evaluating the security of symmetric ciphers. By combining Matsui's bounding conditions with automatic search models, search efficiency can be improved. In this paper, by studying the properties of Matsui's bounding conditions, we give the general form of bounding conditions that can eliminate all the impossible solutions determined by Matsui's bounding conditions. Then, a new method of combining bounding conditions with sequential encoding method is proposed. With the help of some small size Mixed Integer Linear Programming (MILP) models, we can use fewer variables and clauses to build Satisfiability Problem (SAT) models. As applications, we use our new method to search for the optimal differential and linear characteristics of some SPN, Feistel, and ARX block ciphers. The number of variables and clauses and the solving time of the SAT models are decreased significantly. In addition, we find some new differential and linear characteristics covering more rounds.

Idealized constructions in cryptography prove the security of a primitive based on the security of another primitive. The challenge of building a pseudorandom function (PRF) from a random permutation (RP) has only been recently tackled by Chen, Lambooij and Mennink [CRYPTO 2019] who proposed Sum of Even-Mansour (SoEM) with a provable beyond-birthday-bound security. In this work, we revisit the challenge of building a PRF from an RP. On the one hand, we describe Keyed Sum of Permutations (KSoP) that achieves the same provable security as SoEM while being strictly simpler since it avoids a key addition but still requires two independent keys and permutations. On the other hand, we show that it is impossible to further simplify the scheme by deriving the two keys with a simple linear key schedule as it allows a non-trivial birthday-bound key recovery attack. The birthday-bound attack is mostly information-theoretic, but it can be optimized to run faster than a brute-force attack.

Recently, many cryptographic primitives such as homomorphic encryption (HE), multi-party computation (MPC) and zero-knowledge (ZK) protocols have been proposed in the literature which operate on prime field $\mathbb{F}_p$ for some large prime $p$. Primitives that are designed using such operations are called arithmetization-oriented primitives. As the concept of arithmetization-oriented primitives is new, a rigorous cryptanalysis of such primitives is yet to be done. In this paper, we investigate arithmetization-oriented APN functions. More precisely, we investigate APN permutations in the CCZ-classes of known families of APN power functions over prime field $\mathbb{F}_p$. Moreover, we present a new class of APN binomials over $\mathbb{F}_q$ obtained by modifying the planar function $x^2$ over $\mathbb{F}_q$. We also present a class of binomials having differential uniformity at most $5$ defined via the quadratic character over finite fields of odd characteristic. We give sufficient conditions for which this family of binomials is permutation. Computationally it is confirmed that the latter family contains new APN functions for some small parameters. We conjecture it to contain an infinite subfamily of APN functions.

REAMC Report-007(2023) ACORN-QRE: Specification and Analysis of a Method of Generating Secure One-time Pads for Use in Encryption Roy S Wikramaratna (email: [email protected]) Abstract The Additive Congruential Random Number (ACORN) generator is straightforward to implement; it has been demonstrated in previous papers to give rise to sequences with long period which can be proven from theoretical considerations to approximate to being uniform in up to k dimensions (for any given k). The ACORN-QRE algorithm is a straightforward modification of ACORN which effectively avoids the linearity of the original algorithm, while preserving the uniformity of the modified sequence. It provides a new method for generating one-time pads that are resistant to attack either by current computers or by future computing developments, including quantum computers. The pads can use any alphabet (including both binary and alphanumeric) and can be used with a Vernam-type cypher to securely encrypt both files and communications. This report explains how the ACORN-QRE algorithm works and provides evidence for the claim that the resulting one-time pads are inherently not susceptible to cryptanalysis and that they will remain secure against foreseeable developments in computing, including the potential development of quantum computers. The ACORN-QRE algorithm is patented in the UK under Patent No. GB2591467; patent applied for in the US under Application No. 17/795632. The patents are owned by REAMC Limited, 4 Nuthatch Close, Poole, Dorset BH17 7XR, United Kingdom

The random oracle model is an instrument used for proving that protocol has no structural flaws when settling with standard hash properties is impossible or fairly difficult. In practice, however, random oracles have to be instantiated with some specific hash functions, which are not random oracles. Hence, in the real world, an adversary has broader capabilities than considered in the random oracle proof — it can exploit the peculiarities of a specific hash function to achieve its goal. In a case when a hash function is based on some building block, one can go further and show that even if the adversary has access to that building block, the hash function still behaves like a random oracle under some assumptions made about the building block. Thereby, the protocol can be proved secure against more powerful adversaries under less complex assumptions. The indifferentiability notion formalizes that approach. In this paper we study whether Streebog, a Russian standardized hash function, can instantiate a random oracle from that point of view. We prove that Streebog is indifferentiable from a random oracle under an ideal cipher assumption for the underlying block cipher.

We introduce a new security notion that lies right in between pseudorandom permutations (PRPs) and strong pseudorandom permutations (SPRPs). We call this new security notion and any (tweakable) cipher that satisfies it a $\textit{rugged pseudorandom permutation}$ (RPRP). Rugged pseudorandom permutations lend themselves to some interesting applications, have practical benefits, and lead to novel cryptographic constructions. Our focus is on variable-length tweakable RPRPs, and analogous to the encode-then-encipher paradigm of Bellare and Rogaway, we can generically transform any such cipher into different AEAD schemes with varying security properties. However, the benefit of RPRPs is that they can be constructed more efficiently as they are weaker primitives than SPRPs (the notion traditionally required by the encode-then-encipher paradigm). We can construct RPRPs using only two layers of processing, whereas SPRPs typically require three layers of processing over the input data. We also identify a new transformation that yields RUP-secure AEAD schemes with more compact ciphertexts than previously known. Further extending this approach, we arrive at a new generalized notion of authenticated encryption and a matching construction, which we refer to as $\textit{nonce-set AEAD}$. Nonce-set AEAD is particularly well-suited in the context of secure channels, like QUIC and DTLS, that operate over unreliable transports and employ a window mechanism at the receiver's end of the channel. We conclude by presenting a generic construction for transforming a nonce-set AEAD scheme into an order-resilient secure channel. Our channel construction sheds new light on order-resilient channels and additionally leads to more compact ciphertexts when instantiated from RPRPs.

Suppose two parties have hash functions $h_1$ and $h_2$ respectively, but each only trusts the security of their own. We wish to build a hash combiner $C^{h_1, h_2}$ which is secure so long as either one of the underlying hash functions is. This question has been well-studied in the regime of collision resistance. In this case, concatenating the two hash outputs clearly works. Unfortunately, a long series of works (Boneh and Boyen, CRYPTO'06; Pietrzak, Eurocrypt'07; Pietrzak, CRYPTO'08) showed no (noticeably) shorter combiner for collision resistance is possible. We revisit this pessimistic state of affairs, motivated by the observation that collision-resistance is insufficient for many applications of cryptographic hash functions anyway. We argue the right formulation of the "hash combiner" is what we call random oracle (RO) combiners. Indeed, we circumvent the previous lower bounds for collision resistance by constructing a simple length-preserving RO combiner $$\widetilde{C}_{\mathcal{Z}_1,\mathcal{Z}_2}^{h_1,h_2}(M) = h_1(M, \mathcal{Z}_1) \oplus h_2(M, \mathcal{Z}_2),$$ where $\mathcal{Z}_1, \mathcal{Z}_2$ are random salts of appropriate length. We show that this extra randomness is necessary for RO combiners, and indeed our construction is somewhat tight with this lower bound. On the negative side, we show that one cannot generically apply the composition theorem to further replace "monolithic" hashes $h_1$ and $h_2$ by some simpler indifferentiable construction (such as the Merkle-Damgård transformation) from smaller components, such as fixed-length compression functions. Despite this issue, we directly prove collision resistance of the Merkle-Damgård variant of our combiner, where $h_1$ and $h_2$ are replaced by iterative Merkle-Damgård hashes applied to fixed-length compression functions. Thus, we can still subvert the concatenation barrier for collision-resistance combiners using practically small components.

The substitution box (S-box) is an important nonlinear component in most symmetric cryptosystems and thus should have good properties. Its difference distribution table (DDT) and linear approximation table (LAT) affect the security of the cipher against differential and linear cryptanalysis. In most previous work, differential uniformity and linearity of an S-box are two primary cryptographic properties to impact the resistance against differential and linear attacks. In some cases, the branch number and fixed point are also be considered. However, other important cryptographic properties such as the frequency of differential uniformity (resp. linearity) and the number of Bad Input and Bad Output (BIBO) patterns in DDT (resp. LAT) are often ignored. These properties substantially affect lightweight cryptography based on substitution bit permutation networks (SbPN) such as PRESENT, GIFT and RECTANGLE. This paper introduces a new method to search for S-boxes satisfying all above criteria simultaneously. In our strategy, we transform the process of searching for S-boxes under certain constraints on cryptographic properties into a satisfiability (SAT) problem. As applications, we use our new approach to search out 4-bit and 5-bit S-boxes with the same or better cryptographic properties compared with the S-boxes from well-known ciphers. Finally, we also utilize our method to verify a conjecture proposed by Boura et al. in the case of all 3-bit and 4-bit S-boxes. We propose a proposition and two corollaries to reduce the search space in this verification.

Perfect ciphers have been a very attractive cryptographic tool ever since C. Shannon described them. Note that, by definition, if a perfect cipher is used, no one can get any information about the encrypted message without knowing the secret key. We consider the problem of reducing the key length of perfect ciphers, because in many applications the length of the secret key is a crucial parameter. This paper describes a simple method of key length reduction. This method gives a perfect cipher and is based on the use of data compression and randomisation, and the average key length can be made close to Shannon entropy (which is the key length limit). It should be noted that the method can effectively use readily available data compressors (archivers).

Proving security bounds in contexts with a large number of users is one of the central problems in symmetric-key cryptography today. This paper introduces a new method for information-theoretic multi-user security proofs, called ``the Squared-Ratio Method''. At its core, the method requires the expectation of the square of the ratio of observing the so-called good transcripts (from Patarin's H-coefficient technique) in the real and the ideal world. Central to the method is the observation that for information-theoretic adversaries, the KL-divergence for the multi-user security bound can be written as a summation of the KL-divergence of every single user. We showcase the Squared-Ratio Method on three examples: the Xor of two Permutations by Bellare et al. (EUROCRYPT '98) and Hall et al. (CRYPTO '98), the Encrypted Davies-Mayer by Cogliati and Seurin (CRYPTO '16), and the two permutation variant of the nEHtM MAC algorithm by Dutta et al. (EUROCRYPT '19). With this new tool, we provide improved bounds for the multi-user security of these constructions. Our approach is modular in the sense that the multi-user security can be obtained directly from single-user results.

In this paper we present a new representation of the AES key schedule, with some implications to the security of AES-based schemes. In particular, we show that the AES-128 key schedule can be split into four independent parallel computations operating on 32-bit chunks, up to linear transformation. Surprisingly, this property has not been described in the literature after more than 20 years of analysis of AES. We show two consequences of our new representation, improving previous cryptanalysis results of AES-based schemes. First, we observe that iterating an odd number of key schedule rounds results in a permutation with short cycles. This explains an observation of Khairallah on mixFeed, a second-round candidate in the NIST lightweight competition. Our analysis actually shows that his forgery attack on mixFeed succeeds with probability 0.44 (with data complexity 220GB), breaking the scheme in practice. The same observation also leads to a novel attack on ALE, another AES-based AEAD scheme. Our new representation also gives efficient ways to combine information from the first subkeys and information from the last subkeys, in order to reconstruct the corresponding master key. This results in small improvements to previous attacks: we improve impossible differential attacks against several variants of AES (and Rijndael), and a square attack against AES-192.

In order to maintain a similar security level in a post-quantum setting, many symmetric primitives should have to double their keys and increase their state sizes. So far, no generic way for doing this is known that would provide convincing quantum security guarantees. In this paper we propose a new generic construction, QuEME, that allows to double the key and the state size of a block cipher. The QuEME design is inspired by the ECB-Mix-ECB (EME) construction, but is defined for a different choice of mixing function that withstands our new quantum superposition attack that exhibits a periodic property found in collisions and that breaks EME and a large class of variants of it. We prove that QuEME achieves $n$-bit security in the classical setting, where $n$ is the block size of the underlying block cipher, and at least $n/6$-bit security in the quantum setting. We propose a concrete instantiation of this construction, called Double-AES, that is built with variants of AES-128.

This note shows that there exists a nontrivial invariant for the unkeyed round function of QARMAv2-64. It is invariant under translation by a set of $2^{32}$ constants. The invariant does not extend over all rounds of QARMAv2-64 and probably does not lead to full-round attacks. Nevertheless, it might be of interest as it can be expected to give meaningful weak-key attacks on round-reduced instances when combined with other techniques such as integral cryptanalysis.

The duplex construction is already well analyzed with many papers proving its security in the random permutation model. However, so far, the first phase of the duplex, where the state is initialized with a secret key and an initialization vector ($\mathit{IV}$), is typically analyzed in a worst case manner. More detailed, it is always assumed that the adversary is allowed to choose the $\mathit{IV}$ on its will. In this paper, we analyze how the security changes if restrictions on the choice of the $\mathit{IV}$ are imposed, varying from the global nonce case over the random $\mathit{IV}$ case to the $\mathit{IV}$ on key case. The last one, in particular, is the duplex analogue of the use of a nonce masked with a secret in AES-GCM in TLS 1.3. We apply our findings to duplex-based encryption and authenticated encryption, and discuss the practical applications of our results.

For many latency-critical operations in computer systems, like memory reads/writes, adding encryption can have a big impact on the performance. Hence, the existence of cryptographic primitives with good security properties and minimal latency is a key element in the wide-spread implementation of such security measures. In this paper, we introduce two new families of low-latency permutations/block ciphers called Sonic and SuperSonic, inspired by the Simon block ciphers.

The sum of two $n$-bit pseudorandom permutations is known to behave like a pseudorandom function with $n$ bits of security. A recent line of research has investigated the security of two public $n$-bit permutations and its degree of indifferentiability. Mandal et al. (INDOCRYPT 2010) proved $2n/3$-bit security, Mennink and Preneel (ACNS 2015) pointed out a non-trivial flaw in their analysis and re-proved $(2n/3-\log_2(n))$-bit security. Bhattacharya and Nandi (EUROCRYPT 2018) eventually improved the result to $n$-bit security. Recently, Gunsing at CRYPTO 2022 already observed that a proof technique used in this line of research only holds for sequential indifferentiability. We revisit the line of research in detail, and observe that the strongest bound of $n$-bit security has two other serious issues in the reasoning, the first one is actually the same non-trivial flaw that was present in the work of Mandal et al., while the second one discards biases in the randomness influenced by the distinguisher. More concretely, we introduce two attacks that show limited potential of different approaches. We (i) show that the latter issue that discards biases only holds up to $2^{3n/4}$ queries, and (ii) perform a differentiability attack against their simulator in $2^{5n/6}$ queries. On the upside, we revive the result of Mennink and Preneel and show $(2n/3-\log_2(n))$-bit regular indifferentiability security of the sum of public permutations.

In Internet security protocols including TLS 1.3, KEMTLS, MLS and Noise, HMAC is being assumed to be a dual-PRF, meaning a PRF not only when keyed conventionally (through its first input), but also when "swapped" and keyed (unconventionally) through its second (message) input. We give the first in-depth analysis of the dual-PRF assumption on HMAC. For the swap case, we note that security does not hold in general, but completely characterize when it does; we show that HMAC is swap-PRF secure if and only if keys are restricted to sets satisfying a condition called feasibility, that we give, and that holds in applications. The sufficiency is shown by proof and the necessity by attacks. For the conventional PRF case, we fill a gap in the literature by proving PRF security of HMAC for keys of arbitrary length. Our proofs are in the standard model, make assumptions only on the compression function underlying the hash function, and give good bounds in the multi-user setting. The positive results are strengthened through achieving a new notion of variable key-length PRF security that guarantees security even if different users use keys of different lengths, as happens in practice.

Grover's search algorithm gives a quantum attack against block ciphers by searching for a key that matches a small number of plaintext-ciphertext pairs. This attack uses $O(\sqrt{N})$ calls to the cipher to search a key space of size $N$. Previous work in the specific case of AES derived the full gate cost by analyzing quantum circuits for the cipher, but focused on minimizing the number of qubits. In contrast, we study the cost of quantum key search attacks under a depth restriction and introduce techniques that reduce the oracle depth, even if it requires more qubits. As cases in point, we design quantum circuits for the block ciphers AES and LowMC. Our circuits give a lower overall attack cost in both the gate count and depth-times-width cost models. In NIST's post-quantum cryptography standardization process, security categories are defined based on the concrete cost of quantum key search against AES. We present new, lower cost estimates for each category, so our work has immediate implications for the security assessment of post-quantum cryptography. As part of this work, we release Q# implementations of the full Grover oracle for AES-128, -192, -256 and for the three LowMC instantiations used in Picnic, including unit tests and code to reproduce our quantum resource estimates. To the best of our knowledge, these are the first two such full implementations and automatic resource estimations. This is a revised version that corrects the estimates for AES to account for some issues in Q# that made the original estimates inaccurate. We did not revise the estimates for LowMC, so the resource counts are likely lower than possible.

Doubly-extendable cryptographic keyed functions (deck) generalize the concept of message authentication codes (MAC) and stream ciphers in that they support variable-length strings as input and return variable-length strings as output. A prominent example of building deck functions is Farfalle, which consists of a set of public permutations and rolling functions that are used in its compression and expansion layers. By generalizing the compression layer of Farfalle, we prove its universality in terms of the probability of differentials over the public permutation used in it. As the compression layer of Farfalle is inherently parallel, we compare it to a generalization of a serial compression function inspired by Pelican-MAC. The same public permutation may result in different universalities depending on whether the compression is done in parallel or serial. The parallel construction consistently performs better than the serial one, sometimes by a big factor. We demonstrate this effect using Xoodoo[3], which is a round-reduced variant of the public permutation used in the deck function Xoofff.

We introduce a new type of mixing layer for the round function of cryptographic permutations, called circulant twin column parity mixer (CPM), that is a generalization of the mixing layers in KECCAK-f and XOODOO. While these mixing layers have a bitwise differential branch number of 4 and a computational cost of 2 (bitwise) additions per bit, the circulant twin CPMs we build have a bitwise differential branch number of 12 at the expense of an increase in computational cost: depending on the dimension this ranges between $3$ and $3.34$ XORs per bit. Our circulant twin CPMs operate on a state in the form of a rectangular array and can serve as mixing layer in a round function that has as non-linear step a layer of S-boxes operating in parallel on the columns. When sandwiched between two ShiftRow-like mappings, we can obtain a columnwise branch number of 12 and hence it guarantees 12 active S-boxes per two rounds in differential trails. Remarkably, the linear branch numbers (bitwise and columnwise alike) of these mappings is only 4. However, we define the transpose of a circulant twin CPM that has linear branch number of 12 and a differential branch number of 4. We give a concrete instantiation of a permutation using such a mixing layer, named Gaston. It operates on a state of $5 \times 64$ bits and uses $\chi$ operating on columns for its non-linear layer. Most notably, the Gaston round function is lightweight in that it takes as few bitwise operations as the one of NIST lightweight standard ASCON. We show that the best 3-round differential and linear trails of Gaston have much higher weights than those of ASCON. Permutations like Gaston can be very competitive in applications that rely for their security exclusively on good differential properties, such as keyed hashing as in the compression phase of Farfalle.

In this paper we introduce the differential meet-in-the-middle framework, a new cryptanalysis technique for symmetric primitives. Our new cryptanalysis method combines techniques from both meet-in-the- middle and differential cryptanalysis. As such, the introduced technique can be seen as a way of extending meet-in-the-middle attacks and their variants but also as a new way to perform the key recovery part in differential attacks. We apply our approach to SKINNY-128-384 in the single-key model and to AES-256 in the related-key model. Our attack on SKINNY-128-384 permits to break 25 out of the 56 rounds of this variant and improves by two rounds the previous best known attacks. For AES-256 we attack 12 rounds by considering two related keys, thus outperforming the previous best related-key attack on AES-256 with only two related keys by 2 rounds.

Using the representation of bent functions by bent rectangles, that is, special matrices with restrictions on columns and rows, we obtain an upper bound on the number of bent functions that improves previously known bounds in a practical range of dimensions. The core of our method is the following fact based on the recent observation by Potapov (arXiv:2107.14583): a 2-row bent rectangle is completely determined by one of its rows and the remaining values in slightly more than half of the columns.

This paper introduces CLAASP, a Cryptographic Library for the Automated Analysis of Symmetric Primitives. The library is designed to be modular, extendable, easy to use, generic, efficient and fully automated. It is an extensive toolbox gathering state-of-the-art techniques aimed at simplifying the manual tasks of symmetric primitive designers and analysts. CLAASP is built on top of Sagemath and is open-source under the GPLv3 license. The central input of CLAASP is the description of a cryptographic primitive as a list of connected components in the form of a directed acyclic graph. From this representation, the library can automatically: (1) generate the Python or C code of the primitive evaluation function, (2) execute a wide range of statistical and avalanche tests on the primitive, (3) generate SAT, SMT, CP and MILP models to search, for example, differential and linear trails, (4) measure algebraic properties of the primitive, (5) test neural-based distinguishers. In this work, we also present a comprehensive survey and comparison of other software libraries aiming at similar goals as CLAASP.

Advanced cryptographic protocols such as Zero-knowledge (ZK) proofs of knowledge, widely used in cryptocurrency applications such as Zcash, Monero, Filecoin, Tezos, Topos, demand new cryptographic hash functions that are efficient not only over the binary field $\mathbb{F}_2$, but also over large fields of prime characteristic $\mathbb{F}_p$. This need has been acknowledged by the wider community and new so-called Arithmetization-Oriented (AO) hash functions have been proposed, e.g. MiMC-Hash, Rescue-Prime, Poseidon, Reinforced Concrete and Griffin to name a few. In this paper we propose Anemoi: a new family of ZK-friendly permutations, that can be used to construct efficient hash functions and compression functions. The main features of these algorithms are that 1) they are designed to be efficient within multiple proof systems (e.g. Groth16, Plonk, etc.), 2) they contain dedicated functions optimised for specific applications (namely Merkle tree hashing and general purpose hashing), 3) they have highly competitive performance e.g. about a factor of 2 improvement over Poseidon and Rescue-Prime in terms of R1CS constraints, a 21%-35% Plonk constraint reduction over a highly optimized Poseidon implementation, as well as competitive native performance, running between two and three times faster than Rescue-Prime, depending on the field size. On the theoretical side, Anemoi pushes further the frontier in understanding the design principles that are truly entailed by arithmetization-orientation. In particular, we identify and exploit a previously unknown relationship between CCZ-equivalence and arithmetization-orientation. In addition, we propose two new standalone components that can be easily reused in new designs. One is a new S-box called Flystel, based on the well-studied butterfly structure, and the second is Jive -- a new mode of operation, inspired by the ``Latin dance'' symmetric algorithms (Salsa, ChaCha and derivatives). Our design is a conservative one: it uses a very classical Substitution-Permutation Network structure, and our detailed analysis of algebraic attacks highlights can be of independent interest.

We consider the design of a tweakable block cipher from a block cipher whose inputs and outputs are of size $n$ bits. The main goal is to achieve $2^n$ security with a large tweak (i.e., more than $n$ bits). Previously, Mennink at FSE'15 and Wang et al. at Asiacrypt'16 proposed constructions that can achieve $2^n$ security. Yet, these constructions can have a tweak size up to $n$-bit only. As evident from recent research, a tweakable block cipher with a large tweak is generally helpful as a building block for modes of operation, typical applications including MACs, authenticated encryption, leakage-resilient cryptography and full-disk encryption. We begin with how to design a tweakable block cipher with $2n$-bit tweak and $n$-bit security from two block cipher calls. For this purpose, we do an exhaustive search for tweakable block ciphers with $2n$-bit tweaks from two block cipher calls, and show that all of them suffer from birthday-bound attacks. Next, we investigate the possibility to design a tweakable block cipher with $2n$-bit tweak and $n$-bit security from three block cipher calls. We start with some conditions to build a such tweakable block cipher and propose a natural construction, called G1, that likely meets them. After inspection, we find a weakness on G1 which leads to a birthday-bound attack. Based on G1, we then propose another construction, called G2, that can avoid this weakness. We finally prove that G2 can achieve $n$-bit security with $2n$-bit tweak.

Designing symmetric-key primitives for applications in Fully Homomorphic Encryption (FHE) has become important to address the issue of the ciphertext expansion. In such a context, cryptographic primitives with a low-AND-depth decryption circuit are desired. Consequently, quadratic nonlinear functions are commonly used in these primitives, including the well-known $\chi$ function over $\mathbb{F}_2^n$ and the power map over a large finite field $\mathbb{F}_{p^n}$. In this work, we study the growth of the algebraic degree for an SPN cipher over $\mathbb{F}_{2^n}^{m}$, whose S-box is defined as the combination of a power map $x\mapsto x^{2^d+1}$ and an $\mathbb{F}_2$-linearized affine polynomial $x\mapsto c_0+\sum_{i=1}^{w}c_ix^{2^{h_i}}$ where $c_1,\ldots,c_w\neq0$. Specifically, motivated by the fact that the original coefficient grouping technique published at EUROCRYPT 2023 becomes less efficient for $w>1$, we develop a variant technique that can efficiently work for arbitrary $w$. With this new technique to study the upper bound of the algebraic degree, we answer the following questions from a theoretic perspective: 1. can the algebraic degree increase exponentially when $w=1$? 2. what is the influence of $w$, $d$ and $(h_1,\ldots,h_w)$ on the growth of the algebraic degree? Based on this, we show (i) how to efficiently find $(h_1,\ldots,h_w)$ to achieve the exponential growth of the algebraic degree and (ii) how to efficiently compute the upper bound of the algebraic degree for arbitrary $(h_1,\ldots,h_w)$. Therefore, we expect that these results can further advance the understanding of the design and analysis of such primitives.

NIST selected the A SCON family of cryptographic primitives for standardization in February 2023 as the final step in the Lightweight Cryptography Competition. The ASCON submission to the competition provided Authenticated Encryption with Associated Data (AEAD), hashing, and Extensible Output Function (XOF) modes. Real world cryptography systems often need more than packet encryption and simple hashing. Keyed message authentication, key derivation, cryptographically secure pseudo-random number generation (CSPRNG), password hashing, and encryption of sensitive values in memory are also important. This paper defines additional modes that can be deployed on top of ASCON based on proven designs from the literature.

Motivated by new applications such as secure Multi-Party Computation (MPC), Fully Homomorphic Encryption (FHE), and Zero-Knowledge proofs (ZK), many MPC-, FHE- and ZK-friendly symmetric-key primitives that minimize the number of multiplications over $\mathbb F_p$ for a large prime $p$ have been recently proposed in the literature. These symmetric primitives are usually defined via invertible functions, including (i) Feistel and Lai-Massey schemes and (ii) SPN constructions instantiated with invertible non-linear S-Boxes. However, the ``invertibility'' property is actually never required in any of the mentioned applications. In this paper, we discuss the possibility to set up MPC-/FHE-/ZK-friendly symmetric primitives instantiated with non-invertible bounded surjective functions. With respect to one-to-one functions, any output of a $l$-bounded surjective function admits at most $l$ pre-images. The simplest example is the square map $x\mapsto x^2$ over $\mathbb F_p$ for a prime $p\ge 3$, which is (obviously) $2$-bounded surjective. When working over $\mathbb F_p^n$ for $n\ge 2$, we set up bounded surjective functions by re-considering the recent results proposed by Grassi, Onofri, Pedicini and Sozzi at FSE/ToSC 2022 as starting points. Given a quadratic local map $F:\mathbb F_p^m \rightarrow \mathbb F_p$ for $m\in\{1,2,3\}$, they proved that the shift-invariant non-linear function over $\mathbb F_p^n$ defined as $\mathcal S_F(x_0, x_1, \ldots, x_{n-1}) = y_0\| y_1\| \ldots \| y_{n-1}$ where $y_i := F(x_i, x_{i+1})$ is never invertible for any $n\ge 2\cdot m-1$. Here, we prove that - the quadratic function $F:\mathbb F_p^m \rightarrow \mathbb F_p$ for $m\in\{1,2\}$ that minimizes the probability of having a collision for $\mathcal S_F$ over $\mathbb F_p^n$ is of the form $F(x_0, x_1) = x_0^2 + x_1$ (or equivalent); - the function $\mathcal S_F$ over $\mathbb F_p^n$ defined as before via $F(x_0, x_1) = x_0^2 + x_1$ (or equivalent) is $2^n$-bounded surjective. As concrete applications, we propose modified versions of the MPC-friendly schemes MiMC, HadesMiMC, and (partially of) Hydra, and of the FHE-friendly schemes Masta, Pasta, and Rubato. By instantiating them with the bounded surjective quadratic functions proposed in this paper, we are able to improve the security and/or the performances in the target applications/protocols.

In 2013, the Snowden revelations have shown subversion of cryptographic implementations to be a relevant threat. Since then, the academic community has been pushing the development of models and constructions to defend against adversaries able to arbitrarily subvert cryptographic implementations. To capture these strong capabilities of adversaries, Russell, Tang, Yung, and Zhou (CCS'17) proposed CPA-secure encryption in a model that utilizes a trusted party called a watchdog testing an implementation before use to detect potential subversion. This model was used to construct subversion-resilient implementations of primitives such as random oracles by Russell, Tang, Yung, and Zhou (CRYPTO'18) or signature schemes by Chow et al. (PKC'19) but primitives aiming for a CCA-like security remained elusive in any watchdog model. In this work, we present the first subversion-resilient authenticated encryption scheme with associated data (AEAD) without making use of random oracles. At the core of our construction are subversion-resilient PRFs, which we obtain from weak PRFs in combination with the classical Naor-Reingold transformation. We revisit classical constructions based on PRFs to obtain subversion-resilient MACs, where both tagging and verification are subject to subversion, as well as subversion-resilient symmetric encryption in the form of stream ciphers. Finally, we observe that leveraging the classical Encrypt-then-MAC approach yields subversion-resilient AEAD. Our results are based on the trusted amalgamation model by Russell, Tang, Yung, and Zhou (ASIACRYPT'16) and the assumption of honest key generation.

In the design of GIFT, half round key XOR is used. This leads to the undesired consequence that the security against the differential/linear attacks are overestimated. This comes from the observation that; in the usual DDT/LAT based analysis of the differential/linear attacks, the inherent assumption is the full round key is XORed at each round.

Symmetric-key primitives designed over the prime field $\mathbb{F}_p$ with odd characteristics, rather than the traditional $\mathbb{F}_2^{n}$, are becoming the most popular choice for MPC/FHE/ZK-protocols for better efficiencies. However, the security of $\mathbb{F}_p$ is less understood as there are highly nontrivial gaps when extending the cryptanalysis tools and experiences built on $\mathbb{F}_2^{n}$ in the past few decades to $\mathbb{F}_p$. At CRYPTO 2015, Sun et al. established the links among impossible differential, zero-correlation linear, and integral cryptanalysis over $\mathbb{F}_2^{n}$ from the perspective of distinguishers. In this paper, following the definition of linear correlations over $\mathbb{F}_p$ by Baignéres, Stern and Vaudenay at SAC 2007, we successfully establish comprehensive links over $\mathbb{F}_p$, by reproducing the proofs and offering alternatives when necessary. Interesting and important differences between $\mathbb{F}_p$ and $\mathbb{F}_2^n$ are observed. - Zero-correlation linear hulls can not lead to integral distinguishers for some cases over $\mathbb{F}_p$, while this is always possible over $\mathbb{F}_2^n$ proven by Sun et al.. - When the newly established links are applied to GMiMC, its impossible differential, zero-correlation linear hull and integral distinguishers can be increased by up to 3 rounds for most of the cases, and even to an arbitrary number of rounds for some special and limited cases, which only appeared in $\mathbb{F}_p$. It should be noted that all these distinguishers do not invalidate GMiMC's security claims. The development of the theories over $\mathbb{F}_p$ behind these links, and properties identified (be it similar or different) will bring clearer and easier understanding of security of primitives in this emerging $\mathbb{F}_p$ field, which we believe will provide useful guides for future cryptanalysis and design.

This paper presents ``SASQUATCH'', an open-source tool, that aids in finding an unknown substitution box (SBox) given its properties. The inspiration of our work can be directly attributed to the DCC 2022 paper by Lu, Mesnager, Cui, Fan and Wang. Taking their work as the foundation (i.e., converting the problem of SBox search to a satisfiability modulo theory instance and then invoking a solver), we extend in multiple directions (including -- but not limiting to -- coverage of more options, imposing time limit, parallel execution for multiple SBoxes, non-bijective SBox), and package everything within an easy-to-use interface. We also present ASIC benchmarks for some of the SBoxes.

At SAC 2011, Bertoni et al. introduced the keyed duplex construction as a tool to build permutation based authenticated encryption schemes. The construction was generalized to full-state absorption by Mennink et al. (ASIACRYPT 2015). Daemen et al. (ASIACRYPT 2017) generalized it further to cover much more use cases, and proved security of this general construction, and Dobraunig and Mennink (ASIACRYPT 2019) derived a leakage resilience security bound for this construction. Due to its generality, the full-state keyed duplex construction that we know today has plethora applications, but the flip side of the coin is that the general construction is hard to grasp and the corresponding security bounds are very complex. Consequently, the state-of-the-art results on the full-state keyed duplex construction are not used to the fullest. In this work, we revisit the history of the duplex construction, give a comprehensive discussion of its possibilities and limitations, and demonstrate how the two security bounds (of Daemen et al. and Dobraunig and Mennink) can be interpreted in particular applications of the duplex.

Classical Multivariate Cryptography (MP) is searching for special families of functions of kind ^nF=T_1FTT_2 on the vector space V= (F_q)^n where F is a quadratic or cubical polynomial map of the space to itself, T_1 and T^2 are affine transformations and T is the piece of information such that the knowledge of the triple T_1, T_2, T allows the computation of reimage x of given nF(x) in polynomial time O(n^ᾳ). Traditionally F is given by the list of coefficients C(^nF) of its monomial terms ordered lexicographically. We consider the Inverse Problem of MP of finding T_1, T_2, T for F given in its standard form. The solution of inverse problem is harder than finding the procedure to compute the reimage of ^nF in time O(n^ᾳ). For general quadratic or cubic maps nF this is NP hard problem. In the case of special family some arguments on its inclusion to class NP has to be given.

Recent constructions of (tweakable) block ciphers with an embedded cryptographic backdoor relied on the existence of probability-one differentials or perfect (non-)linear approximations over a reduced-round version of the primitive. In this work, we study how the existence of probability-one differentials or perfect linear approximations over two rounds of a substitution-permutation network can be avoided by design. More precisely, we develop criteria on the s-box and the linear layer that guarantee the absence of probability-one differentials for all keys. We further present an algorithm that allows to efficiently exclude the existence of keys for which there exists a perfect linear approximation.

In this paper we propose a new construction for building universal hash functions, a specific instance called multi-265, and provide proofs for their universality. Our construction follows the key-then-hash parallel paradigm. In a first step it adds a variable length input message to a secret key and splits the result in blocks. Then it applies a fixed-length public function to each block and adds their results to form the output. The innovation presented in this work lies in the public function: we introduce the multiply-transform-multiply-construction that makes use of field multiplication and linear transformations. We prove upper bounds for the universality of key-then-hash parallel hash functions making use of a public function with our construction provided the linear transformation are maximum-distance-separable (MDS). We additionally propose a concrete instantiation of our construction multi-265, where the underlying public function uses a near-MDS linear transformation and prove it to be $2^{-154}$-universal. We also make the reference code for multi-265 available.

The construction of invertible non-linear layers over $\mathbb F_p^n$ that minimize the multiplicative cost is crucial for the design of symmetric primitives targeting Multi Party Computation (MPC), Zero-Knowledge proofs (ZK), and Fully Homomorphic Encryption (FHE). At the current state of the art, only few non-linear functions are known to be invertible over $\mathbb F_p$, as the power maps $x\mapsto x^d$ for $\gcd(d,p-1)=1$. When working over $\mathbb F_p^n$ for $n\ge2$, a possible way to construct invertible non-linear layers $\mathcal S$ over $\mathbb F_p^n$ is by making use of a local map $F:\mathbb F_p^m\rightarrow \mathbb F_p$ for $m\le n$, that is, $\mathcal S_F(x_0, x_1, \ldots, x_{n-1}) = y_0\|y_1\|\ldots \|y_{n-1}$ where $y_i = F(x_i, x_{i+1}, \ldots, x_{i+m-1})$. This possibility has been recently studied by Grassi, Onofri, Pedicini and Sozzi at FSE/ToSC 2022. Given a quadratic local map $F:\mathbb F_p^m \rightarrow \mathbb F_p$ for $m\in\{1,2,3\}$, they proved that the shift-invariant non-linear function $\mathcal S_F$ over $\mathbb F_p^n$ defined as before is never invertible for any $n\ge 2\cdot m-1$. In this paper, we face the problem by generalizing such construction. Instead of a single local map, we admit multiple local maps, and we study the creation of nonlinear layers that can be efficiently verified and implemented by a similar shift-invariant lifting. After formally defining the construction, we focus our analysis on the case $\mathcal S_{F_0, F_1}(x_0, x_1, \ldots, x_{n-1}) = y_0\|y_1\|\ldots \|y_{n-1}$ for $F_0, F_1 :\mathbb F_p^2\rightarrow \mathbb F_p$ of degree at most 2. This is a generalization of the previous construction using two alternating functions $F_0,F_1$ instead of a single $F$. As main result, we prove that (i) if $n\ge3$, then $\mathcal S_{F_0, F_1}$ is never invertible if both $F_0$ and $F_1$ are quadratic, and that (ii) if $n\ge 4$, then $\mathcal S_{F_0, F_1}$ is invertible if and only if it is a Type-II Feistel scheme.

The graphs ${\cal G}_F=\{(x,F(x)); x\in \mathbb{F}_2^n\}$ of those $(n,n)$-functions $F:\mathbb{F}_2^n\mapsto \mathbb{F}_2^n$ that are almost perfect nonlinear (in brief, APN; an important notion in symmetric cryptography) are, equivalently to their original definition by K. Nyberg, those Sidon sets (an important notion in combinatorics) $S$ in $({\Bbb F}_2^n\times {\Bbb F}_2^n,+)$ such that, for every $x\in {\Bbb F}_2^n$, there exists a unique $y\in {\Bbb F}_2^n$ such that $(x,y)\in S$. Any subset of a Sidon set being a Sidon set, an important question is to determine which Sidon sets are maximal relatively to the order of inclusion. In this paper, we study whether the graphs of APN functions are maximal (that is, optimal) Sidon sets. We show that this question is related to the problem of the existence / non-existence of pairs of APN functions lying at distance 1 from each others, and to the related problem of the existence of APN functions of algebraic degree $n$. We revisit the conjectures that have been made on these latter problems.

Machine Learning (ML) is almost ubiquitously used in multiple disciplines nowadays. Recently, we have seen its usage in the realm of differential distinguishers for symmetric key ciphers. In this work, we explore the possibility of a number of ciphers with respect to various ML-based distinguishers. We show new distinguishers on the unkeyed and round reduced version of SPECK-32, SPECK-128, ASCON, SIMECK-32, SIMECK-64 and SKINNY-128. We explore multiple avenues in the process. In summary, we use neural network as well as support vector machine in various settings (such as varying the activation function), apart from experimenting with a number of input difference tuples. Among other results, we show a distinguisher of 8-round SPECK-32 that works with practical data complexity (most of the experiments take a few hours on a personal computer).

SPEEDY is a family of ultra-lightweight block ciphers designed by Leander et al. at CHES 2021. There are three recommended variants denoted as SPEEDY-$r$-192 with $r$∈{5,6,7}. All of them support the 192-bit block and the 192-bit key. The main focus during its design is to ensure hardware-aware low latency, thus, whether it is designed to have enough security is worth to be studied. Recently, the full-round security of SPEEDY-7-192 is announced to be broken by Boura et al. at EUROCRYPT 2023 under the chosen-ciphertext setting, where a round-reduced attack on SPEEDY-6-192 is also proposed. However, no valid attack on SPEEDY-5-192 is given due to its more restricted security parameters. Up to now, the best key recovery attack on this variant only covers 3 rounds proposed by Rohit et al. at AFRICACRYPT 2022. In this paper, we give three full-round attacks on SPEEDY-7-192. Using the divide-and-conquer strategy and other new proposed techniques, we found a 5.5-round differential distinguisher which can be used to mount the first chosen-plaintext full-round key recovery attack. With a similar strategy, we also found a 5-round linear distinguisher which leads to the first full-round attack under the known-plaintext setting. Meanwhile, the 5.5-round differential distinguisher also helps us slightly improve the full-round attack in the chosen-ciphertext setting compared with the previous result. Besides, we also present a 4-round differential attack on SPEEDY-5-192, which is the best attack on this variant in terms of the number of rounds so far. A faster key recovery attack covering the same rounds is also given using a differential-linear distinguisher. Both attacks cannot threaten the full round security of SPEEDY-5-192.

In this paper we formally introduce a novel mode of operation based on the cipher block chaining mode. The main idea of this mode is to use a stateful block cipher instead of a stateless one. Afterwards, we show how to implement our proposal and present a performance analysis of our mode. Next, we provide a concrete security analysis by computing a tight bound on the success of adversaries based on their resources. The results of our performance and security analyses are that this novel mode is more secure than the cipher block chaining mode for large files, but the encryption/decryption time doubles/triples. Therefore, our novel mode is suitable for encrypting large files, when higher security is required, but speed is not paramount. Note that the changes required to transform the software implementations of the cipher block chaining mode into this new mode are minimal, and therefore transitioning to this new mode is straightforward.

Authenticated Encryption (AE) achieves privacy and authenticity with a single scheme. It is possible to obtain an AE scheme gluing together an encryption scheme (privacy secure) and a Message Authentication Code (authenticity secure). This approach is called generic composition and its security has been studied by Namprempre et al. [NRS14]. They looked into all the possible gluings of an encryption scheme with a secure MAC to obtain a nonce-based AE-scheme. The encryption scheme is either IV-based (that is, with an additional random input, the initialization vector [IV]) or nonce-based (with an input to be used once, the nonce). Nampremepre et al. assessed the security/insecurity of all possible composition combinations except for 4 (N4, A10, A11 and A12). Berti et al. [BPP18a] showed that N4 is insecure and that the remaining modes (A10, A11, and A12) are either all secure or insecure. Here, we prove that these modes are all insecure with a counterexample.

The boomerang attack is a cryptanalysis technique that combines two short differentials instead of using a single long differential. It has been applied to many primitives, and results in the best known attacks against several AES-based ciphers (Kiasu-BC, Deoxys-BC). In this paper, we introduce a general framework for boomerang attacks with truncated differentials. While the underlying ideas are already known, we show that a careful analysis provides a significant improvement over the best boomerang attacks in the literature. In particular, we take into account structures on the plaintext and ciphertext sides, and include an analysis of the key recovery step. On 6-round AES, we obtain a structural distinguisher with complexity $2^{87}$ and a key recovery attack with complexity $2^{61}$. The truncated boomerang attacks is particularly effective against tweakable AES variants. We apply it to 8-round Kiasu-BC, resulting in the best known attack with complexity $2^{83}$ (rather than $2^{103}$). We also show an interesting use of the 6-round distinguisher on TNT-AES, a tweakable block-cipher using 6-round AES as a building block. Finally, we apply this framework to Deoxys-BC, using a MILP model to find optimal trails automatically. We obtain the best attacks against round-reduced versions of all variants of Deoxys-BC.

A line of recent work has highlighted the importance of context commitment security, which asks that authenticated encryption with associated data (AEAD) schemes will not decrypt the same adversarially-chosen ciphertext under two different, adversarially-chosen contexts (secret key, nonce, and associated data). Despite a spate of recent attacks, many open questions remain around context commitment; most obviously nothing is known about the commitment security of important schemes such as CCM, EAX, and SIV. We resolve these open questions, and more. Our approach is to, first, introduce a new framework that helps us more granularly define context commitment security in terms of what portions of a context are adversarially controlled. We go on to formulate a new notion, called context discoverability security, which can be viewed as analogous to preimage resistance from the hashing literature. We show that unrestricted context commitment security (the adversary controls all of the two contexts) implies context discoverability security for a class of schemes encompassing most schemes used in practice. Then, we show new context discovery attacks against a wide set of AEAD schemes, including CCM, EAX, SIV, GCM, and OCB3, and, by our general result, this gives new unrestricted context commitment attacks against them. Finally, we consider restricted context commitment security for the original SIV mode, for which no prior attack techniques work (including our context discovery based ones). We are nevertheless able to give a novel $O(2^{n/3})$ attack using Wagner's k-tree algorithm for the generalized birthday problem.

In this paper, we present the ``DORCIS'' tool, which finds depth-optimized quantum circuit implementations for arbitrary 3- and 4-bit S-boxes. It follows up from the previous LIGHTER-R tool (which only works for 4-bit S-boxes) by extending it in multiple ways. LIGHTER-R only deals at the top level (i.e., Toffoli gates), whereas DORCIS takes quantum decomposition (i.e., Clifford + T gates) into account. Further, DORCIS optimizes for quantum depth and T depth. We match, if not surpass, other optimized quantum circuit implementations put forth in the other papers. Similar to LIGHTER-R, our tool is also easy to use, and we provide an extended interface to IBM's Qiskit.

The idea of hybrid homomorphic encryption (HHE) is to drastically reduce bandwidth requirements when using homomorphic encryption (HE) at the cost of more expensive computations in the encrypted domain. To this end, various dedicated schemes for symmetric encryption have already been proposed. However, it is still unclear if those ideas are already practically useful, because (1) no cost-benefit analysis was done for use cases and (2) very few implementations are publicly available. We address this situation in several ways. We build an open-source benchmarking framework involving several use cases covering three popular libraries. Using this framework, we explore properties of the respective HHE proposals. It turns out that even medium-sized use cases are infeasible, especially when involving integer arithmetic. Next, we propose Pasta, a cipher thoroughly optimized for integer HHE use cases. Pasta is designed to minimize the multiplicative depth, while also leveraging the structure of two state-of-the-art integer HE schemes (BFV and BGV) to minimize the homomorphic evaluation latency. Using our new benchmarking environment, we extensively evaluate Pasta in SEAL and HElib and compare its properties to 8 existing ciphers in two use cases. Our evaluations show that Pasta outperforms its competitors for HHE both in terms of homomorphic evaluation time and noise consumption, showing its efficiency for applications in real-world HE use cases. Concretely, Pasta outperforms Agrasta by a factor of up to 82, Masta by a factor of up to 6 and Hera up to a factor of 11 when applied to the two use cases.

Zero-correlation linear attack is a powerful attack of block ciphers, the lower number of rounds (LNR) which no its distinguisher (named zero-correlation linear approximation, ZCLA) exists reflects the ability of a block cipher against the zero-correlation linear attack. However, due to the large search space, showing there are no ZCLAs exist for a given block cipher under a certain number of rounds is a very hard task. Thus, present works can only prove there no ZCLAs exist in a small search space, such as 1-bit/nibble/word input and output active ZCLAs, which still exist very large gaps to show no ZCLAs exist in the whole search space. In this paper, we propose the meet-in-the-middle method and double-collision method to show there no ZCLAs exist in the whole search space. The basic ideas of those two methods are very simple, but they work very effectively. As a result, we apply those two methods to AES, Midori64, and ARIA, and show that there no ZCLAs exist for $5$-round AES without the last Mix-Column layer, $7$-round Midori64 without the last Mix-Column layer, and $5$-round ARIA without the last linear layer. As far as we know, our method is the first automatic method that can be used to show there no ZCLAs exist in the whole search space, which can provide sufficient evidence to show the security of a block cipher against the zero-correlation linear attack in the distinguishers aspect, this feature is very useful for designing block ciphers.

As the prevalence of quantum computing is growing in leaps and bounds over the past few years, there is an ever-growing need to analyze the symmetric-key ciphers against the upcoming threat. Indeed, we have seen a number of research works dedicated to this. Our work delves into this aspect of block ciphers, with respect to the SPECK family and LowMC family. The SPECK family received two quantum analysis till date (Jang et al., Applied Sciences, 2020; Anand et al., Indocrypt, 2020). We revisit these two works, and present improved benchmarks SPECK (all 10 variants). Our implementations incur lower full depth compared to the previous works. On the other hand, the quantum circuit of LowMC was explored earlier in Jaques et al.'s Eurocrypt 2020 paper. However, there is an already known bug in their paper, which we patch. On top of that, we present two versions of LowMC (on L1, L3 and L5 variants) in quantum, both of which incur significantly less full depth than the bug-fixed implementation.

At Eurocrypt 2016, Méaux et al. presented FLIP, a new family of stream ciphers {that aimed to enhance the efficiency of homomorphic encryption frameworks. Motivated by FLIP, recent research has focused on the study of Boolean functions with good cryptographic properties when restricted to subsets of the space $\mathbb{F}_2^n$. If an $n$-variable Boolean function has the property of balancedness when restricted to each set of vectors with fixed Hamming weight between $1$ and $n-1$, it is a weightwise perfectly balanced (WPB) Boolean function. In the literature, a few algebraic constructions of WPB functions are known, in which there are some constructions that use iterative method based on functions with low degrees of 1, 2, or 4. In this paper, we generalize the iterative method and contribute a unified construction of WPB functions based on functions with algebraic degrees that can} be any power of 2. For any given positive integer $d$ not larger than $m$, we first provide a class of $2^m$-variable Boolean functions with a degree of $2^{d-1}$. Utilizing these functions, we then present a construction of $2^m$-variable WPB functions $g_{m;d}$. In particular, $g_{m;d}$ includes four former classes of WPB functions as special cases when $d=1,2,3,m$. When $d$ takes other integer values, $g_{m;d}$ has never appeared before. In addition, we prove the algebraic degree of the constructed WPB functions and compare the weightwise nonlinearity of WPB functions known so far in 8 and 16 variables.

We consider the problem of constructing an unconditionally secure cipher with a short key for the case where the probability distribution of encrypted messages is unknown. Note that unconditional security means that an adversary with no computational constraints can obtain only a negligible amount of information ("leakage") about an encrypted message (without knowing the key). Here we consider the case of a priori (partially) unknown message source statistics. More specifically, the message source probability distribution belongs to a given family of distributions. We propose an unconditionally secure cipher for this case. As an example, one can consider constructing a single cipher for texts written in any of the languages of the European Union. That is, the message to be encrypted could be written in any of these languages.

Randomness cannot be compressed, hence expanded randomness is ‘contaminated randomness’ where hidden pattern is used. Current cryptography uses little randomness (the key) to generate large randomness (the ciphertext). The pattern used for this expansion is subject to cryptanalysis. By contrast, Vernam and the new breed of Trans-Vernam ciphers project security with sufficient supply of genuine randomness. Having no hidden pattern in their process, they expose no vulnerability to cryptanalysis, other than brute force, the efficacy of which, is well gauged by using enough randomness to brute-force through. Unlike the original genuine randomness cipher (the Vernam cipher; US patent: 1,310,719), the new breed of Trans-Vernam ciphers (US patents: 10,541,802, 10,911,215, 11,159,317 to name a few) projects security with shared randomness (between transmitter and recipient) as well as with unilateral randomness determined ad hoc by the transmitter, thereby controlling the vulnerability of the transmitted message, including eliminating it all together, rising to Vernam grade. The new Trans-Vernam ciphers exploit new technologies for generating high-grade randomness, storing it and communicating it in large quantities. Their security is mathematically established and barring faulty implementation these ciphers are unbreakable. We are looking at a flat cyberspace, no more hierarchy based on math skills: Vernam grade security delivered through modern Trans-Vernam ciphers. Robust privacy of communication will be claimed by all – for good and for ill; law-enforcement and national security will have to adjust. It's a new cryptography, and a new society.

In this paper, we present an AES-based authenticated-encryption with associated-data scheme called Rocca, with the purpose to reach the requirements on the speed and security in 6G systems. To achieve ultrafast software implementations, the basic design strategy is to take full advantage of the AES-NI and SIMD instructions as that of the AEGIS family and Tiaoxin-346. Although Jean and Nikolić have generalized the way to construct efficient round functions using only one round of AES (aesenc) and 128-bit XOR operation and have found several efficient candidates, there still seems to exist potential to further improve it regarding speed and state size. In order to minimize the critical path of one round, we remove the case of applying both aesenc and XOR in a cascade way for one round. By introducing a cost-free block permutation in the round function, we are able to search for candidates in a larger space without sacrificing the performance. Consequently, we obtain more efficient constructions with a smaller state size than candidates by Jean and Nikolić. Based on the newly-discovered round function, we carefully design the corresponding AEAD scheme with 256-bit security by taking several reported attacks on the AEGIS family and Tiaxion-346 into account. Our AEAD scheme can reach 178 Gbps which is almost 5 times faster than the AEAD scheme of SNOW-V. Rocca is also much faster than other efficient schemes with 256-bit key length, e.g. AEGIS-256 and AES-256-GCM. As far as we know, Rocca is the first dedicated cryptographic algorithm targeting 6G systems, i.e., 256-bit key length and the speed of more than 100 Gbps.

We study authenticated encryption (AE) modes dedicated to very short messages, which are crucial for Internet-of-things applications. Since the existing general-purpose AE modes need at least three block cipher calls for non-empty messages, we explore the design space for AE modes that use at most two calls. We proposed a family of AE modes, dubbed Manx, that work when the total input length is less than $2n$ bits, using an $n$-bit block cipher. Notably, the second construction of Manx can encrypt almost n-bit plaintext and saves one or two block cipher calls from the standard modes, such as GCM or OCB, keeping the comparable provable security. We also present benchmarks on popular 8/32-bit microprocessors using AES. Our results show the clear advantage of Manx over the previous modes for such short messages.

In a recent presentation, we promoted the use of 12-round instances of Keccak, collectively called “TurboSHAKE”, in post-quantum cryptographic schemes, but without defining them further. The goal of this note is to fill this gap: The definition of the TurboSHAKE family simply consists in exposing and generalizing the primitive already defined inside KangarooTwelve.

Grover’s algorithm is a quantum searching algorithm that poses a threat to symmetric cryptography. Due to their smaller key sizes, lightweight cryptographic algorithms such as Simplified-AES face a much more immediate threat from Grover’s algorithm than traditional cryptographic algorithms. By analyzing different S-boxes, it was discovered that the S-box 946C753AE8FBD012 may be more quantum resistant than the S-box that Simplified-AES uses, 94ABD1856203CEF7. In addition to this, 16x4 S-boxes (or 4 4x4 S-boxes) showed to be significantly more quantum secure than 4x4 S-boxes. This is because the number of gates needed to model a $2^n$x4 S-box increases at an exponential rate. It was also found that this property extends to $2^n$x8 S-boxes, implying the existence of a more quantum secure 8x8 S-box that AES could use. However, an increase in quantum security does not equate to an increase in classical security, as some of the least quantum secure S-boxes analyzed displayed some of the best classical security. Finally, an alteration of Simplified-AES that used a 16x4 S-box was found that displayed better classical and quantum security than Simplified-AES and did not require an increase in key size.

This work surveys mathematical aspects of division property, which is a state of the art technique in cryptanalysis of symmetric-key algorithms, such as authenticated encryption, block ciphers and stream ciphers. It aims to find integral distinguishers and cube attacks, which exploit weakness in the algebraic normal forms of the output coordinates of the involved vectorial Boolean functions. Division property can also be used to provide arguments for security of primitives against these attacks. The focus of this work is a formal presentation of the theory behind the division property, including rigorous proofs, which were often omitted in the existing literature. This survey covers the two major variants of division property, namely conventional and perfect division property. In addition, we explore relationships of the technique with classic degree bounds.

Motivated by new applications such as secure Multi-Party Computation (MPC), Fully Homomorphic Encryption (FHE), and Zero-Knowledge proofs (ZK), many MPC-, FHE- and ZK-friendly symmetric-key primitives that minimize the number of multiplications over $\mathbb{F}_p$ for a large prime $p$ have been recently proposed in the literature. This goal is often achieved by instantiating the non-linear layer via power maps $x\mapsto x^d$. In this paper, we start an analysis of new non-linear permutation functions over $\mathbb{F}_p^n$ that can be used as building blocks in such symmetric-key primitives. Given a local map $F:\mathbb{F}_p^m \rightarrow \mathbb{F}_p$, we limit ourselves to focus on S-Boxes over $\mathbb{F}_p^n$ for $n\ge m$ defined as $\mathcal{S}_F(x_0, x_1, \ldots, x_{n-1}) = y_0\| y_1\| \ldots \| y_{n-1}$ where $y_i := F(x_i, x_{i+1}, \ldots, x_{i+m-1} )$. As main results, we prove that - given any quadratic function $F:\mathbb{F}_p^2 \rightarrow \mathbb{F}_p$, the corresponding S-Box $\mathcal{S}_F$ over $\mathbb{F}_p^n$ for $n\ge 3$ is never invertible; - similarly, given any quadratic function $F:\mathbb{F}_p^3 \rightarrow \mathbb{F}_p$, the corresponding S-Box $\mathcal{S}_F$ over $\mathbb{F}_p^n$ for $n\ge 5$ is never invertible. Moreover, for each $p\ge 3$, we present (1st) generalizations of the Lai-Massey construction over $\mathbb{F}_p^n$ defined as before via functions $F:\mathbb{F}_p^m \rightarrow \mathbb{F}_p$ for each $n=m\ge 2$ and (2nd) (non-trivial) quadratic functions $F:\mathbb{F}_p^3 \rightarrow \mathbb{F}_p$ such that $\mathcal{S}_F$ over $\mathbb{F}_p^n$ for $n\in \{3,4\}$ is invertible. As an open problem for future work, we conjecture that for each $m\ge 1$ there exists a \textit{finite} integer $n_{\text{max}}(m)$ such that $\mathcal{S}_F$ over $\mathbb{F}_p^n$ defined as before via a quadratic function $F:\mathbb{F}_p^m \rightarrow \mathbb{F}_p$ is \textit{not} invertible for each $n\ge n_{\text{max}}(m)$. Finally, as a concrete application, we propose Neptune, a variant of the sponge hash function Poseidon, whose non-linear layer is designed by taking into account the results presented in this paper. We show that this variant leads to a concrete multiplication reduction with respect to Poseidon.

Duplex-based authenticated encryption modes with a sufficiently large key length are proven to be secure up to the birthday bound 2^(c/2), where c is the capacity. However this bound is not known to be tight and the complexity of the best known generic attack, which is based on multicollisions, is much larger: it reaches (2^c)/α where α represents a small security loss factor. There is thus an uncertainty on the true extent of security beyond the bound 2^(c/2) provided by such constructions. In this paper, we describe a new generic attack against several duplex-based AEAD modes. Our attack leverages random functions statistics and produces a forgery in time complexity O(2^(3c/4)) using negligible memory and no encryption queries. Furthermore, for some duplex-based modes, our attack recovers the secret key with a negligible amount of additional computations. Most notably, our attack breaks a security claim made by the designers of the NIST lightweight competition candidate Xoodyak. This attack is a step further towards determining the exact security provided by duplex-based constructions.

A central problem in cryptanalysis is to find all the significant deviations from randomness in a given $n$-bit cryptographic primitive. When $n$ is small (e.g., an $8$-bit S-box), this is easy to do, but for large $n$, the only practical way to find such statistical properties was to exploit the internal structure of the primitive and to speed up the search with a variety of heuristic rules of thumb. However, such bottom-up techniques can miss many properties, especially in cryptosystems which are designed to have hidden trapdoors. In this paper we consider the top-down version of the problem in which the cryptographic primitive is given as a structureless black box, and reduce the complexity of the best known techniques for finding all its significant differential and linear properties by a large factor of $2^{n/2}$. Our main new tool is the idea of using {\it surrogate differentiation}. In the context of finding differential properties, it enables us to simultaneously find information about all the differentials of the form $f(x) \oplus f(x \oplus \alpha)$ in all possible directions $\alpha$ by differentiating $f$ in a single arbitrarily chosen direction $\gamma$ (which is unrelated to the $\alpha$'s). In the context of finding linear properties, surrogate differentiation can be combined in a highly effective way with the Fast Fourier Transform. For $64$-bit cryptographic primitives, this technique makes it possible to automatically find in about $2^{64}$ time all their differentials with probability $p \geq 2^{-32}$ and all their linear approximations with bias $|p| \geq 2^{-16}$; previous algorithms for these problems required at least $2^{96}$ time. Similar techniques can be used to significantly improve the best known time complexities of finding related key differentials, second-order differentials, and boomerangs. In addition, we show how to run variants of these algorithms which require no memory, and how to detect such statistical properties even in trapdoored cryptosystems whose designers specifically try to evade our techniques.

The area of multi-party computation (MPC) has recently increased in popularity and number of use cases. At the current state of the art, Ciminion, a Farfalle-like cryptographic function, achieves the best performance in MPC applications involving symmetric primitives. However, it has a critical weakness. Its security highly relies on the independence of its subkeys, which is achieved by using an expensive key schedule. Many MPC use cases involving symmetric pseudo-random functions (PRFs) rely on secretly shared symmetric keys, and hence the expensive key schedule must also be computed in MPC. As a result, Ciminion's performance is significantly reduced in these use cases. In this paper we solve this problem. Following the approach introduced by Ciminion's designers, we present a novel primitive in symmetric cryptography called Megafono. Megafono is a keyed extendable PRF, expanding a fixed-length input to an arbitrary-length output. Similar to Farfalle, an initial keyed permutation is applied to the input, followed by an expansion layer, involving the parallel application of keyed ciphers. The main novelty regards the expansion of the intermediate/internal state for "free", by appending the sum of the internal states of the first permutation to its output. The combination of this and other modifications, together with the impossibility for the attacker to have access to the input state of the expansion layer, make Megafono very efficient in the target application. As a concrete example, we present the PRF Hydra, an instance of Megafono based on the Hades strategy and on generalized versions of the Lai--Massey scheme. Based on an extensive security analysis, we implement Hydra in an MPC framework. The results show that it outperforms all MPC-friendly schemes currently published in the literature.

In CRYPTO'03, Patarin conjectured a lower bound on the number of distinct solutions $(P_1, \ldots, P_{q}) \in (\{0, 1\}^{n})^{q}$ satisfying a system of equations of the form $X_i \oplus X_j = \lambda_{i,j}$ such that $P_1, P_2, \ldots$, $P_{q}$ are pairwise distinct. This result is known as \emph{``$P_i \oplus P_j$ Theorem for any $\xi_{\max}$''} or alternatively as \emph{Mirror Theory for general $\xi_{\max}$}, which was later proved by Patarin in ICISC'05. Mirror theory for general $\xi_{\max}$ stands as a powerful tool to provide a high-security guarantee for many blockcipher-(or even ideal permutation-) based designs. Unfortunately, the proof of the result contains gaps that are non-trivial to fix. In this work, we present the first complete proof of the $P_i \oplus P_j$ theorem for a wide range of $\xi_{\max}$, typically up to order $O(2^{n/4}/\sqrt{n})$. Furthermore, our proof approach is made simpler by using a new type of equation, dubbed link-deletion equation, that roughly corresponds to half of the so-called orange equations from earlier works. As an illustration of our result, we also revisit the security proofs of two optimally secure blockcipher-based pseudorandom functions, and $n$-bit security proof for six round Feistel cipher, and provide updated security bounds.

The widespread deployment of low-power and handheld devices opens an opportunity to design lightweight authenticated encryption schemes. The schemes so proposed must also prove their resilience under various security notions. Romulus-N1 is an authenticated encryption scheme with associated data based on a tweakable blockcipher, a primary variant of Romulus-N family which is NIST (National Institute of Standards and Technology) lightweight cryptography competition finalist; provides beyond birthday bound security for integrity security in nonce respecting scenario but fails to provide the integrity security in nonce misuse and RUP (release of unverified plaintext) scenarios. In this paper, we propose lynx, a family with $14$ members of 1-pass and rate-1 lightweight authenticated encryption schemes with associated data based on a tweakable blockcipher, that provides birthday bound security for integrity security in both nonce respecting as well as nonce misuse and RUP scenarios and birthday bound security for privacy in nonce respecting scenario. For creating such a family of schemes we propose a family of function $\mathcal{F}$ that provides a total of $72$ cases out of which we show that only $14$ of them can be used for creating authenticated encryption schemes. We provide the implementation of one of the members of lynx family on six different hardware platforms and compare it with Romulus-N1. The comparison clearly shows that the lynx member outperforms Romulus-N1 on all the six platforms.

In this paper we, for the first time, study the question under which circumstances decomposing a round function of a Substitution-Permutation Network is possible uniquely. More precisely, we provide necessary and sufficient criteria for the non-linear layer on when a decomposition is unique. Our results in particular imply that, when cryptographically strong S-boxes are used, the decomposition is indeed unique. We then apply our findings to the notion of alignment, pointing out that the previous definition allows for primitives that are both aligned and unaligned simultaneously. As a second result, we present experimental data that shows that alignment might only have limited impact. For this, we compare aligned and unaligned versions of the cipher PRESENT.

Differential attacks are among the most important families of cryptanalysis against symmetric primitives. Since their introduction in 1990, several improvements to the basic technique as well as many dedicated attacks against symmetric primitives have been proposed. Most of the proposed improvements concern the key-recovery part. However, when designing a new primitive, the security analysis regarding differential attacks is often limited to finding the best trails over a limited number of rounds with branch and bound techniques, and a poor heuristic is then applied to deduce the total number of rounds a differential attack could reach. In this work we analyze the security of the SPEEDY family of block ciphers against differential cryptanalysis and show how to optimize many of the steps of the key-recovery procedure for this type of attacks. For this, we implemented a search for finding optimal trails for this cipher and their associated multiple probabilities under some constraints and applied non-trivial techniques to obtain optimal data and key-sieving. This permitted us to fully break SPEEDY-7-192, the 7-round variant of SPEEDY supposed to provide 192-bit security. Our work demonstrates among others the need to better understand the subtleties of differential cryptanalysis in order to get meaningful estimates on the security offered by a cipher against these attacks.

The Meet-in-the-Middle (MitM) attack has been widely applied to preimage attacks on Merkle-Damg{\aa}rd (MD) hashing. In this paper, we introduce a generic framework of the MitM attack on sponge-based hashing. We find certain bit conditions can significantly reduce the diffusion of the unknown bits and lead to longer MitM characteristics. To find good or optimal configurations of MitM attacks, e.g., the bit conditions, the neutral sets, and the matching points, we introduce the bit-level MILP-based automatic tools on Keccak, Ascon and Xoodyak. To reduce the scale of bit-level models and make them solvable in reasonable time, a series of properties of the targeted hashing are considered in the modelling, such as the linear structure and CP-kernel for Keccak, the Boolean expression of Sbox for Ascon. Finally, we give an improved 4-round preimage attack on Keccak-512/SHA3, and break a nearly 10 years’ cryptanalysis record. We also give the first preimage attacks on 3-/4-round Ascon-XOF and 3-round Xoodyak-XOF.

Security against side-channels and faults is a must for the deployment of embedded cryptography. A wide body of research has investigated solutions to secure implementations against these attacks at different abstraction levels. Yet, to a large extent, current solutions focus on one or the other threat. In this paper, we initiate a mode-level study of cryptographic primitives that can ensure security in a (new and practically-motivated) adversarial model combining leakage and faults. Our goal is to identify constructions that do not require a uniform protections of all their operations against both attack vectors. For this purpose, we first introduce a versatile and intuitive model to capture leakage and faults. We then show that a MAC introduced at Asiacrypt 2021 natively enables a leveled implementation where only its underlying tweakable block cipher must be protected, as long as only its tag verification can be faulted. We finally describe two approaches to amplify security in the case where also the tag generation can be faulted. One is based on iteration and requires the adversary to inject increasingly large faults to succeed. The other is based on randomness and allows provable security against differential faults.

Virtually all modern blockciphers are iterated. In this paper, we ask: to construct a secure iterated blockcipher "non-trivially", how many calls to random functions and permutations are necessary? When security means indistinguishability from a random permutation, optimality is achieved by the Even-Mansour scheme using 1 call to a public permutation. We seek for the arguably strongest security indifferentiability from an ideal cipher, a notion introduced by Maurer et al. (TCC 2004) and popularized by Coron et al. (JoC, 2014). We provide the first generic negative result/lower bounds: when the key is not too short, no iterated blockcipher making 3 calls is (statistically) indifferentiable. This proves optimality for a 4-call positive result of Guo et al. (Eprint 2016). Furthermore, using 1 or 2 calls, even indifferentiable iterated blockciphers with polynomial keyspace are impossible. To prove this, we develop an abstraction of idealized iterated blockciphers and establish various basic properties, and apply Extremal Graph Theory results to prove the existence of certain (generalized) non-random properties such as the boomerang and yoyo.

The sponge construction is a popular method for hashing. Quickly after its introduction, the sponge was proven to be tightly indifferentiable from a random oracle up to $ \approx 2^{c/2}$ queries, where $c$ is the capacity. However, this bound is not tight when the number of message blocks absorbed is restricted to $\ell <\lceil \frac{c}{2(b-c)}\rceil + 1$ (but still an arbitrary number of blocks can be squeezed). In this work, we show that this restriction leads to indifferentiability from a random oracle up to $\approx \min \left\{2^{b/2}, \max\left\{2^{c/2}, 2^{b- \ell \times (b-c)} \right\}\right\}$ queries, where $b>c$ is the permutation size. Depending on the parameters chosen, this result allows to have enhanced security or to absorb at a larger rate for applications that require a fixed-length input hash function.

This note describes a new efficient bit-slice implementation DenseQMC of the Quine-McCluskey algorithm for finding all prime implicants of a Boolean function in the dense case. It is practically feasible for n <= 23 when run on a common laptop or for n <= 27 when run on a server with 1 TiB RAM. This note also outlines a very common mistake in the implementations of the Quine-McCluskey algorithm, leading to a quadratic slowdown. An optimized corrected implementation of the classic approach is also given (called SparseQMC). The implementation is freely available at https://github.com/hellman/Quine-McCluskey .

We analyze nonce-misuse resilience (NMRL) security of Romulus-N and GIFT-COFB, the two finalists of NIST Lightweight Cryptography project for standardizing lightweight authenticated encryption. NMRL, introduced by Ashur et al. at CRYPTO 2017, is a relaxed security notion from a stronger, nonce-misuse resistance notion. We proved that Romulus-N and GIFT-COFB have nonce-misuse resilience. For Romulus-N, we showed the perfect privacy (NMRL-PRIV) and n/2-bit authenticity (NMRL-AUTH) with graceful degradation with respect to nonce repetition. For GIFT-COFB, we showed n/4-bit security for both NMRL-PRIV and NMRL-AUTH notions.

We introduce flexible password-based encryption (FPBE), an extension of traditional password-based encryption designed to meet the operational and security needs of contemporary applications like end-to-end secure cloud storage. Operationally, FPBE supports nonces, associated data and salt reuse. Security-wise, it strengthens the usual privacy requirement, and, most importantly, adds an authenticity requirement, crucial because end-to-end security must protect against a malicious server. We give an FPBE scheme called DtE that is not only proven secure, but with good bounds. The challenge, with regard to the latter, is in circumventing partitioning-oracle attacks, which is done by leveraging key-robust (also called key-committing) encryption and a notion of authenticity with corruptions. DtE can be instantiated to yield an efficient and practical FPBE scheme for the target applications.

All academic methods to secure software implementations of block ciphers against adversaries with full control of the device have been broken. Despite the huge progress in the cryptanalysis of these white-box implementations, no recent progress has been made on the design side. Most of the white-box designs follow the CEJO framework, where each round is encoded by composing it with small random permutations. While several generic attacks have been proposed on the CEJO framework, no generic analysis has been performed on self-equivalence encodings, a different design where only the affine layer of each round is encoded with random self-equivalences of the S-box layer, that is, affine permutations commuting with the non-linear layer. In this work, we analyse the security of white-box implementations based on self-equivalence encodings for a broad class of SPN ciphers. First, we characterize the self-equivalence groups of S-box layers, and we prove that all the self-equivalences of a cryptographically strong S-box layer have a diagonal shape. Then, we propose the first generic attack on self-equivalence encodings. Our attack, based on affine equivalence problems, identifies the connection between the security of self-equivalence encodings and the self-equivalence structure of the cipher components. While we show that traditional SPN ciphers with cryptographically strong S-box layers cannot be secured with self-equivalence encodings, our analysis shows that self-equivalence encodings resist the generic attack if the cipher components satisfy several conditions, revealing the potential of self-equivalence encodings to secure other types of ciphers.

Synthesis and optimization of quantum circuits are important and fundamental research topics in quantum computation, due to the fact that qubits are very precious and decoherence time which determines the computation time available is very limited. Specifically in cryptography, identifying the minimum quantum resources for implementing an encryption process is crucial in evaluating the quantum security of symmetric-key ciphers. In this work, we investigate the problem of optimizing the depth of quantum circuits for linear layers while utilizing a small number of qubits and quantum gates. To this end, we present a framework for the implementation and optimization of linear Boolean functions, by which we significantly reduce the depth of quantum circuits for many linear layers used in symmetric-key ciphers without increasing the gate count.

In CRYPTO'21, Shen et al. have proved in the ideal cipher model that $\textsf{Two-Keyed-DbHtS}$ construction is secure up to $2^{2n/3}$ queries in the multi-user setting independent of the number of users, where the underlying double-block hash function $\textsf{H}$ of the \textsf{Two-Keyed-DbHtS} construction is realized as the concatenation of two independent $n$-bit keyed hash functions $(\textsf{H}_{K_h,1}, \textsf{H}_{K_h, 2})$ such that each of the $n$-bit keyed hash function is $O(2^{-n})$ universal and regular. They have also demonstrated the applicability of their result to the key-reduced variants of \textsf{DbHtS} MACs, including \textsf{2K-SUM-ECBC}, $\textsf{2K-PMAC_Plus}$ and $\textsf{2K-LightMAC_Plus}$ without requiring domain separation technique and proved $2n/3$-bit multi-user security of these constructions in the ideal cipher model. Recently, Guo and Wang have invalidated the security claim of Shen et al.'s result by exhibiting three constructions, which are the instantiations of the $\textsf{Two-Keyed-DbHtS}$ framework, such that each of their $n$-bit keyed hash functions being $O(2^{-n})$ universal and regular, while the constructions themselves are secure only up to the birthday bound. In this work, we show a sufficient condition on the underlying Double-block Hash ($\textsf{DbH}$) function, under which we prove $3n/4$-bit multi-user security of the $\textsf{Two-Keyed-DbHtS}$ construction in the ideal-cipher model. As an instantiation, we show that two-keyed Polyhash-based $\textsf{DbHtS}$ construction is multi-user secure up to $2^{3n/4}$ queries in the ideal-cipher model. Furthermore, due to the generic attack on $\textsf{DbHtS}$ constructions by Ga\"etan et al. in CRYPTO'18, our derived bound for the construction is tight.

The ChaCha20-Poly1305 AEAD scheme is being increasingly widely deployed in practice. Practitioners need proven security bounds in order to set data limits and rekeying intervals for the scheme. But the formal security analysis of ChaCha20-Poly1305 currently lags behind that of AES-GCM. The only extant analysis (Procter, 2014) contains a flaw and is only for the single-user setting. We rectify this situation. We prove a multi-user security bound on the AEAD security of ChaCha20-Poly1305 and establish the tightness of each term in our bound through matching attacks. We show how our bound differs both qualitatively and quantitatively from the known bounds for AES-GCM, highlighting how subtle design choices lead to distinctive security properties. We translate our bound to the nonce-randomized setting employed in TLS 1.3 and elsewhere, and we additionally improve the corresponding security bounds for GCM. Finally, we provide a simple yet stronger variant of ChaCha20-Poly1305 that addresses the deficiencies highlighted by our analysis.

In recent years there have been several attempts to build white-box block ciphers whose implementation aims to be incompressible. This includes the weak white-box ASASA construction by Bouillaguet, Biryukov and Khovratovich from Asiacrypt 2014, and the recent space-hard construction by Bogdanov and Isobe at CCS 2016. In this article we propose the first constructions aiming at the same goal while offering provable security guarantees. Moreover we propose concrete instantiations of our constructions, which prove to be quite efficient and competitive with prior work. Thus provable security comes with a surprisingly low overhead.

The Feistel construction is one of the most studied ways of building block ciphers. Several generalizations were proposed in the literature, leading to the Generalized Feistel Network (GFN) construction, in which the round function operates on each pair of blocks in parallel until all branches are permuted. At FSE'10, Suzaki and Minematsu studied the diffusion of such construction, raising the question of how many rounds are required so that each block of the ciphertext depends on all blocks of the plaintext. Exhausting all possible permutations up to 16 blocks, they observed that there were always optimal permutations mapping even-number input blocks to odd-number output blocks and vice versa. Recently, both Cauchois et al. and Derbez et al. proposed new algorithms to build optimal even-odd permutations for up to 36 blocks. In this paper, we present a new algorithm based on iterative path building to search for optimal Feistel permutation. This algorithm is much faster in exhausting optimal non-even-odd permutations than all the previous approaches. Our first result is a computational proof that no non-even-odd permutation reaches a better diffusion round than optimal even-odd permutations up to 32 blocks. Furthermore, it is well known that permutations with an optimal diffusion round do not always lead to optimal permutations against differential cryptanalysis. We investigate several new criteria to build permutations leading to more secure GFN.

In CRYPTO 2019, Gohr made a pioneering attempt and successfully applied deep learning to the differential cryptanalysis against NSA block cipher Speck32/64, achieving higher accuracy than the pure differential distinguishers. By its very nature, mining effective features in data plays a crucial role in data-driven deep learning. In this paper, in addition to considering the integrity of the information from the training data of the ciphertext pair, domain knowledge about the structure of differential cryptanalysis is also considered into the training process of deep learning to improve the performance. Meanwhile, taking the performance of the differential-neural distinguisher of Simon32/64 as an entry point, we investigate the impact of input difference on the performance of the hybrid distinguishers to choose the proper input difference. Eventually, we improve the accuracy of the neural distinguishers of Simon32/64, Simon64/128, Simeck32/64, and Simeck64/128. We also obtain related-key differential-based neural distinguishers on round-reduced versions of Simon32/64, Simon64/128, Simeck32/64, and Simeck64/128 for the first time.

A nonce-respecting tweakable blockcipher is the building-block for the OCB authenticated encryption mode. An XEX-based TBC is used to process each block in OCB. However, XEX can provide at most birthday bound privacy security, whereas in Asiacrypt 2017, beyond-birthday-bound (BBB) forging security of OCB3 was shown by Bhaumik and Nandi. In this paper we study how at a small cost we can construct a nonce-respecting BBB-secure tweakable blockcipher. We propose the OTBC-3 construction, which maintains a cache that can be easily updated when used in an OCB-like mode. We show how this can be used in a BBB-secure variant of OCB with some additional keys and a few extra blockcipher calls but roughly the same amortised rate.

It was long thought that symmetric cryptography was only mildly affected by quantum attacks, and that doubling the key length was sufficient to restore security. However, recent works have shown that Simon's quantum period finding algorithm breaks a large number of MAC and authenticated encryption algorithms when the adversary can query the MAC/encryption oracle with a quantum superposition of messages. In particular, the OCB authenticated encryption mode is broken in this setting, and no quantum-secure mode is known with the same efficiency (rate-one and parallelizable). In this paper we generalize the previous attacks, show that a large class of OCB-like schemes is unsafe against superposition queries, and discuss the quantum security notions for authenticated encryption modes. We propose a new rate-one parallelizable mode named QCB inspired by TAE and OCB and prove its security against quantum superposition queries.

Cryptanalysis of symmetric-key ciphers, e.g., linear/differential cryptanalysis, requires an adversary to know the internal structures of the target ciphers. On the other hand, deep learning-based cryptanalysis has attracted significant attention because the adversary is not assumed to have knowledge about the target ciphers with the exception of the algorithm interfaces. Such cryptanalysis in a blackbox setting is extremely strong; thus, we must design symmetric-key ciphers that are secure against deep learning-based cryptanalysis. However, almost previous attacks do not clarify what features or internal structures affect success probabilities. Although Benamira et al. (Eurocrypt 2021) and Chen et al. (ePrint 2021) analyzed Gohr’s results (CRYPTO 2019), they did not find any deep learning specific characteristic where it affects the success probabilities of deep learning-based attacks but does not affect those of linear/differential cryptanalysis. Therefore, it is difficult to employ the results of such cryptanalysis to design deep learning-resistant symmetric-key ciphers. In this paper, we propose deep learning-based output prediction attacks in a blackbox setting. As preliminary experiments, we first focus on two toy SPN block ciphers (small PRESENT-[4] and small AES-[4]) and one toy Feistel block cipher (small TWINE-[4]). Due to its small internal structures with a block size of 16 bits, we can construct deep learning models by employing the maximum number of plaintext/ciphertext pairs, and we can precisely calculate the rounds in which full diffusion occurs. Next, based on the preliminary experiments, we explore whether the evaluation results obtained by our attacks against three toy block ciphers can be applied to block ciphers with large block sizes, e.g., 32 and 64 bits. As a result, we demonstrate the following results, specifically for the SPN block ciphers: First, our attacks work against a similar number of rounds that the linear/differential attacks can be successful. Next, our attacks realize output predictions (precisely ciphertext prediction and plaintext recovery) that are much stronger than distinguishing attacks. Then, swapping or replacing the internal components of the target block ciphers affects the average success probabilities of the proposed attacks. It is particularly worth noting that this is a deep learning specific characteristic because swapping/replacing does not affect the average success probabilities of the linear/differential attacks. Finally, by analyzing the influence of the differences in the characteristics of three S-boxes (i.e., the original PRESENT S-box and two known weak S-boxes) on deep learning specific characteristics, we clarify that the resistance of the target ciphers to differential/linear attacks can affect the success probability of deep learning-based attacks. We also confirm whether the proposed attacks work on the Feistel block cipher. We expect that our results will be an important stepping stone in the design of deep learning-resistant symmetric-key ciphers.

A family of block ciphers parametrized by an optimal quasigroup is proposed in this paper. The proposed cipher uses sixteen $4\times 4$ bits S-boxes as an optimal quasigroup of order 16. Since a maximum of $16!$ optimal quasigroups of order 16 can be formed, the family consists of $C^{16!}_1$ cryptosystems. All the sixteen S-boxes have the highest algebraic degree and are optimal with the lowest linearity and differential characteristics. Therefore, these S-boxes are secure against linear and differential attacks. The proposed cipher is analyzed against various attacks, including linear and differential attacks, and we found it to be resistant to these attacks. The proposed cipher is implemented in C++, compared its performance with existing quasigroup based block ciphers, and we found that our proposal is more efficient than existing quasigroup based proposals. We also evaluated our cipher using various statistical tests of the NIST-STS test suite, and we found it to pass these tests. We also established in this study that the randomness of our cipher is almost the same as that of the AES-128.

We propose a new hash function Reinforced Concrete, which is the first generic purpose hash that is fast both for a zero-knowledge prover and in native x86 computations. It is suitable for a various range of zero-knowledge proofs and protocols, from set membership to generic purpose verifiable computation. Being up to 15x faster than its predecessor Poseidon hash, Reinforced Concrete inherits security from traditional time-tested schemes such as AES, whereas taking the zero-knowledge performance from a novel and efficient decomposition of a prime field into compact buckets. The new hash function is suitable for a wide range of applications like privacy-preserving cryptocurrencies, verifiable encryption, protocols with state membership proofs, or verifiable computation. It may serve as a drop-in replacement for various prime-field hashes such as variants of MiMC, Poseidon, Pedersen hash, and others.

FRIET is a duplex-based authenticated encryption scheme proposed at EUROCRYPT 2020. It follows a novel design approach for built-in countermeasures against fault attacks. By a judicious choice of components, the designers propose the permutation FRIET-PC that can be used to build an authenticated encryption cipher denoted as FRIET-AE. And FRIET-AE provides a 128-bit security claim for integrity and confidentiality. In this paper, we research the propagation of pairs of differences and liner masks through the round function of FRIET-PC. For the full-round FRIET-PC, we can construct a differential distinguisher whose probability is 1 and a linear distinguisher whose absolute value of correlation is 1. Moreover, we use the differential distinguisher with probability 1 to construct a set consisting of valid tags and ciphertexts which are not created by legal users. This breaks FRIET-AE's security claim for integrity and confidentiality. As far as we know, this is the first practical attack that threatens the security of FRIET-AE.

To achieve semantic security, symmetric encryption schemes classically require ciphertext expansion. In this paper we provide a means to achieve semantic security while preserving the length of messages at the cost of mildly sacrificing correctness. Concretely, we propose a new scheme that can be interpreted as a secure alternative to (or wrapper around) plain Electronic Codebook (ECB) mode of encryption, and for this reason we name it Secure Codebook (SCB). Our scheme is the first length-preserving encryption scheme to effectively achieve semantic security.

There are many recent results on reverse-engineering (potentially hidden) structure in cryptographic S-boxes. The problem of recovering structure in the other main building block of symmetric cryptographic primitives, namely, the linear layer, has not been paid that much attention so far. To fill this gap, in this work, we develop a systematic approach to decomposing structure in the linear layer of a substitution-permutation network (SPN), covering the case in which the specification of the linear layer is obfuscated from applying secret linear transformations to the S-boxes. We first present algorithms to decide whether an $ms \times ms$ matrix with entries in a prime field $\mathbb{F}_p$ can be represented as an $m \times m$ matrix over the extension field $\mathbb{F}_{p^s}$. We then study the case of recovering structure in MDS matrices by investigating whether a given MDS matrix follows a Cauchy construction. As an application, for the first time, we show that the $8 \times 8$ MDS matrix over $\mathbb{F}_{2^8}$ used in the hash function Streebog is a Cauchy matrix.