In this paper we study cryptanalysis with non-linear polynomials cf. Eurocrypt’95 (adapted to Feistel ciphers at Crypto 2004). Previously researchers had serious difficulties in making such attacks work. Even though this is less general than a general space partitioning attack (FSE’97), a polynomial algebraic approach has enormous advantages. Properties are more intelligible and algebraic computational methods can be applied in order to discover or construct the suitable properties. In this paper we show how round invariants can be found for more or less any block cipher, by solving a certain surprisingly simple single algebraic equation (or two). Then if our equation has solutions, which is far from being obvious, it will guarantee that some polynomial invariant will work for an arbitrarily large number of encryption rounds. This paper is a proof of concept showing that it IS possible, for at least one specific quite complex real-life cipher to construct in a systematic way, a non-linear component and a variety of non-linear polynomial invariants holding with probability 1 for any number of rounds and any key/IV. Thus we are able to weaken a block cipher in a permanent and pervasive way. An example of a layered attack with two stages is also shown. Moreover we show that sometimes our equation reduces to zero, and this leads to yet stronger invariants, which work for any Boolean function including the original historical one used in 1970-1990.

Highly efficient encryption and authentication of short messages has been identified as an essential requirement for enabling security in constrained computation and communication scenarios such as the CAN FD in automotive systems (with maximum message length of 64 bytes), massive IoT and critical communication domains of 5G, and Narrowband IoT (NB-IoT), to mention some. Accordingly, NIST has specified, as a design requirement in the lightweight cryptography project, that AEAD submissions shall be “optimized to be efficient for short messages (e.g., as short as 8 bytes)”. We propose AEAD schemes that exceed in efficiency over all previous general-purpose modular AEAD designs at processing (very) short inputs. The main ingredient in our solution is a new low-level primitive, called a tweakable forkcipher, which we introduce and formalize in this paper. We give an instance of the tweakable forkcipher and dub it ForkAES. It is based on the tweakable blockcipher KIASU, which relies on the round function of AES and uses the TWEAKEY framework to derive round keys from a 128-bit secret key and a 64-bit tweak. Finally, we demonstrate the applicability of a tweakable forkcipher by designing several provably secure nonce-based AEAD modes of operation, optimized to be efficient for short messages. Considering the AES block size (16 bytes) as a reference, our new AE schemes can beat all known schemes for single-block messages while still performing better than majority of the existing schemes for combined message and associated data lengths up to 4 blocks. While ForkAES as a concrete instantiation for a forkcipher is based on KIASU, we note that our solution provides a general recipe for lightweight AEAD for short messages, even for very resource-constrained scenarios in which AES may not be considered a lightweight option. In those environments, our schemes can be instantiated using a forkcipher that is realized based on the best off-the-shelf lightweight blockcipher, following the TWEAKEY framework.

The lightweight encryption design DoT was published by Patil et al in 2019. It is based on SPN (substitution permutation network) structure. Its block and key size are 64-bit and 128-bit respectively. In this paper, we analyse the security of DoT against differential attack and present a series of differential distinguishers for full-round DOT. Our analysis proves that DoT we can be distinguished from a random permutation with probability equal to 2^62. Diffusion layer of DoT is a combination of byte shuffling, 8-P permutation, 32-bit word shuffling and circular shift operations. We analyse the security of DoT with and without 8-P permutation in its diffusion layer. Our results indicate that DoT provides better resistance to differential attack without using the 8-P permutation.

$\texttt{CRAFT}$ is a lightweight tweakable block cipher introduced in FSE 2019. One of the main design criteria of $\texttt{CRAFT}$ is the efficient protection of its implementations against differential fault analysis. While the authors of $\texttt{CRAFT}$ provide several cryptanalysis results in several attack models, they do not claim any security of $\texttt{CRAFT}$ against related-key differential attacks. In this paper, we utilize the simple key schedule of $\texttt{CRAFT}$ to propose a systematic method for constructing several repeatable 2-round related-key differential characteristics with probability $2^{-2}$. We then employ one of these characteristics to mount a key recovery attack on full-round $\texttt{CRAFT}$ using $2^{31}$ queries to the encryption oracle and $2^{85}$ encryptions, and $2^{41}$ 64-bit blocks of memory. Additionally, we manage to use 8 related-key differential distinguishers, with 8 related-key differences, in order to mount a key recovery attack on the full-round cipher with $2^{35.17}$ queries to the encryption oracle, $2^{32}$ encryptions and about $2^6$ 64-bit blocks of memory. Furthermore, we present another attack that recovers the whole master key with $2^{36.09}$ queries to the encryption oracle and only $11$ encryptions with $2^7$ blocks of memory using 16 related-key differential distinguishers.

Although it is widely deemed impossible to overcome the information theoretic optimality of the one-time pad (OTP) cipher in pre and post-quantum cryptography, this work shows that the optimality of information theoretic security (ITS) of OTP is paradoxical from the perspective of information conservational computing and cryptography. To prove this point, ITS of OTP is extended to information conservational security (ICS) of scalable OTP (S-OTP) with percentage-based key extension where total key length can be reduced to a condensed tiny minimum through “black hole” keypad compression coupled with “big bang” data recovery. The cost is a limited increase in total data length and network traffic; the gain is making the transmission of long messages possible without weakening information theoretic security. It is proven that if ITS/OTP were optimal, ICS/S-OTP would be impossible; on the other hand, if ICS/S-OTP were not information theoretically secure, ITS/OTP would not be secure either. Thus, we have a proof by contradiction on the paradoxical nature of OTP optimality. It is further proven that a summation with percentage distribution is a special case of equilibrium-based bipolar quantum cellular automata. This proof bridges a classical world with a quantum world and makes it possible to combine the advantages of both approaches for pre and post-quantum cryptography. It is suggested that the findings of this work form an analytical paradigm of quantum intelligence machinery toward perfect information conservational security. Some mysteries in Nature and science are identified. In particular, the question is posted: Could modern science have been like a well-founded building with a floor of observable beings, truths, and entropy but missing its roof for equilibrium, harmony, information conservation, and logically definable causality?

We studied the applicability of differential cryptanalysis to cryptosystems based on operation of addition modulo $2^n$. We obtained an estimate (accurate up to an additive constant) of expected value of entropy $H_n$ in rows of DDT of corresponding mapping. Moreover, the $k$-th moments of $2^{H_n}$ are explored. In particular, asymptotic inequalities that describe the behavior of values $\mathbb{E}2^{H_n}$ and $\mathbb{D}2^{H_n}$ as $n \to \infty$ were obtained. A simple analytical formula for the size of any given equivalence class was obtained. This formula helped to effectively compute the entropy distribution.

The first related-key attack on 3-round (of 9) Kuznyechik with 2-round (of 8) key schedule was presented in CTCrypt'18. This article describes a related-key attack on 5-round cipher with the same key schedule. The presented one also has a practical complexity ($2^{32}$ operations, $2^{30}$ memory, $2^{16}$ related keys) and verified in practice. We obtained result due to the simultaneous use of the integral properties of the cipher transformations and the key schedule.

In this paper, we propose some improved quantum circuits to implement the Sbox of AES. Our improved quantum circuits are based on the following strategies. First, we try to find the minimum set of the intermediate variables that can be used to compute the 8-bit output of the Sbox. Second, we check whether some wires store intermediate variables and remain idle until the end. And we can reduce the number of qubit by reusing some certain wires. Third, we try to compute the output of the Sbox without ancillas qubits, because we do not need to be clean up the wires storing the output of the Sbox. This operation will reduce the number of Toffoli gates. Our first quantum circuit only needs 26 qubits and 46 Toffoli gates, while quantum circuit proposed by Langenberg \emph{et al.} required 32 qubits and 55 Toffoli gates. Furthermore, we can also construct our second quantum circuit with 22 qubits and 60 Toffoli gates.

We introduce an independent research project on symmetric cryptography with a focus on foreseeable industrial needs and higher post-quantum security compared to currently used symmetric algorithms. It was initiated by the independent IT-Security experts Kovac and Underhill. The result is the new symmetric cryptographic algorithm eAES, which is intended to be a stronger brother of the widely used Advanced Encryption Standard, the standardized version of the Rijndael algorithm. In this analysis we show, that eAES offers an enhanced complexity by a factor ≥ 2^126 regarding the quantum cryptanalysis Grover’s search algorithm compared to AES for 256 bit keys. Furthermore we outline the basic facts and open questions regarding quantum algebraic attacks on eAES.

While designers of cryptographic algorithms are rarely considered as potential adversaries, past examples, such as the standardization of the Dual EC PRNG highlights that the story might be more complicated. To prevent the existence of backdoors, the concept of rigidity was introduced in the specific context of curve generation. The idea is to first state a strict scope statement for the properties that the curve needs to have and then pick e.g. the one with the smallest parameters. The aim is to ensure that the designers did not have the degrees of freedom that allows the addition of a trapdoor. In this paper, we apply this approach to symmetric algorithms. The task is challenging because the corresponding primitives are more complex: they consist of several sub-components of different types, and the properties required by these sub-components to achieve the desired security level are not as clearly defined. Furthermore, security often comes in this case from the interplay between these components rather than from their individual properties. In this paper, we argue that it is nevertheless necessary to demand that symmetric algorithms have a similar but, due to their different nature, more complex property which we call "unswervingness". We motivate this need via a study of the literature on symmetric "kleptography" and via the study of some real-world standards. We then suggest some guidelines that could be used to leverage the unswervingness of a symmetric algorithm to standardize a highly trusted and equally safe variant of it.

We present a general framework for the related-key linear attack that can be applied to iterative block ciphers with linear key schedules. The attack utilizes a newly introduced related-key linear approximation that is obtained directly from a linear trail. The attack makes use of a known related-key data consisting of triplets of a plaintext, a ciphertext, and a key difference such that the ciphertext is the encrypted value of the plaintext under the key that is the xor of the key to be recovered and the specified key difference. If such a block cipher has a linear trail with linear correlation \epsilon, it admits attacks with related-key data of size \epsilon^{-2} just as in the case of classical Matsui's Algorithms. But since the attack makes use of a related-key data, the attacker can use a linear trail with the squared correlation less than 2^{-n}, n being the block size, in case the key size is larger than n. Moreover, the standard key hypotheses seem to be appropriate even when the trail is not dominant as validated by experiments. The attack can be applied in two ways. First, using a linear trail with squared correlation smaller than 2^{-n}, one can get an effective attack covering more rounds than existing attacks against some ciphers, such as Simon48/96, Simon64/128 and Simon128/256. Secondly, using a trail with large squared correlation, one can use related-key data for key recovery even when the data is not suitable for existing linear attacks.

The use of a small block length is a common strategy when designing lightweight (tweakable) block ciphers (TBCs), and several $64$-bit primitives have been proposed. However, when such a $64$-bit primitive is used for an authenticated encryption with birthday-bound security, it has only $32$-bit data complexity, which is subject to practical attacks. To employ a short block length without compromising security, we propose PFB, a lightweight TBC-based authenticated encryption with associated data mode, which achieves beyond birthday-bound security. For this purpose, we extend iCOFB, which is originally defined with a tweakable random function. Unlike iCOFB, the proposed method can be instantiated with a TBC using a fixed tweak length and can handle variable-length data. Moreover, its security bound is improved and independent of the data length; this improves the key lifetime, particularly in lightweight blocks with a small size. The proposed method also covers a broader class of feedback functions because of the generalization presented in our proof. We evaluate the concrete hardware performances of PFB, which benefits from the small block length and shows particularly good performances in threshold implementation.

The Gimli permutation was proposed in CHES 2017 and the hash mode Gimli-Hash is now included in the Round 2 candidate Gimli in NIST's Lightweight Cryptography Standardization process. In the Gimli document, the security of the Gimli permutation has been intensively investigated. However, little is known about the security of Gimli-Hash. The designers of Gimli have claimed $2^{128}$ security against all attacks on Gimli-Hash, whose hash is a 256-bit value. Firstly, we present the trivial generic preimage attack on the structure of Gimli-Hash matching the $2^{128}$ security bound, both, in time and memory complexity. Following such a generic preimage attack framework, we then describe specific preimage attacks on the first 2/3/4/5 rounds and the last 2/3/4 rounds (out of 24) of Gimli-Hash using the divide-and-conquer methods. As will be shown, the application of the divide-and-conquer methods much benefits from the properties of the SP-box and the linear layer of Gimli. Therefore, this work can also be viewed as a first step to exploit specific properties of the SP-box. Finally, the divide-and-conquer method was also applied to a collision attack on up to 5-round Gimli-Hash. Among all the attacks, the preimage attacks on the first and the last 2 rounds of Gimli-Hash are practical. The collision attack on the first 3 rounds of Gimli-Hash is practical. The collision attack and second preimage attack on the last 3 rounds of Gimli-Hash are practical. All practical attacks are experimentally verified. We hope our analysis can advance the understanding of Gimli-Hash.

Boomerang attacks are extensions of differential attacks, that make it possible to combine two unrelated differential properties of the first and second part of a cryptosystem with probabilities $p$ and $q$ into a new differential-like property of the whole cryptosystem with probability $p^2q^2$ (since each one of the properties has to be satisfied twice). In this paper we describe a new version of boomerang attacks which uses the counterintuitive idea of throwing out most of the data (including potentially good cases) in order to force equalities between certain values on the ciphertext side. This creates a correlation between the four probabilistic events, which increases the probability of the combined property to $p^2q$ and increases the signal to noise ratio of the resultant distinguisher. We call this variant a retracing boomerang attack since we make sure that the boomerang we throw follows the same path on its forward and backward directions. To demonstrate the power of the new technique, we apply it to the case of 5-round AES. This version of AES was repeatedly attacked by a large variety of techniques, but for twenty years its complexity had remained stuck at $2^{32}$. At Crypto'18 it was finally reduced to $2^{24}$ (for full key recovery), and with our new technique we can further reduce the complexity of full key recovery to the surprisingly low value of $2^{16.5}$ (i.e., only 90,000 encryption/decryption operations are required for a full key recovery on half the rounds of AES). In addition to improving previous attacks, our new technique unveils a hidden relationship between boomerang attacks and two other cryptanalytic techniques, the yoyo game and the recently introduced mixture differentials.

The slide attack is a powerful cryptanalytic tool which has the unusual property that it can break iterated block ciphers with a complexity that does not depend on their number of rounds. However, it requires complete self similarity in the sense that all the rounds must be identical. While this can be the case in Feistel structures, this rarely happens in SP networks since the last round must end with an additional post-whitening subkey. In addition, in many SP networks the final round has additional asymmetries -- for example, in AES the last round omits the MixColumns operation. Such asymmetry in the last round can make it difficult to utilize most of the advanced tools which were developed for slide attacks, such as deriving from one slid pair additional slid pairs by repeatedly re-encrypting their ciphertexts. In this paper we overcome this "last round problem" by developing four new types of slide attacks. We demonstrate their power by applying them to many types of AES-like structures (with and without linear mixing in the last round, with known or secret S-boxes, with 1,2 and 3 periodicity in their subkeys, etc). In most of these cases, the time complexity of our attack is close to $2^{n/2}$, which is the smallest possible complexity for slide attacks. Our new slide attacks have several unique properties: The first attack uses slid sets in which each plaintext from the first set forms a slid pair with some plaintext from the second set, but without knowing the exact correspondence. The second attack makes it possible to create from several slid pairs an exponential number of new slid pairs which form a hypercube spanned by the given pairs. The third attack has the unusual property that it is always successful, and the fourth attack can use known messages instead of chosen messages, with only slightly higher time complexity.

The NIST-approved lightweight cryptography competition is an ongoing project to look for some algorithms as lightweight cryp- tographic standards. Recently, NIST chooses 32 algorithms from the 57 submissions as Round 2 candidates. Gimli and Ascon are both the Round 2 candidates. In this paper, we analyze the security of their hash mode against collision attacks. Con- cretely, we mount collision attacks on three hash functions: Gimli-Hash, Ascon-Xof and Ascon-Hash. These three hash functions are all based on sponge constructions. We give two attack strategies for searching collisions in sponge-based hash functions. Following one strategy, we give two non-practical collision attacks: a 6-round collision attack on Gimli-Hash with time complexity 2113and a 2-round collision attack on Ascon-Hash with time complexity 2125. Following the other strategy, we give a practical attack on 2-round Ascon-Xof with a 64-bit output. The time complexity is 215. We search for the differential characteristics using the MILP technique and the target differential algorithm.

We study a class of MACs, which we call corruption detectable MAC, that is able to not only check the integrity of the whole message, but also detect a part of the message that is corrupted. It can be seen as an application of the classical Combinatorial Group Testing (CGT) to message authentication. However, previous work on this application has inherent limitation in communication. We present a novel approach to combine CGT and a class of linear MACs (XOR-MAC) that enables to break this limit. Our proposal, XOR-GTM, has a significantly smaller communication cost than any of the previous ones, keeping the same corruption detection capability. Our numerical examples for storage application show a reduction of communication by a factor of around 15 to 70 compared with previous schemes. XOR-GTM is parallelizable and is as efficient as standard MACs. We prove that XOR-GTM is provably secure under the standard pseudorandomness assumptions.

Secure cloud storage is considered as one of the most important problems that both businesses and end-users take into account before moving their private data to the cloud. Lately, we have seen some interesting approaches that are based either on the promising concept of Symmetric Searchable Encryption (SSE) or on the well-studied field of Attribute-Based Encryption (ABE). Our construction, MicroSCOPE, combines both ABE and SSE to utilize the advantages that each technique has to offer. We use an SSE scheme to ensure that data stored on the cloud will be protected against both internal and external attacks. Moreover, through the use of a Ciphertext-Policy ABE (CP-ABE) scheme, our construction allows efficient data sharing between multiple data owners and users. Finally, we enhance our construction with an access control mechanism by utilizing the functionality provided by SGX.

In this paper, we study the relation of single-key impossible differentials with the related-tweakey/key ones and propose an interesting algorithm that can efficiently derive longer related-tweakey/key impossible differentials from single-key ones. With application of the MILP technique, the algorithm can be converted an automatic tool for searching related-tweakey/key impossible differentials. We use this automatic tool to analyze QARMA-64 and give a 11-round key recovery attack, which attacks one more round than the best previous result. Moreover, we also analyze Joltik-BC-128, a internal tweakable block cipher of an authenticated encryption candidate of the CAESAR competition Joltik and our result can attack two more rounds than the result given by the cipher designers.

Abstract - Research on Side Channel Analysis (SCA) is very active and progressing at a fast pace. The idea of using Machine Learning (ML), and more recently Deep Learning(DL), to help SCA data is explored extensively. One issue facing security researchers interested in contributing to this cause is the difficulties getting started. While replicating previous works with open source code is not difficult, taking the next steps from there can be daunting. The presented open-source DLSCA tool is created to aid with research on DL-based SCA and to help newcomers to DL to get started. It is hoped to contribute to investigating the strengths and limitations of ML-based SCA. Keywords - Machine Learning, Side Channel Attack, Software Tool

This work introduces Algorithm Substitution Attacks (ASAs) on message authentication schemes. In light of revelations concerning mass surveillance, ASAs were initially introduced by Bellare, Paterson and Rogaway as a novel attack class against the confidentiality of encryption schemes. Such an attack replaces one or more of the regular scheme algorithms with a subverted version that aims to reveal information to an adversary (engaged in mass surveillance), while remaining undetected by users. While most prior work focused on subverting encryption systems, we study options to subvert symmetric message authentication protocols. In particular we provide powerful generic attacks that apply e.g. to HMAC or Carter-Wegman based schemes, inducing only a negligible implementation overhead. As subverted authentication can act as an enabler for subverted encryption (software updates can be manipulated to include replacements of encryption routines), we consider attacks of the new class highly impactful and dangerous.

Cube attacks are an important type of key recovery attacks against NFSR-based cryptosystems. The key step in cube attacks closely related to key recovery is recovering superpolies. However, in the previous cube attacks including original, division property based, and correlation cube attacks, the algebraic normal form of superpolies could hardly be shown to be exact due to an unavoidable failure probability or a requirement of large time complexity. In this paper, we propose an algebraic method aiming at recovering the exact algebraic normal forms of superpolies practically. Our method is developed based on degree evaluation method proposed by Liu in Crypto-2017. As an illustration, we apply our method to Trivium. As a result, we recover the algebraic normal forms of some superpolies for the 818-, 835-, 837-, and 838-round Trivium. Based on these superpolies, on a large set of weak keys, we can recover at least five key bits equivalently for up to the 838-round Trivium with a complexity of about $2^{37}$. Besides, for the cube proposed by Liu in Crypto-2017 as a zero-sum distinguisher for the 838-round Trivium, it is proved that its superpoly is not zero-constant. Hopefully, our method would provide some new insights on cube attacks against NFSR-based ciphers.

Symmetric cryptographic primitives with low multiplicative complexity have been proposed to improve the performance of emerging applications such as secure Multi-Party Computation. However, primitives composed of round functions with low algebraic degree require a careful evaluation to assess their security against algebraic cryptanalysis, and in particular interpolation attacks. This paper proposes new low-memory interpolation attacks on symmetric key primitives of low degree. Moreover, we present generic attacks on block ciphers with a simple key schedule; our attacks require either constant memory or constant data complexity. The improved attack is applied to the block cipher MiMC which aims to minimize the number of multiplications in large finite fields. As a result, we can break MiMC-$129/129$ with $38$ rounds with time and data complexity $2^{65.5}$ and $2^{60.2}$ respectively and with negligible memory; this attack invalidates one of the security claims of the designers. Our attack indicates that for MiMC-$129/129$ the full $82$ rounds are necessary even with restrictions on the memory available to the attacker. For variants of MiMC with larger keys, we present new attacks with reduced complexity. Our results do not affect the security claims of the full round MiMC.

Persistent faults mark a new class of injections that perturb lookup tables within block ciphers with the overall goal of recovering the encryption key. Unlike earlier fault types persistent faults remain intact over many encryptions until the affected device is rebooted, thus allowing an adversary to collect a multitude of correct and faulty ciphertexts. It was shown to be an efficient and effective attack against substitution-permutation networks. In this paper, the scope of persistent faults is further broadened and explored. More specifically, we show how to construct a key-recovery attack on generic Feistel schemes in the presence of persistent faults. In a second step, we leverage these faults to reverse-engineer AES- and PRESENT-like ciphers in a chosen-key setting, in which some of the computational layers, like substitution tables, are kept secret. Finally, we propose a novel, dedicated, and low-overhead countermeasure that provides adequate protection for hardware implementations against persistent fault injections.

The customary formulation of authenticated encryption (AE) requires the decrypting party to supply the correct nonce with each ciphertext it decrypts. To enable this, the nonce is often sent in the clear alongside the ciphertext. But doing this can forfeit anonymity and degrade usability. Anonymity can also be lost by transmitting associated data (AD) or a session-ID (used to identify the operative key). To address these issues, we introduce anonymous AE, wherein ciphertexts must conceal their origin even when they are understood to encompass everything needed to decrypt (apart from the receiver's secret state). We formalize a type of anonymous AE we call anAE, anonymous nonce-based AE, which generalizes and strengthens conventional nonce-based AE, nAE. We provide an efficient construction for anAE, NonceWrap, from an nAE scheme and a blockcipher. We prove NonceWrap secure. While anAE does not address privacy loss through traffic-flow analysis, it does ensure that ciphertexts, now more expansively construed, do not by themselves compromise privacy.

In this paper we present exchange-equivalence attacks which is a new cryptanalytic attack technique suitable for SPN-like block cipher designs. Our new technique results in the first secret-key chosen plaintext distinguisher for 6-round AES. The complexity of the distinguisher is about $2^{88.2}$ in terms of data, memory and computational complexity. The distinguishing attack for AES reduced to six rounds is a straight-forward extension of an exchange attack for 5-round AES that requires $2^{30}$ in terms of chosen plaintexts and computation. This is also a new record for AES reduced to five rounds. The main result of this paper is that AES up to at least six rounds is biased when restricted to exchange-invariant sets of plaintexts.

Recent papers show how to construct polynomial invariant attacks for block ciphers, however almost all such results are somewhat weak: invariants are simple and low degree and the Boolean functions tend by very simple if not degenerate. Is there a better more realistic attack, with invariants of higher degree and which is likely to work with stronger Boolean functions? In this paper we show that such attacks exist and can be constructed explicitly through on the one side, the study of Fundamental Equation of eprint/2018/807, and on the other side, a study of the space of Annihilators of any given Boolean function. The main contribution of this paper is that to show that the ``product attack'' where the invariant polynomial is a product of simpler polynomials is interesting and quite powerful. Our approach is suitable for backdooring a block cipher in presence of an arbitrarily strong Boolean function not chosen by the attacker. The attack is constructed using excessively simple paper and pencil maths. We also outline a potential application to Data Encryption Standard (DES).

The block cipher Jarvis and the hash function Friday, both members of the MARVELlous family of cryptographic primitives, are among the first proposed solutions to the problem of designing symmetric-key algorithms suitable for transparent, post-quantum secure zero-knowledge proof systems such as ZK-STARKs. In this paper we describe an algebraic cryptanalysis of Jarvis and Friday and show that the proposed number of rounds is not sufficient to provide adequate security. In Jarvis, the round function is obtained by combining a finite field inversion, a full-degree affine permutation polynomial and a key addition. Yet we show that even though the high degree of the affine polynomial may prevent some algebraic attacks (as claimed by the designers), the particular algebraic properties of the round function make both Jarvis and Friday vulnerable to Gröbner basis attacks. We also consider MiMC, a block cipher similar in structure to Jarvis. However, this cipher proves to be resistant against our proposed attack strategy. Still, our successful cryptanalysis of Jarvis and Friday does illustrate that block cipher designs for “algebraic platforms” such as STARKs, FHE or MPC may be particularly vulnerable to algebraic attacks.

S-boxes are functions with an input so small that the simplest way to specify them is their lookup table (LUT). Unfortunately, some algorithm designers exploit this fact to avoid providing the algorithm used to generate said lookup table. In this paper, we provide tools for finding the hidden structure in an S-box or to identify it as the output of a complex generation process rather than a random sample. We introduce various "anomalies". These real numbers are such that a property with an anomaly equal to $a$ should be found roughly once in a set of $2^{a}$ random S-boxes. First, we revisit the literature on S-box reverse-engineering to present statistical anomalies based on the distribution of the coefficients in the difference distribution table, linear approximation table, and for the first time, the boomerang connectivity table. We then count the number of S-boxes that have block-cipher like structures to estimate the anomaly associated to those. In order to recover these structures, we show that the most general tool for decomposing S-boxes is an algorithm efficiently listing all the vector spaces of a given dimension contained in a given set, and we present such an algorithm. Finally, we propose general methods to formally quantify the complexity of any S-box. It relies on the production of the smallest program evaluating it and on combinatorial arguments. Combining these approaches, we show that all permutations that are actually picked uniformly at random always have essentially the same cryptographic properties, and can never be decomposed in a simpler way. These conclusions show that multiple claims made by the designers of the latest Russian standards are factually incorrect.

In symmetric cryptanalysis, the model of superposition queries has lead to surprising results, with many constructions being broken in polynomial time thanks to Simon's period-finding algorithm. But the practical implications of these attacks remain blurry. In contrast, the results obtained so far for a quantum adversary making classical queries only are less impressive. In this paper, we introduce a new quantum algorithm which uses Simon's subroutines in a novel way. We manage to leverage the algebraic structure of cryptosystems in the context of a quantum attacker limited to classical queries and offline quantum computations. We obtain improved quantum-time/classical-data tradeoffs with respect to the current literature, while using only as much hardware requirements (quantum and classical) as a standard exhaustive search using Grover's algorithm. In particular, we are able to break the Even-Mansour construction in quantum time $O(2^{n/3})$, with $O(2^{n/3})$ classical queries and $O(n^2)$ qubits only. In addition, we propose an algorithm that allows to improve some previous superposition attacks by reducing the data complexity from exponential to polynomial, with the same time complexity. Our approach can be seen in two complementary ways: reusing superposition queries during the iteration of a search using Grover's algorithm, or alternatively, removing the memory requirement in some quantum attacks based on a collision search, thanks to their algebraic structure. We provide a list of cryptographic applications, including the Even-Mansour construction, the FX construction, some Sponge authenticated modes of encryption, and many more.

Whereas it is widely deemed an impossible task to scale down One-Time Pad (OTP) key length without sacrificing information theoretic security or network traffic, this project started with the attempt to develop a paradigm of Scalable One-Time Pad (S-OTP) ciphers based on information conservational computing/cryptography (ICC). This line of research, however, hits a dead-end at the limitation of information entropy and computational precision for full information conservation when long messages are transmitted. The dead-end suggests a 2-phase study. First, to explore the boundaries of scalability with data compression to reduce a long message to a tiny minimum but assuming only partial information conservation. Second, to explore the possibility of scalability with full information conservation but with limited increase of network traffic for transmitting long messages with information theoretic security. This paper reports results of the first phase. This study suggests two future directions of ICC: (1) using S-OTP to scale down key length at the expense of limited increase of network traffic for full information conservation (See solution at https://eprint.iacr.org/2019/913.pdf ); (2) develop a type of quantum crypto machine for full information conservation.

Highly efficient encryption and authentication of short messages is an essential requirement for enabling security in constrained scenarios such as the CAN FD in automotive systems (max. message size 64 bytes), massive IoT, critical communication domains of 5G, and Narrowband IoT, to mention a few. In addition, one of the NIST lightweight cryptography project requirements is that AEAD schemes shall be “optimized to be efficient for short messages (e.g., as short as 8 bytes)”. In this work we introduce and formalize a novel primitive in symmetric cryptography called a forkcipher. A forkcipher is a keyed function expanding a fixed-length input to a fixed-length output. We define its security as indistinguishability under chosen ciphertext attack. We give a generic construction validation via the new iterate-fork-iterate design paradigm. We then propose ForkSkinny as a concrete forkcipher instance with a public tweak and based on SKINNY: a tweakable lightweight block cipher constructed using the TWEAKEY framework. We conduct extensive cryptanalysis of ForkSkinny against classical and structure-specific attacks. We demonstrate the applicability of forkciphers by designing three new provably-secure, nonce-based AEAD modes which offer performance and security tradeoffs and are optimized for efficiency of very short messages. Considering a reference block size of 16 bytes, and ignoring possible hardware optimizations, our new AEAD schemes beat the best SKINNY-based AEAD modes. More generally, we show forkciphers are suited for lightweight applications dealing with predominantly short messages, while at the same time allowing handling arbitrary messages sizes. Furthermore, our hardware implementation results show that when we exploit the inherent parallelism of ForkSkinny we achieve the best performance when directly compared with the most efficient mode instantiated with the SKINNY block cipher.

Threshold Implementations (TI) are secure algorithmic countermeasures against side-channel attacks in the form of differential power analysis. The strength of TI lies in its minimal algorithmic requirements. These requirements have been studied over more than 10 years and many efficient implementations for symmetric primitives have been proposed. Thus, over the years the practice of protecting implementations matured, however, the theory behind threshold implementations remained the same. In this work, we revise this theory by looking at the properties of correctness, non-completeness, and uniformity as a composable security model. We prove that this model provides first-order and higher-order univariate security in the glitch-robust probing model which lets us expand the theoretic framework of TI. We first provide a link between uniformity and the notion of non-interference, a known composable security notion building out the probing model. We then relax the notion of non-completeness which helps the design of secure expansion and compression functions. Lastly, we provide generalisations of the threshold notions to allow for general secret sharing schemes and provide examples of how different sharing schemes affect the security and efficiency of the countermeasure.

In order to study the resistance of a block cipher against boomerang attacks, a tool called the Boomerang Connectivity Table (BCT) for S-boxes was recently introduced. Very little is known today about the properties of this table especially for bijective S-boxes defined for $n$ variables with $n\equiv 0 \mod{4}$. In this work we study the boomerang uniformity of some popular constructions used for building large S-boxes, e.g. for 8 variables, from smaller ones. We show that the BCTs of all the studied constructions have abnormally high values in some positions. This remark permits us in some cases to link the boomerang properties of an S-box with other well-known cryptanalytic techniques on such constructions while in other cases it leads to the discovery of new ones. A surprising outcome concerns notably the Feistel and MISTY networks. While these two structures are very similar, their boomerang uniformity can be very different. In a second time, we investigate the boomerang uniformity under EA-equivalence for Gold and the inverse function (as used respectively in MPC-friendly ciphers and the AES) and we prove that the boomerang uniformity is EA-invariant in these cases. Finally, we present an algorithm for inverting a given BCT and provide experimental results on the size of the BCT-equivalence classes for some $4$ and $8$-bit S-boxes.

We study the security of symmetric primitives against key-correlated attacks (KCA), whereby an adversary can arbitrarily correlate keys, messages, and ciphertexts. Security against KCA is required whenever a primitive should securely encrypt key-dependent data, even when it is used under related keys. KCA is a strengthening of the previously considered notions of related-key attack (RKA) and key-dependent message (KDM) security. This strengthening is strict, as we show that 2-round Even–Mansour fails to be KCA secure even though it is both RKA and KDM secure. We provide feasibility results in the ideal-cipher model for KCAs and show that 3-round Even–Mansour is KCA secure under key offsets in the random-permutation model. We also give a natural transformation that converts any authenticated encryption scheme to a KCA-secure one in the random-oracle model. Conceptually, our results allow for a unified treatment of RKA and KDM security in idealized models of computation.

In different contexts such as filtered LFSR, Goldreich's PRG, and FLIP stream ciphers, the security of a cryptographic primitive mostly depends on the algebraic properties of one Boolean function. Since the Seventies, more and more efficient attacks have been exhibited in this context, related to more and more general algebraic properties, such as the degree, the algebraic immunity, and finally, the fast algebraic immunity. Once the properties to estimate the attack complexities are identified, it remains to determine the exact parameters of interesting families of functions with these properties. Then, these functions can be combined in secondary constructions to guarantee the good algebraic properties of a main function. In particular, the family of symmetric functions, and more precisely the subclass of majority functions, has been intensively studied in the area of cryptography, because of their practical advantages and good properties. The degree of all these functions is known, and they have been proven to reach the optimal algebraic immunity, but still very few is known about its fast algebraic immunity. For a function in $n=2^m+j$ variables, an upper bound is known for all $m$ and $j$, proving that these functions do not reach the optimal fast algebraic immunity. However, the exact fast algebraic immunity is known only for very few families indexed by $j$, where the parameter is exhibited for all members of the family since $m$ is big enough. Recent works gave exact values for $j=0$ and $j=1$ (in the first case), and for $j=2$ and $j=3$ with $m\geq2$ (in the second case). In this work, we determine the exact fast algebraic immunity for all possible values of $j$, for all member of the family assuming $m\geq 1+\log_2(j+1)$.

At Eurocrypt'18, Cid, Huang, Peyrin, Sasaki, and Song introduced a new tool called Boomerang Connectivity Table (BCT) for measuring the resistance of a block cipher against the boomerang attack which is an important cryptanalysis technique introduced by Wagner in 1999 against block ciphers. Next, Boura and Canteaut introduced an important parameter related to the BCT for cryptographic Sboxes called boomerang uniformity. The purpose of this paper is to present a brief state-of-the-art on the notion of boomerang uniformity of vectorial Boolean functions (or Sboxes) and provide new results. More specifically, we present a slightly different but more convenient formulation of the boomerang uniformity and prove some new identities. Moreover, we focus on quadratic permutations in even dimension and obtain general criteria by which they have optimal BCT. {As a consequence of the new criteria}, two previously known results can be derived, and many new quadratic permutations with optimal BCT (optimal means that the maximal value in the Boomerang Connectivity Table equals the lowest known differential uniformity) can be found. In particular, we show that the boomerang uniformity of the binomial differentially $4$-uniform permutations presented by Bracken, Tan, and Tan equals $4$. Furthermore, we show a link between the boomerang uniformity and the nonlinearity for some special quadratic permutations. {Finally, we present a characterization of quadratic permutations with boomerang uniformity $4$. With this characterization, we show that the boomerang uniformity of a quadratic permutation with boomerang uniformity $4$ is preserved by the extended affine (EA) equivalence.

The goal of this paper is to investigate the linear cryptanalysis of random functions and permutations. The motivation of this work is twofold. First, before a practical cipher can be distinguished from an ideal one, the cryptanalyst must have an accurate understanding of the statistical behavior of the ideal cipher. Secondly, this issue has been neglected both in old and in more recent studies, particularly when multiple linear approximations are being used simultaneously. Traditionally, the models have been based on the average behavior and simplified using other artificial assumptions such as independence of the linear approximations. The new models given in this paper are realistic, accurate and easy to use. They are backed up by standard statistical tools such as Pearson's chi-squared test and finite population correction and shown to work well in small practical examples.

Recently Budaghyan, Calderini and Villa (2018) introduced a procedure for investigating if CCZ-equivalence can be more general than EA-equivalence together with inverse transformation (when applicable). In this paper, we show that it is possible to use this procedure for classifying, up to EA-equivalence, all known APN functions in dimension 6. We also give some discussion for dimension 7, 8 and 9. In particular, in these cases it is possible to give an upper bound on the EA-classes contained in the CCZ-classes of the known APN functions.

Side-channel attacks, especially differential power analysis (DPA), pose a serious threat to cryptographic implementations deployed in a malicious environment. One way to counter side-channel attacks is to design cryptographic schemes to withstand them, an area that is covered amongst others by leakage resilient cryptography. So far, however, leakage resilient cryptography has predominantly focused on block cipher based designs, and insights in permutation based leakage resilient cryptography are scarce. In this work, we consider leakage resilience of the keyed duplex construction: we present a model for leakage resilient duplexing, derive a fine-grained bound on the security of the keyed duplex in said model, and map it to ideas of Taha and Schaumont (HOST 2014) and Dobraunig et al. (ToSC 2017) in order to use the duplex in a leakage resilient manner.

In this paper we are proposing a new member in the SNOW family of stream ciphers, called SNOW-V. The motivation is to meet an industry demand of very high speed encryption in a virtualized environment, something that can be expected to be relevant in a future 5G mobile communication system. We are revising the SNOW 3G architecture to be competitive in such a pure software environment, making use of both existing acceleration instructions for the AES encryption round function as well as the ability of modern CPUs to handle large vectors of integers (e.g. SIMD instructions). We have kept the general design from SNOW 3G, in terms of linear feedback shift register (LFSR) and Finite State Machine (FSM), but both entities are updated to better align with vectorized implementations. The LFSR part is new and operates 8 times the speed of the FSM. We have furthermore increased the total state size by using 128-bit registers in the FSM, we use the full AES encryption round function in the FSM update, and, finally, the initialization phase includes a masking with key bits at its end. The result is an algorithm generally much faster than AES-256 and with expected security not worse than AES-256.

We improve the attack of Durak and Vaudenay (CRYPTO'17) on NIST Format-Preserving Encryption standard FF3, reducing the running time from $O(N^5)$ to $O(N^{17/6})$ for domain $Z_N \times Z_N$. Concretely, DV's attack needs about $2^{50}$ operations to recover encrypted 6-digit PINs, whereas ours only spends about $2^{30}$ operations. In realizing this goal, we provide a pedagogical example of how to use distinguishing attacks to speed up slide attacks. In addition, we improve the running time of DV's known-plaintext attack on 4-round Feistel of domain $Z_N \times Z_N$ from $O(N^3)$ time to just $O(N^{5/3})$ time. We also generalize our attacks to a general domain $Z_M \times Z_N$, allowing one to recover encrypted SSNs using about $2^{50}$ operations. Finally, we provide some proof-of-concept implementations to empirically validate our results.

RIPEMD-160 is a hash function published in 1996, which shares similarities with other hash functions designed in this time-period like MD4, MD5 and SHA-1. However, for RIPEMD-160, no (semi-free-start) collision attacks on the full number of steps are known. Hence, it is still used, e.g., to generate Bitcoin addresses together with SHA-256, and is an ISO/IEC standard. Due to its dual-stream structure, even semi-free-start collision attacks starting from the first step only reach 36 steps, which were firstly shown by Mendel et al. at Asiacrypt 2013 and later improved by Liu, Mendel and Wang at Asiacrypt 2017. Both of the attacks are based on a similar freedom degree utilization technique as proposed by Landelle and Peyrin at Eurocrypt 2013. However, the best known semi-free-start collision attack on 36 steps of RIPEMD-160 presented at Asiacrypt 2017 still requires $2^{55.1}$ time and $2^{32}$ memory. Consequently, a practical semi-free-start collision attack for the first 36 steps of RIPEMD-160 still requires a significant amount of resources. Considering the structure of these previous semi-free-start collision attacks for 36 steps of RIPEMD-160, it seems hard to extend it to more steps. Thus, we develop a different semi-free-start collision attack framework for reduced RIPEMD-160 by carefully investigating the message expansion of RIPEMD-160. Our new framework has several advantages. First of all, it allows to extend the attacks to more steps. Second, the memory complexity of the attacks is negligible. Hence, we were able to mount semi-free-start collision attacks on 36 and 37 steps of RIPEMD-160 with practical time complexity $2^{41}$ and $2^{49}$ respectively. Additionally, we describe semi-free-start collision attacks on 38 and 40 (out of 80) steps of RIPEMD-160 with time complexity $2^{52}$ and $2^{74.6}$, respectively. To the best of our knowledge, these are the best semi-free-start collision attacks for RIPEMD-160 starting from the first step with respect to the number of steps, including the first practical colliding message pairs for 36 and 37 steps of RIPEMD-160.

MiMC and GMiMC are families of MPC-friendly block ciphers and hash functions. In this note, we show that the block ciphers MiMC-$2n/n$ (or Feistel-MiMC) and univariate GMiMC are vulnerable to an attack which allows a key recovery in $2^{n/2}$ operations. This attack, which is reminiscent of a slide attack, only relies on their weak key schedules, and is independent of the round function ($x^3$ here) and the number of rounds.

In this paper, we study the results of the recently proposed exchange attack in an adaptive setting. As expected, it leads to present a better 6-round key-independent distinguisher in terms of data and computational complexities. More specifically, our 6-round adaptive distinguisher requires $2^{83}$ chosen plaintexts and $2^{83}$ adaptively chosen ciphertexts and has a computational cost of $2^{83}$ encryption.

The iterated Even-Mansour construction is an elegant construction that idealizes block cipher designs such as the AES. In this work we focus on the simplest variant, the 2-round Even-Mansour construction with a single key. This is the most minimal construction that offers security beyond the birthday bound: there is a security proof up to $2^{2n/3}$ evaluations of the underlying permutations and encryption, and the best known attacks have a complexity of roughly $2^n/n$ operations. We show that attacking this scheme with block size $n$ is related to the 3-XOR problem with element size $w = 2n$, an important algorithmic problem that has been studied since the nineties. In particular the 3-XOR problem is known to require at least $2^{w/3}$ queries, and the best known algorithms require around $2^{w/2} / w$ operations: this roughly matches the known bounds for the 2-round Even-Mansour scheme. Using this link we describe new attacks against the 2-round Even-Mansour scheme. In particular, we obtain the first algorithms where both the data and the memory complexity are significantly lower than $2^n$ . From a practical standpoint, previous works with a data and/or memory complexity close to $2^n$ are unlikely to be more efficient than a simple brute-force search over the key. Our best algorithm requires just $\lambda n$ known plaintext/ciphertext pairs, for some constant $0 < \lambda < 1$, $2^n/\lambda n$ time, and $2^{\lambda n}$ memory. For instance, with $n = 64$ and $\lambda = 1/2$, the memory requirement is practical, and we gain a factor 32 over brute-force search. We also describe an algorithm with asymptotic complexity $O(2^n (\ln^2{n/n^2})$, improving the previous asymptotic complexity of $O(2^n/n)$, using a variant of the 3-SUM algorithm of Baran, Demaine, and Patrascu.

This paper has four main contributions. First, we calculate the predicted difference distribution of Speck32/64 with one specific input difference under the Markov assumption completely for up to eight rounds and verify that this yields a globally fairly good model of the difference distribution of Speck32/64. Secondly, we show that contrary to conventional wisdom, machine learning can produce very powerful cryptographic distinguishers: for instance, in a simple low-data, chosen plaintext attack on nine rounds of Speck, we present distinguishers based on deep residual neural networks that achieve a mean key rank roughly five times lower than an analogous classical distinguisher using the full difference distribution table. Thirdly, we develop a highly selective key search policy based on a variant of Bayesian optimization which, together with our neural distinguishers, can be used to reduce the remaining security of 11-round Speck32/64 to roughly 38 bits. This is a significant improvement over previous literature. Lastly, we show that our neural distinguishers successfully use features of the ciphertext pair distribution that are invisible to all purely differential distinguishers even given unlimited data. While our attack is based on a known input difference taken from the literature, we also show that neural networks can be used to rapidly (within a matter of minutes on our machine) find good input differences without using prior human cryptanalysis.

The ongoing NIST lightweight standardization process explicitly puts forward a requirement of side-channel security, which has renewed the interest for Authenticated Encryption schemes (AEs) with light(er)-weight side-channel secure implementations. To address this challenge, we investigate the leakage-resilience of a generic duplex-based stream cipher, and prove the classical bound, i.e., $\approx2^{c/2}$, under an assumption of non-invertible leakage. Based on this, we propose a new 1-pass AE mode TETSponge, which carefully combines a tweakable block cipher that must have strong protections against side-channel attacks and is scarcely used, and a duplex-style permutation that only needs weak side-channel protections and is used to frugally process the message and associated data. TETSponge offers: (i) provable resistance against side-channel attacks during both encryption and decryption, (ii) some level of nonce misuse robustness, and (iii) black-box AE security with good bounds in the multi-user setting as well. We conclude that TETSponge offers an appealing option for the implementation of lightweight AE in settings where side-channel attacks are an actual concern. Our analysis offers the first rigorous methodology for the analysis of the leakage-resilience of sponge/duplex-based AEs. It can be easily adapted to others: we demonstrate this by showcasing brief analyzes of two other 1-pass AEs Ascon, GIBBON, and two 2-pass AEs TEDTSponge and ISAP. These provide various insights for both designs and implementations.

The stream cipher FOUNTAIN was introduced in April 2019 as one of the candidates in the NIST lightweight crypto standardization process. In this paper we introduce a slide attack that leads to the construction of 32 relations on key bits, with time complexity around $17\times 2^{80}$. The success of the attack is around 98%. We also present some properties of the internal state transitions that allow the identification of (key-iv-ad) input data that produce identical ciphertexts, with probability of $2^{-32}$.

In this paper, we investigate the security of Limdolen and HERN which are Round 1 submissions of the ongoing NIST Lightweight Cryptography Standardization Project. We show that some non-conservative design choices made by the designers solely to achieve a lightweight design lead to practical forgery attacks. In particular, we create associated data-only, ciphertext-only and associated data and ciphertext forgeries which require a feasible number of forging attempts. Limdolen employs a tweaked PMAC based construction to offer authenticated encryption functionality. It has two variants, Limdolen-128 and Limdolen-256 with key sizes 128 and 256 bits, respectively. The designers claim 128(256)-bit integrity security for Limdolen-128(256). Our main observation is that it uses a sequence of period 2 consisting of only two distinct secret masks. This structural flaw attributes to a successful forgery (all three types) with probability 1 after observing the output of a single encryption query. While, HERN is a 128-bit authenticated encryption scheme whose high level design is inspired from the CAESAR finalist Acorn. We show a message modification strategy by appending/removing a sequence of consecutive ‘0’ bits. Accordingly, we can construct associated data-only, ciphertext-only and associated data and ciphertext forgery with the success rate of $2^{-1}$, $2^{-1}$ and 1 after 2, 4 and 2 encryption queries, respectively. Overall, our attacks defeat the claim of 128(256) and 128-bit integrity security of Limdolen-128(256) and HERN, respectively. We have experimentally verified the correctness of our attacks with the reference implementations. Notably, these are the first cryptanalytic results on both algorithms. Consequently, our results are expected to help in further understanding of similar designs.

Many cryptographic constructions are based on the famous problem LWE \cite{LWERegev05}. In particular, this cryptographic problem is currently the most relevant to build FHE. In some LWE-based schemes, encrypting $x$ consists of randomly choosing a vector $c$ satisfying $\langle s,c\rangle=x+\textsf{noise}\pmod q$ where $s$ is a secret size-$n$ vector. While the vector sum is a homomorphic operator, such a scheme is intrinsically vulnerable to lattice-based attacks. To overcome this, we propose to define $c$ as a pair of vectors $(u,v)$ satisfying $\langle s,u\rangle/\langle s,v\rangle=x+\textsf{noise}\pmod q$. This simple scheme is based on a new cryptographic problem intuitively not easier than LWE, called Fractional LWE (FLWE). While some homomorphic properties are lost, the secret vector $s$ could be hopefully chosen shorter leading to more efficient constructions. We extensively study the hardness of FLWE. We first prove that the decision and search versions are equivalent provided $q$ is a \textit{small} prime. We then propose lattice-based cryptanalysis showing that $n$ could be chosen logarithmic in $\log q$.

We propose a new nonce-misuse-resistant authenticated encryption scheme, which instantiates the SIV paradigm of Rogaway and Shrimpton. In contrast to the GCM-SIV approach proposed by Gueron and Lindell, we do only use a single type of cryptographic primitive, which can be advantageous in restricted embedded devices. Furthermore, we use three independent and fixed subkeys derived from a single master key. Similar to the CCM mode, our scheme uses a combination of the CTR mode for the symmetric encryption and a MAC based on the CBC construction and is therefore called CCM-SIV. We provide a detailed security proof for our scheme. Furthermore, we outline its extension to a nonce-based key derivation as the AES-GCM-SIV approach.

Lilliput-AE is a tweakable block cipher submitted as a candidate to the NIST lightweight cryptography standardization process. It is based upon the lightweight block cipher Lilliput, whose cryptanalysis so far suggests that it has a large security margin. In this note we present an extremely efficient forgery attack on Lilliput-AE: Given a single arbitrary message of length about 2^36 bytes, we can instantly produce another valid message that leads to the same tag, along with the corresponding ciphertext. The attack uses a weakness in the tweakey schedule of Lilliput-AE which leads to the existence of a related tweak differential characteristic with probability 1 in the underlying block cipher. The weakness we exploit, which does not exist in Lilliput, demonstrates the potential security risk in using a very simple tweakey schedule in which the same part of the key/tweak is re-used in every round, even when round constants are employed to prevent slide attacks. Following this attack, the Lilliput-AE submission to NIST was tweaked.

We show that Legendre PRF, recently suggested as an MPC-friendly primitive in a prime field $Z_p$, admits key recovery attacks of complexity $O(\sqrt{p})$ rather than previously assumed $O(p)$. We also demonstrate new attacks on high-degree versions of this PRF, improving on the previous results by Russell and Shparlinski.

At the FSE conference of ToSC 2018, Kranz et al. presented their results on shortest linear programs for the linear layers of several well known block ciphers in literature. Shortest linear programs are essentially the minimum number of 2-input xor gates required to completely describe a linear system of equations. In the above paper the authors showed that the commonly used metrics like d-xor/s-xor count that are used to judge the ``lightweightedness'' do not represent the minimum number of xor gates required to describe a given MDS matrix. In fact they used heuristic based algorithms of Boyar/Peralta and Paar to find implementations of MDS matrices with even fewer xor gates than was previously known. They proved that the AES mixcolumn matrix can be implemented with as little as 97 xor gates. In this paper we show that the values reported in the above paper are not optimal. By suitably including random bits in the instances of the above algorithms we can achieve implementations of almost all matrices with lesser number of gates than were reported in the above paper. As a result we report an implementation of the AES mixcolumn matrix that uses only 95 xor gates. In the second part of the paper, we observe that most standard cell libraries contain both 2 and 3-input xor gates, with the silicon area of the 3-input xor gate being smaller than the sum of the areas of two 2-input xor gates. Hence when linear circuits are synthesized by logic compilers (with specific instructions to optimize for area), most of them would return a solution circuit containing both 2 and 3-input xor gates. Thus from a practical point of view, reducing circuit size in presence of these gates is no longer equivalent to solving the shortest linear program. In this paper we show that by adopting a graph based heuristic it is possible to convert a circuit constructed with 2-input xor gates to another functionally equivalent circuit that utilizes both 2 and 3-input xor gates and occupies less hardware area. As a result we obtain more lightweight implementations of all the matrices listed in the ToSC paper.

To quantify security levels in a post-quantum scenario, it is common to use the quantum resources needed to attack AES as a reference value. Specifically, in NIST’s ongoing post-quantum standardization effort, different security categories are defined that reflect the quantum resources needed to attack AES-128, AES-192, and AES-256. This paper presents a quantum circuit to implement the S-box of AES. Leveraging also an improved implementation of the key expansion, we identify new quantum circuits for all three AES key lengths. For AES-128, the number of Toffoli gates can be reduced by more than 88% compared to Almazrooie et al.'s and Grassl et al.'s estimates, while simultaneously reducing the number of qubits. Our circuits can be used to simplify a Grover-based key search for AES.

Recently Bar-On et al. proposed the DLCT for a tighter analysis of probabilities for differential-linear distinguishers. We extend the analysis of the DLCT, and gain new insights about this notion. The DLCT entries correspond to the autocorrelation spectrum of the component functions and thus the DLCT is nothing else as the ACT. We note that the ACT spectrum is invariant under some equivalence relations. Interestingly the ACT spectrum is not invariant under inversion (and thus not under CCZ equivalence), implying that it might be beneficial to look at the decryption for a differential-linear cryptanalysis. Furthermore, while for Boolean functions a lower bound for the maximal absolute autocorrelation, the absolute indicator, is not known, the case for vectorial Boolean functions is different. Here, we prove that for any vectorial Boolean function, its absolute indicator is lower bounded by $2^{n/2}$. Eventually, for APN functions we show a connection of the absolute indicator to the linearity of balanced Boolean functions, and exhibit APN permutations with absolute indicator bounded by $2^{(n+1)/2}$.

Plantlet is a lightweight stream cipher designed by Mikhalev, Armknecht and Müller in \texttt{IACR ToSC} 2017. It has a Grain-like structure with two state registers of size $40$ and $61$ bits. In spite of this, the cipher does not seem to lose in security against generic Time-Memory-Data Tradeoff attacks due to the novelty of its design. The cipher uses a 80-bit secret key and a 90-bit IV. In this paper, we first present a key recovery attack on Plantlet that requires around $2^{76.26}$ Plantlet encryptions. The attack leverages the fact that two internal states of Plantlet that differ in the 43rd LFSR location are guaranteed to produce keystream that are either equal or unequal in 45 locations with probability 1. Thus an attacker can with some probability guess that when 2 segments of keystream blocks possess the 45 bit difference just mentioned, they have been produced by two internal states that differ only in the 43rd LFSR location. Thereafter by solving a system of polynomial equations representing the keystream bits, the attacker can find the secret key if his guess was indeed correct, or reach some kind of contradiction if his guess was incorrect. In the latter event, he would repeat the procedure for other keystream blocks with the given difference. We show that the process when repeated a finite number of times, does indeed yield the value of the secret key. In the second part of the paper, we observe that the previous attack was limited to internal state differences that occurred at time instances that were congruent to $0\bmod 80$. We further observe that by generalizing the attack to include internal state differences that are congruent to all equivalence classed modulo 80, we lower the total number of keystream bits required to perform the attack and in the process reduce the attack complexity to $2^{69.98}$ Plantlet encryptions.

Tweakable block cipher (TBC), a stronger notion than standard block ciphers, has wide-scale applications in symmetric-key schemes. At a high level, it provides flexibility in design and (possibly) better security bounds. In multi-keyed applications, a TBC with short tweak values can be used to replace multiple keys. However, the existing TBC construction frameworks, including TWEAKEY and XEX, are designed for general purpose tweak sizes. Specifically, they are not optimized for short tweaks, which might render them inefficient for certain resource constrained applications. So a dedicated paradigm to construct short-tweak TBCs (tBC) is highly desirable. In this paper, we present a dedicated framework, called the Elastic-Tweak framework (ET in short), to convert any reasonably secure SPN block cipher into a secure tBC. We apply the ET framework on GIFT and AES to construct efficient tBCs, named TweGIFT and TweAES. We present hardware and software results to show that the performance overheads for these tBCs are minimal. We perform comprehensive security analysis and observe that TweGIFT and TweAES provide sufficient security without any increase in the number of block cipher rounds when compared to GIFT and AES. We also show some concrete applications of ET-based tBCs, which are better than their block cipher counterparts in terms of key size, state size, number of block cipher calls, and short message processing. Some notable applications include, Twe-FCBC (reduces the key size of FCBC and gives better security than CMAC), Twe-LightMAC Plus (better rate than LightMAC Plus), Twe-CLOC, and Twe-SILC (reduces the number of block cipher calls and simplifies the design of CLOC and SILC).

The Tire Pressure Monitoring System (TPMS) is used to monitor the pressure of the tires and to inform the driver of it. This equipment is mandatory for vehicles in US and EU. To ensure the security of TPMS, it is important to reduce the cost of the cryptographic mechanisms implemented in resourced-constrained devices. To address this problem, previous work has proposed countermeasures employing lightweight block ciphers such as PRESENT, SPECK, or KATAN. However, it is not clear to us that any of these works have addressed the issues of software optimization that considers TPMS-packet protection as well as session key updates for architectures consisting of the vehicle TPMS ECU and four low-cost TPM sensors equipped with the tires. In this paper, we propose to application of the ISO/IEC 29192-5 lightweight hash function Lesamnta-LW to address this issue. Our approach is to apply the known method of converting Lesamnta-LW to multiple independent pseudo-random functions (PRFs) in TPMS. In our case, we generate five PRFs this way and then use one PRF for MAC-generation and four for key derivation. Although we follow the NIST SP 800-108 framework of converting PRFs to key derivation functions, we confirm the significant advantage of Lesamnta-LW-based PRFs over HMAC-SHA-256 by evaluating the performance on AVR 8-bit micro-controllers, on which we consider simulating TPMS sensors. We expect that our method to achieve multiple-purposes with a single cryptographic primitive will help to reduce the total implementation cost required for TPMS security.

XTS is an encryption scheme for storage devices standardized by IEEE and NIST. It is based on Rogaway's XEX tweakable block cipher and is known to be secure up to the collisions between the blocks, thus up to around $2^{n/2}$ blocks for $n$-bit blocks. However this only implies that the theoretical indistinguishability notion is broken with $O(2^{n/2})$ queries and does not tell the practical risk against the plaintext recovery if XTS is targeted. We show several plaintext recovery attacks against XTS beyond collisions, and evaluate their practical impacts.

We study a question whether the currently known families of quadratic APN polynomials are pairwise different up to CCZ-equivalence. We reduce the list of these families to those CCZ-inequivalent to each other. In particular, we prove that the families of APN trinomials (constructed by Budaghyan and Carlet in 2008) and multinomials (constructed by Bracken et al. 2008) are CCZ-equivalent to the APN hexanomial family introduced by Budaghyan and Carlet in 2008. We also prove that a generalization of these trinomial and multinomial families given by Duan et al. (2014) is CCZ-equivalent to the family of hexanomials as well.

Symmetric Searchable encryption (SSE) is an encryption technique that allows users to search directly on their outsourced encrypted data, in a way that the privacy of both the files and the search queries is preserved. Naturally, with every search query, some information is leaked. The leakage becomes even bigger when the scheme is dynamic (i.e. supports file insertions and deletions). To deal with this problem we design a forward private dynamic SSE scheme where file insertions do not leak any information about previous queries. Moreover, our construction supports the multi-client model, in the sense that every user that holds the secret key can perform search queries. Finally, our scheme also focuses on the problem of synchronization by utilizing the functionality offered by Intel SGX.

Many cryptographers have focused on lightweight cryptography, and a huge number of lightweight block ciphers have been proposed. On the other hand, designing lightweight stream ciphers is a challenging task due to the well-known security criteria, i.e., the state size of stream ciphers must be at least twice the key size. The designers of Sprout addressed this issue by involving the secret key not only in the initialization but also in the keystream generation, and the state size of such stream ciphers can be smaller than twice the key size. After the seminal work, some small-state stream ciphers have been proposed such as Fruit, Plantlet, and LIZARD. Unlike conventional stream ciphers, these small-state stream ciphers have the limitation of keystream bits that can be generated from the same key and IV pair. In this paper, our motivation is to show whether the data limitation claimed by the designers is proper or not. The correlation attack is one of the attack methods exploiting many keystream bits generated from the same key and IV pair, and we apply it to Fruit-80 and Plantlet. As a result, we can break the full Fruit-80, i.e., the designers' data limitation is not sufficient. We can also recover the secret key of Plantlet if it allows about $2^{53}$ keystream bits from the same key and IV pair.

SAE (Simultaneous Authentication of Equals), is a password authenticated key exchange protocol, which is designed to replace the WPA2-PSK based authentication. The SAE Authentication Protocol supports the peer to peer (P2P) authentication, and is a major authentication mechanism of the Authentication and Key Management Suite (AKM). The SAE key exchange protocol and its variants, i.e, the Dragonfly key exchange protocol, have previously received some cryptanalysis, in which the authors pointed out Dragonfly protocol is vulnerable to the sub-group attack. This paper investigates some further vulnerabilities using impersonation attacks and suggests some protocol amendments for protection. It is recommended that SAE implementations should be upgraded to ensure protection against these attacks.

The fast correlation attack (FCA) is one of the most important cryptanalytic techniques against LFSR-based stream ciphers. In CRYPTO 2018, Todo et al. found a new property for the FCA and proposed a novel algorithm which was successfully applied to the Grain family of stream ciphers. Nevertheless, these techniques can not be directly applied to Grain-like small state stream ciphers with keyed update, such as Plantlet, Fruit-v2, and Fruit80. In this paper, we study the security of Grain-like small state stream ciphers by the fast correlation attack. We first observe that the number of required parity-check equations can be reduced when there are multiple different parity-check equations. With exploiting the Skellam distribution, we introduce a sufficient condition to identify the correct LFSR initial state and derive a new relationship between the number and bias of the required parity-check equations. Then a modified algorithm is presented based on this new relationship, which can recover the LFSR initial state no matter what the round key bits are. Under the condition that the LFSR initial state is known, an algorithm is given against the degraded system and to recover the NFSR state at some time instant, along with the round key bits. As cases study, we apply our cryptanalytic techniques to Plantlet, Fruit-v2 and Fruit-80. As a result, for Plantlet our attack takes $ 2^{73.75} $ time complexity and $ 2^{73.06} $ keystream bits to recover the full 80-bit key. Regarding Fruit-v2, $ 2^{55.34} $ time complexity and $ 2^{55.62} $ keystream bits are token to determine the secret key. As for Fruit-80, $2^{64.47}$ time complexity and $2^{62.82}$ keystream bits are required to recover the secret key. More flexible attacks can be obtained with lower data complexity at cost of increasing attack time. Especially, for Fruit-v2 a key recovery attack can be launched with data complexity of $2^{42.38}$ and time complexity of $2^{72.63}$. Moreover, we have implemented our attack methods on a toy version of Fruit-v2. The attack matches the expected complexities predicted by our theoretical analysis quite well, which proves the validity of our cryptanalytic techniques.

Fuzzy extractors (Dodis et al., Eurocrypt 2004) convert repeated noisy readings of a high-entropy source into the same uniformly distributed key. The functionality of a fuzzy extractor outputs the key when provided with a value close to the original reading of the source. A necessary condition for security, called fuzzy min-entropy, is that the probability of every ball of values of the noisy source is small. Many noisy sources are best modeled using continuous metric spaces. To build continuous-source fuzzy extractors, prior work assumes that the system designer has a good model of the distribution (Verbitskiy et al., IEEE TIFS 2010). However, it is impossible to build an accurate model of a high entropy distribution just by sampling from the distribution. Model inaccuracy may be a serious problem. We demonstrate a family of continuous distributions V that is impossible to secure. No fuzzy extractor designed for V extracts a meaningful key from an average element of V. This impossibility result is despite the fact that each element W in V has high fuzzy min-entropy. We show a qualitatively stronger negative result for secure sketches, which are used to construct most fuzzy extractors. Our results are for the Euclidean metric and are information-theoretic in nature. To the best of our knowledge all continuous-source fuzzy extractors argue information-theoretic security. Fuller, Reyzin, and Smith showed comparable negative results for a discrete metric space equipped with the Hamming metric (Asiacrypt 2016). Continuous Euclidean space necessitates new techniques.

We propose definitions and constructions of authenticated encryption (AE) schemes that offer security guarantees even in the presence of nonce misuse and side-channel leakages. This is part of an important ongoing effort to make AE more robust, while preserving appealing efficiency properties. Our definitions consider an adversary enhanced with the leakages of all the computations of an AE scheme, together with the possibility to misuse nonces, be it during all queries (in the spirit of misuse-resistance), or only during training queries (in the spirit of misuse-resilience recently introduced by Ashur et al.). These new definitions offer various insights on the effect of leakages in the security landscape. In particular, we show that, in contrast with the black-box setting, leaking variants of INT-CTXT and IND-CPA security do not imply a leaking variant IND-CCA security, and that leaking variants of INT-PTXT and IND-CCA do not imply a leaking variant of INT-CTXT. Eventually, we propose first instances of modes of operations that satisfy our definitions. In order to optimize their efficiency, we aim at modes that support "leveled implementations" such that the encryption and decryption operations require the use of a small constant number of evaluations of an expensive and heavily protected component, while the bulk of the computations can be performed by cheap and weakly protected block cipher implementations.

We give the first practical instance – BISON – of the Whitened Swap-Or-Not construction. After clarifying inherent limitations of the construction, we point out that this way of building block ciphers allows easy and very strong arguments against differential attacks.

TRIFLE is a Round 1 candidate of the NIST Lightweight Cryptography Standardization process. In this paper, we present an interesting 1-round iterative differential characteristic of the underlying block cipher TRIFLE-BC used in TRIFLE, which holds with probability of $2^{-3}$. Consequently, it allows to mount distinguishing attack on TRIFLE-BC for up to 43 (out of 50) rounds with data complexity $2^{124}$ and time complexity $2^{124}$. Most importantly, with such an iterative differential characteristic, the forgery attack on TRIFLE can reach up to 21 (out of 50) rounds with data complexity $2^{63}$ and time complexity $2^{63}$. Finally, to achieve key recovery attack on reduced TRIFLE, we construct a differential characteristic covering three blocks by carefully choosing the positions of the iterative differential characteristic. As a result, we can mount key-recovery attack on TRIFLE for up to 11 rounds with data complexity $2^{63}$ and time complexity $2^{104}$. Although the result in this paper cannot threaten the security margin of TRIFLE, we hope it can help further understand the security of TRIFLE.

We report on a simple technique that supports some recent developments on AES by Grassi and Rechberger and Bao, Guo and List. We construct a weight transition probability matrix related to AES that characterises fixed configurations of active bytes in differences of ciphertexts when plaintext differences are fixed to some (possibly other) configuration of active bytes. The construction is very simple and requires only a little bit of linear algebra. The derived probabilities are essentially identical to recent results on 5- and 6-rounds AES derived through more sophisticated means, indicating that it might be worth a further investigation.

In this paper we investigate the security of 5-round AES against two different attacks in an adaptive setting. We present a practical key-recovery attack on 5-round AES with a secret s-box that requires $2^{32}$ adaptively chosen ciphertexts, which is as far as we know a new record. In addition, we present a new and practical key-independent distinguisher for 5-round AES which requires $2^{27.2}$ adaptively chosen ciphertexts. While the data complexity of this distinguisher is in the same range as the current best 5-round distinguisher, it exploits new structural properties of 5-round AES.

In recent literature, there has been a particular interest in studying nonce based AE schemes in the light of fault based attacks as they seem to present an automatic protection against Differential Fault Attacks (DFA). In this work, we present the first DFA on nonce based CAESAR scheme NORX. We demonstrate a scenario when faults introduced in NORX in parallel mode can be used to collide the internal state to produce an \emph{all-zero} state. We later show how this can be used to replay NORX despite being instantiated by different nonces, messages. Once replayed, we show how the key of NORX can be recovered using secondary faults and using the faulty tags. We use different fault models to showcase the versatility of the attack strategy. A detailed theoretical analysis of the expected number of faults required under various models is also furnished. Under the random bit flip model, around 1384 faults are to be induced to reduce the key space from $2^{128}$ to $2^{32}$ while the random byte flip model requires 136 faults to uniquely identify the key. To the best of our knowledge, this is the first fault attack that uses \emph{both internal} and \emph{classical differentials} to mount a DFA on a nonce based authenticated cipher which is otherwise believed to be immune to DFA.

The two-terminal key agreement problem with biometric or physical identifiers is considered. Two linear code constructions based on Wyner-Ziv coding are developed. The first construction uses random linear codes and achieves all points of the key-leakage-storage regions of the generated-secret and chosen-secret models. The second construction uses nested polar codes for vector quantization during enrollment and error correction during reconstruction. Simulations show that the nested polar codes achieve privacy-leakage and storage rates that improve on existing code designs. One proposed code achieves a rate tuple that cannot be achieved by existing methods.

The combination of universal hashing and encryption is a fundamental paradigm for the construction of symmetric-key MACs, dating back to the seminal works by Wegman and Carter, Shoup, and Bernstein. While fully sufficient for many practical applications, the Wegman-Carter construction, however, is well-known to break if nonces are ever repeated, and provides only birthday-bound security if instantiated with a permutation. Those limitations inspired the community to several recent proposals that addressed them, initiated by Cogliati et al.'s Encrypted Wegman-Carter Davies-Meyer (EWCDM) construction. This work extends this line of research by studying two constructions based on the sum of PRPs: (1) a stateless deterministic scheme that uses two hash functions, and (2) a nonce-based scheme with one hash-function call and a nonce. We show up to 2n/3-bit security for both of them if the hash function is universal. Compared to the EWCDM construction, our proposals avoid the fact that a single reuse of a nonce can lead to a break.

At Eurocrypt 2017 the first secret-key distinguisher for 5-round AES -- based on the “multiple-of-8” property -- has been presented. Although it allows to distinguish a random permutation from an AES-like one, it seems rather hard to implement a key-recovery attack different than brute-force like using such a distinguisher. In this paper we introduce “Mixture Differential Cryptanalysis” on round-reduced AES-like ciphers, a way to translate the (complex) “multiple-of-8” 5-round distinguisher into a simpler and more convenient one (though, on a smaller number of rounds). Given a pair of chosen plaintexts, the idea is to construct new pairs of plaintexts by mixing the generating variables of the original pair of plaintexts. Here we theoretically prove that for 4-round AES the corresponding ciphertexts of the original pair of plaintexts lie in a particular subspace if and only if the corresponding pairs of ciphertexts of the new pairs of plaintexts have the same property. Such secret-key distinguisher -- which is independent of the secret-key, of the details of the S-Box and of the MixColumns matrix (except for the branch number equal to 5) -- can be used as starting point to set up new key-recovery attacks on round-reduced AES. Besides a theoretical explanation, we also provide a practical verification both of the distinguisher and of the attack. As a second contribution, we show how to combine this new 4-round distinguisher with a modified version of a truncated differential distinguisher in order to set up new 5-round distinguishers, that exploit properties which are independent of the secret key, of the details of the S-Box and of the MixColumns matrix. As a result, while a “classical” truncated differential distinguisher exploits the probability that a couple of texts satisfies or not a given differential trail independently of the others couples, our distinguishers work with sets of N >> 1 (related) couples of texts. In particular, our new 5-round AES distinguishers exploit the fact that such sets of texts satisfy some properties with a different probability than a random permutation. Even if such 5-round distinguishers have higher complexity than e.g. the “multiple-of-8” one present in the literature, one of them can be used as starting point to set up the first key-recovery attack on 6-round AES that exploits directly a 5-round secret-key distinguisher. The goal of this paper is indeed to present and explore new approaches, showing that even a distinguisher like the one presented at Eurocrypt -- believed to be hard to exploit - can be used to set up a key-recovery attack.

Hash combiners are a practical way to make cryptographic hash functions more tolerant to future attacks and compatible with existing infrastructure. A combiner combines two or more hash functions in a way that is hopefully more secure than each of the underlying hash functions, or at least remains secure as long as one of them is secure. Two classical hash combiners are the exclusive-or (XOR) combiner $H_1(M) \oplus H_2(M)$ and the concatenation combiner $H_1(M) \parallel H_2(M)$. Both of them process the same message using the two underlying hash functions in parallel. Apart from parallel combiners, there are also cascade constructions sequentially calling the underlying hash functions to process the message repeatedly, such as Hash-Twice $H_2(H_1(IV,M),M)$ and the Zipper hash $H_2(H_1(IV,M),\overleftarrow{M})$, where $\overleftarrow{M}$ is the reverse of the message $M$. In this work, we study the security of these hash combiners by devising the best-known generic attacks. The results show that the security of most of the combiners is not as high as commonly believed. We summarize our attacks and their computational complexities (ignoring the polynomial factors) as follows: 1. Several generic preimage attacks on the XOR combiner: -- A first attack with a best-case complexity of $2^{5n/6}$ obtained for messages of length $2^{n/3}$. It relies on a novel technical tool named Interchange Structure. It is applicable for combiners whose underlying hash functions follow the Merkle-Damgård construction or the HAIFA framework. -- A second attack with a best-case complexity of $2^{2n/3}$ obtained for messages of length $ 2^{n/2} $. It exploits properties of functional graphs of random mappings. It achieves a significant improvement over the first attack but is only applicable when the underlying hash functions use the Merkle-Damgård construction. -- An improvement upon the second attack with a best-case complexity of $2^{5n/8}$ obtained for messages of length $2^{5n/8}$. It further exploits properties of functional graphs of random mappings and uses longer messages. These attacks show a rather surprising result: regarding preimage resistance, the sum of two $n$-bit narrow-pipe hash functions following the considered constructions can never provide $ n $-bit security. 2. A generic second-preimage attack on the concatenation combiner of two Merkle Damgård hash functions. This attack finds second preimages faster than $2^n$ for challenges longer than $2^{2n/7}$ and has a best-case complexity of $2^{3n/4}$ obtained for challenges of length $2^{3n/4}$. It also exploits properties of functional graphs of random mappings. 3. The first generic second-preimage attack on the Zipper hash with underlying hash functions following the Merkle-Damgård construction. The best-case complexity is $2^{3n/5}$, obtained for challenge messages of length $2^{2n/5}$. 4. An improved generic second-preimage attack on Hash-Twice with underlying hash functions following the Merkle-Damgård construction. The best-case complexity is $2^{13n/22}$, obtained for challenge messages of length $2^{13n/22}$. The last three attacks show that regarding second-preimage resistance, the concatenation and cascade of two $n$-bit narrow-pipe Merkle-Damgård hash functions do not provide much more security than that can be provided by a single $n$-bit hash function. Our main technical contributions include the following: 1. The interchange structure, which enables simultaneously controlling the behaviours of two hash computations sharing the same input. 2. The simultaneous expandable message, which is a set of messages of length covering a whole appropriate range and being multi-collision for both of the underlying hash functions. 3. New ways to exploit the properties of functional graphs of random mappings generated by fixing the message block input to the underlying compression functions.

We show that the correlation of any quadratic Boolean function can be read out from its so-called disjoint quadratic form. We further propose a polynomial-time algorithm that can transform an arbitrary quadratic Boolean function into its disjoint quadratic form. With this algorithm, the exact correlation of quadratic Boolean functions can be computed efficiently. We apply this method to analyze the linear trails of MORUS (one of the seven finalists of the CAESAR competition), which are found with the help of a generic model for linear trails of MORUS-like key-stream generators. In our model, any tool for finding linear trails of block ciphers can be used to search for trails of MORUS-like key-stream generators. As a result, a set of trails with correlation $2^{-38}$ is identified for all versions of full MORUS, while the correlations of previously published best trails for MORUS-640 and MORUS-1280 are $2^{-73}$ and $2^{-76}$ respectively (ASIACRYPT 2018). This significantly improves the complexity of the attack on MORUS-1280-256 from $2^{152}$ to $2^{76}$. These new trails also lead to the first distinguishing and message-recovery attacks on MORUS-640-128 and MORUS-1280-128 with surprisingly low complexities around $2^{76}$. Moreover, we observe that the condition for exploiting these trails in an attack can be more relaxed than previously thought, which shows that the new trails are superior to previously published ones in terms of both correlation and the number of ciphertext blocks involved.

We first introduce a family of binary $pq^2$ -periodic sequences based on the Euler quotients modulo $pq$, where $p$ and $q$ are two distinct odd primes and $p$ divides $q - 1$. The minimal polynomials and linear complexities are determined for the proposed sequences provided that $2^{q-1} \not \equiv 1 \pmod q^2$ . The results show that the proposed sequences have high linear complexities.

In this paper we show that a large class of diverse problems have a bicomposite structure which makes it possible to solve them with a new type of algorithm called {\it dissection}, which has much better time/memory tradeoffs than previously known algorithms. A typical example is the problem of finding the key of multiple encryption schemes with $r$ independent $n$-bit keys. All the previous error-free attacks required time $T$ and memory $M$ satisfying $TM = 2^{rn}$, and even if ``false negatives'' are allowed, no attack could achieve $TM<2^{3rn/4}$. Our new technique yields the first algorithm which never errs and finds all the possible keys with a smaller product of $TM$, such as $T=2^{4n}$ time and $M=2^{n}$ memory for breaking the sequential execution of r=7 block ciphers. The improvement ratio we obtain increases in an unbounded way as $r$ increases, and if we allow algorithms which can sometimes miss solutions, we can get even better tradeoffs by combining our dissection technique with parallel collision search. To demonstrate the generality of the new dissection technique, we show how to use it in a generic way in order to improve rebound attacks on hash functions and to solve with better time complexities (for small memory complexities) hard combinatorial search problems, such as the well known knapsack problem.

Block cipher modes of operation provide a way to securely encrypt using a block cipher, and different modes of operation achieve different tradeoffs of security, performance and simplicity. In this paper, we present a new authenticated encryption scheme that is designed for the lightweight cryptography setting, but can be used in standard settings as well. Our mode of encryption is extremely simple, requiring only a single block cipher primitive (in forward direction) and minimal padding, and supports streaming (online encryption). In addition, our mode achieves very strong security bounds, and can even provide good security when the block size is just 64 bits. As such, it is highly suitable for lightweight settings, where the lifetime of the key and/or overall amount encrypted may be high. Our new scheme can be seen as an improved version of CCM that supports streaming, and provides much better bounds.

Troika is a recently proposed sponge-based hash function for IOTA's ternary architecture and platform, which is developed by CYBERCRYPT. In this paper, we introduce the preimage attack on 2 and 3 rounds of Troika with a divide-and-conquer approach. Instead of directly matching a given hash value, we propose equivalent conditions to determine whether a message is the preimage before computing the complete hash value. As a result, for the two-round hash value that can be generated with one block, we can search the preimage only in a valid space and efficiently enumerate the messages which can satisfy most of the equivalent conditions with a guess-and-determine technique. For the three-round preimage attack, an MILP-based method is applied to separate the one-block message space into two parts in order to obtain the best advantage over brute force. Our experiments show that the time complexity of the preimage attack on 2 (out of 24) rounds of Troika can be improved to $3^{79}$, which is $3^{164}$ times faster than the brute force. For the preimage attack on 3 (out of 24) rounds of Troika, we can obtain an advantage of $3^{25.7}$ over brute force. In addition, how to construct the second preimage for two-round Troika in seconds is presented as well. Our attacks do not threaten the security of Troika.

Lightweight cryptography in computationally constrained devices is actively studied. In contrast to advances of lightweight blockcipher in the last decade, lightweight mode of operation is seemingly not so mature, yet it has large impact in performance. Therefore, there is a great demand for lightweight mode of operation, especially that for authenticated encryption with associated data (AEAD). Among many known properties of conventional modes of operation, the following four properties are essential for constrained devices: 1. Minimum State Size: the state size equals to a block size of a blockcipher. 2. Inverse Free: no need for a blockcipher decryption. 3. XOR Only: only XOR is needed in addition to a blockcipher encryption. 4. Online: a data block is processed only once. The properties 1 and 4 contribute to small memory usage, and the properties 2 and 3 contribute to small program/circuit footprint. On top of the above properties, the fifth property regarding associated data (AD) is also important for performance: 5. Efficient Handling of Static AD: static AD can be precomputed. We design a lightweight blockcipher-based AEAD mode of operation called SAEB: the first mode of operation that satisfies all the five properties to the best of our knowledge. Performance of SAEB is evaluated in various software and hardware platforms. The evaluation results show that SAEB outperforms conventional blockcipher-based AEAD modes of operation in various performance metrics for lightweight cryptography.

Assuring security of the Internet of Things (IoT) is much more challenging than assuring security of centralized environments, like the cloud. A reason for this is that IoT devices are often deployed in domains that are remotely managed and monitored. Thus, their physical security cannot be guaranteed as reliably as physical security of data centers. Some believe that physical security becomes less important if all data processed and stored within a device is encrypted. However, an attacker with a physical access to a device implementing an encryption algorithm may be able to extract the encryption key and decrypt data. As a demonstration, in this paper we attack ACORN stream cipher, a finalist of CESAR competition for authenticated encryption. By injecting a single stuck-at-0 fault into ACORN's implementation, we reduce its non-linear feedback function to a linear one. Since this obviously makes ACORN weaker, many known attacks can be applied to break it. We apply an algebraic attack which recovers the key from $2^{15.34}$ keystream bits using $2^{35.46}$ operations.

We revisit the definition of Transparency Order (TO) and that of Modified Transparency Order (MTO) as well, which were proposed to measure the resistance of an S-box against Differential Power Analysis (DPA). We spot a definitional flaw in original TO, which is proved to have significantly affected the soundness of TO and hinder it to be a good quantitative security criterion. Regretfully, the flaw itself remains virtually undiscovered in MTO, either. Surprisingly, MTO overlooks this flaw and yet it happens to incur no bad effects on the correctness of its formulation, even though the start point of this formulation is highly questionable. It is also this neglect of the flaw that made MTO take a variant of multi-bit DPA attack into consideration, which was mistakenly thought to appropriately serve as an alternative powerful attack. Based on this observation, we also find that MTO introduces such an alternative adversary that it might overestimate the resistance of an S-box in some cases, as the variant of multi-bit DPA attack considered in MTO is not that powerful as one may think. This implies the soundness of MTO is also more or less arguable. Consequently, we fix this definitional flaw, and provide a revised definition in which a powerful adversary is also involved. For demonstrating validity and soundness of our revised TO (RTO), we adopt both optimal $4\times4$ S-boxes and $8\times8$ S-boxes as study cases, and present simulated and practical DPA attacks as well on implementations of those S-boxes. The results of our attacks verify our findings and analysis as well. Furthermore, as a concrete application of the revised TO, we also present the distribution of RTO values for sixteen optimal affine equivalence classes of $4\times4$ S-boxes. Finally, we give some recommended guidelines on how to select optimal $4\times4$ S-boxes in practical implementations.

In this paper, using Mixed Integer Linear Programming, a new automatic search tool for truncated differential characteristic is presented. Our method models the problem of finding a maximal probability truncated differential characteristic, which is able to distinguish the cipher from a pseudo random permutation. Using this method, we analyse Midori64, SKINNY64/X and CRAFT block ciphers, for all of which the existing results are improved. In all cases, the truncated differential characteristic is much more efficient than the (upper bound of) bit-wise differential characteristic proven by the designers, for any number of rounds. More specifically, the highest possible rounds, for which an efficient differential characteristic can exist for Midori64, SKINNY64/X and CRAFT are 6, 7 and 10 rounds respectively, for which differential characteristics with maximum probabilities of $2^{-60}$, $2^{-52}$ and $2^{-62.61}$ (may) exist. Using our new method, we introduce new truncated differential characteristics for these ciphers with respective probabilities $2^{-54}$, $2^{-4}$ and $2^{-24}$ at the same number of rounds. Moreover, the longest truncated differential characteristics found for SKINNY64/X and CRAFT have 10 and 12 rounds, respectively. This method can be used as a new tool for differential analysis of SPN block ciphers.

In this paper we analyze for the first time the post-quantum security of AES. AES is the most popular and widely used block cipher, established as the encryption standard by the NIST in 2001. We consider the secret key setting and, in particular, AES-256, the recommended primitive and one of the few existing ones that aims at providing a post-quantum security of 128 bits. In order to determine the new security margin, i.e., the lowest number of non-attacked rounds in time less than $2^{128}$ encryptions, we first provide generalized and quantized versions of the best known cryptanalysis on reduced-round AES, as well as a discussion on attacks that don't seem to benefit from a significant quantum speed-up. We propose a new framework for structured search that encompasses both the classical and quantum attacks we present, and allows to efficiently compute their complexity. We believe this framework will be useful for future analysis. Our best attack is a quantum Demirci-Selçuk meet-in-the-middle attack. Unexpectedly, using the ideas underlying its design principle also enables us to obtain new, counter-intuitive classical TMD trade-offs. In particular, we can reduce the memory in some attacks against AES-256 and AES-128. One of the building blocks of our attacks is solving efficiently the AES S-Box differential equation, with respect to the quantum cost of a reversible S-Box. We believe that this generic quantum tool will be useful for future quantum differential attacks. Judging by the results obtained so far, AES seems a resistant primitive in the post-quantum world as well as in the classical one, with a bigger security margin with respect to quantum generic attacks.

We study approaches to generalized Feistel constructions with low-degree round functions with a focus on x -> x^3 . Besides known constructions, we also provide a new balanced Feistel construction with improved diffusion properties. This then allows us to propose more efficient generalizations of the MiMC design (Asiacrypt’16), which we in turn evaluate in three application areas. Whereas MiMC was not competitive at all in a recently proposed new class of PQ-secure signature schemes, our new construction leads to about 30 times smaller signatures than MiMC. In MPC use cases, where MiMC outperforms all other competitors, we observe improvements in throughput by a factor of more than 4 and simultaneously a 5-fold reduction of preprocessing effort, albeit at the cost of a higher latency. Another use case where MiMC already outperforms other designs, in the area of SNARKs, sees modest improvements. Additionally, this use case benefits from the flexibility to use smaller fields.

A new generation of stream ciphers, small-state stream ciphers (SSCs), was born in 2015 with the introduction of the Sprout cipher. The new generation is based on using key bits not only in the initialization but also continuously in the keystream generation phase. The new idea allowed designing stream ciphers with significantly smaller area size and low power consumption. A distinguishing time-memory-data tradeoff (TMDTO) attack was successfully applied against all SSCs in 2017 by Hamann et al. [1]. They suggested using not only key bits but also initial value (IV) bits continuously in the keystream generation phase to strengthen SSCs against TMDTO attacks. Then, Hamann and Krause [2] proposed a construction based on using only IV bits continuously in packet mode. They suggested an instantiation of an SSC and claimed that it is resistant to TMDTO attacks. We point out that storing IV bits imposes an overhead on cryptosystems that is not acceptable in many applications. More importantly, we show that the proposed SSC remains vulnerable to TMDTO attacks. To resolve security threat, the current paper proposes constructions, based on storing key or IV bits, that are the first to provide full security against TMDTO attacks. It is possible to obtain parameters for secure SSCs based on these suggested constructions. Our constructions are a fruitful research direction in stream ciphers.

In Eurocrypt 2018, Cid et al. proposed a novel notion called the boomerang connectivity table, which formalised the switch property in the middle round of boomerang distinguishers in a unified approach. In this paper, we present a generic model of the boomerang connectivity table with automatic search technique for the first time, and search for (related-key) boomerang distinguishers directly by combining with the search of (related-key) differential characteristics. With the technique, we are able to find 19-round related-key boomerang distinguishers in the lightweight block cipher \textsc{Gift}-64 and \textsc{Gift}-128. Interestingly, a transition that is not predictable by the conventional switches is realised in a boomerang distinguisher predicted by the boomerang connectivity table. In addition, we experimentally extend the 19-round distinguisher by one more round. A 23-round key-recovery attack is presented on \textsc{Gift}-64 based on the distinguisher, which covers more rounds than previous known results in the single-key setting. Although the designers of \textsc{Gift} do not claim related-key security, bit positions of the key addition and 16-bit rotations were chosen to optimize the related-key differential bound. Indeed, the designers evaluated related-key differential attacks. This is the first work to present better related-key attacks than the simple related-key differential attack.

At Asiacrypt 2014, Sun et al. proposed a MILP model to search for differential characteristics of bit-oriented block ciphers. In this paper, we improve this model to search for differential characteristics of GIFT, a new lightweight block cipher proposed at CHES 2017. GIFT has two versions, namely GIFT-64 and GIFT-128. For GIFT-64, we find the best 12-round differential characteristic and a number of iterative 4-round differential characteristics with our MILP-based model. We give a key-recovery attack on 19-round GIFT-64. For GIFT-128, we find a 18-round differential characteristic and give the first attack on 22-round GIFT-128.

Deep learning side-channel attacks are an emerging threat to the security of implementations of cryptographic algorithms. The attacker first trains a model on a large set of side-channel traces captured from a chip with a known key. The trained model is then used to recover the unknown key from a few traces captured from a victim chip. The first successful attacks have been demonstrated recently. However, they typically train and test on power traces captured from the same device. In this paper, we show that it is important to train and test on traces captured from different boards and using diverse implementations of the cryptographic algorithm under attack. Otherwise, it is easy to overestimate the classification accuracy. For example, if we train and test an MLP model on power traces captured from the same board, we can recover all key byte values with 96% accuracy from a single trace. However, the single-trace attack accuracy drops to 2.45% if we test on traces captured from a board different from the one we used for training, even if both boards carry identical chips.

The study of non-linearity (linearity) of Boolean function was initiated by Rothaus in 1976. The classical non-linearity of a Boolean function is the minimum Hamming distance of its truth table to that of affine functions. In this note we introduce new "multidimensional" non-linearity parameters $(N_f,H_f)$ for conventional and vectorial Boolean functions $f$ with $m$ coordinates in $n$ variables. The classical non-linearity may be treated as a 1-dimensional parameter in the new definition. $r$-dimensional parameters for $r\geq 2$ are relevant to possible multidimensional extensions of the Fast Correlation Attack in stream ciphers and Linear Cryptanalysis in block ciphers. Besides we introduce a notion of optimal vectorial Boolean functions relevant to the new parameters. For $r=1$ and even $n\geq 2m$ optimal Boolean functions are exactly perfect nonlinear functions (generalizations of Rothaus' bent functions) defined by Nyberg in 1991. By a computer search we find that this property holds for $r=2, m=1, n=4$ too. That is an open problem for larger $n,m$ and $r\geq 2$. The definitions may be easily extended to $q$-ary functions.

The classic simple substitution cipher is modified by randomly inserting key-defined noise characters into the ciphertext in encryption which are ignored in decryption. Interestingly, this yields a finite-key cipher system with unbounded unicity.

We define ZOCB and ZOTR for nonce-based authenticated encryption with associated data, and analyze their provable security. These schemes use a tweakable blockcipher (TBC) as the underlying primitive, and fully utilize its input to process a plaintext and associated data (AD). This property is commonly referred to as full absorption, and this has been explored for schemes based on a permutation or a pseudorandom function (PRF). Our schemes improve the efficiency of TBC-based counterparts of OCB and OTR called $\Theta$CB3 (Krovetz and Rogaway, FSE 2011) and $\mathbb{OTR}$ (Minematsu, EUROCRYPT 2014). Specifically, $\Theta$CB3 and $\mathbb{OTR}$ have an independent part to process AD, and our schemes integrate this process into the encryption part of a plaintext by using the tweak input of the TBC. Up to a certain length of AD, ZOCB and ZOTR completely eliminate the independent process for it. Even for longer AD, our schemes process it efficiently by fully using the tweak input of the TBC. For this purpose, based on previous tweak extension schemes for TBCs, we introduce a scheme called $\mathsf{XTX}^{\ast}$. To our knowledge, ZOCB and ZOTR are the first efficiency improvement of $\Theta$CB3 and $\mathbb{OTR}$ in terms of the number of TBC calls. Compared to Sponge-based and PRF-based schemes, ZOCB and ZOTR allow fully parallel computation of the underlying primitive, and have a unique design feature that an authentication tag is independent of a part of AD. We present experimental results illustrating the practical efficiency gain and clarifying the efficiency cost for it with a concrete instantiation. The results show that for long input data, our schemes have gains, while we have efficiency loss for short input data.

In this paper, we study DFA attacks on some of the CAESAR competition winners. We study the challenges imposed by the design of these modes, such as masking of the ciphertext. We also show that a very small number of nonce repetition and faults is required, which makes it very practical. We show that OCB and COLM need 1 nonce repetition and 3 faults only to uniquely identify the Key.

In this paper, we introduce an alternative method to find ordinary cube variables for Keccak-MAC by making full use of the key-independent bit conditions. First, we select some potential candidates for ordinary cube variables by properly adding key-independent bit conditions, which do not multiply with the chosen conditional cube variables in the first two rounds. Then, we carefully determine the ordinary cube variables from the candidates to establish the conditional cube tester. Finally, based on our new method to recover the 128-bit key, the conditional cube attack on 7-round Keccak-MAC-128/256/384 is improved to $2^{71}$ and 6-round Keccak-MAC-512 can be attacked with at most $2^{40}$ calls to 6-round Keccak internal permutation. It should be emphasized that our new approach does not require sophisticated modeling. As far as we know, it is the first time to clearly reveal how to utilize the key-independent bit conditions to select ordinary cube variables for Keccak-MAC.

RIPEMD-160 is an ISO/IEC standard and has been applied to generate the Bitcoin address with SHA-256. Due to the complex dual-stream structure, the first collision attack on reduced RIPEMD-160 presented by Liu, Mendel and Wang at Asiacrypt 2017 only reaches 30 steps, having a time complexity of $2^{70}$. Apart from that, several semi-free-start collision attacks have been published for reduced RIPEMD-160 with the start-from-the-middle method. Inspired from such start-from-the middle structures, we propose two novel efficient collision attack frameworks for reduced RIPEMD-160 by making full use of the weakness of its message expansion. Those two frameworks are called dense-left-and-sparse-right (DLSR) framework and sparse-left-and-dense-right (SLDR) framework. As it turns out, the DLSR framework is more efficient than SLDR framework since one more step can be fully controlled, though with extra $2^{32}$ memory complexity. To construct the best differential characteristics for the DLSR framework, we carefully build the linearized part of the characteristics and then solve the corresponding nonlinear part using a guess-and-determine approach. Based on the newly discovered differential characteristics, we provide colliding messages pairs for the first practical collision attacks on 30 and 31 (out of 80) steps of RIPEMD-160 with time complexity $2^{35.9}$ and $2^{41.5}$ respectively. In addition, benefiting from the partial calculation, we can attack 33 and 34 (out of 80) steps of RIPEMD-160 with time complexity $2^{67.1}$ and $2^{74.3}$ respectively. When applying the SLDR framework to the differential characteristic used in the Asiacrypt 2017 paper, we significantly improve the time complexity by a factor of $2^{13}$. However, it still cannot compete with the results obtained from the DLSR framework. To the best of our knowledge, these are the best collision attacks on reduced RIPEMD-160 with respect to the number of steps, including the first colliding message pairs for 30 and 31 steps of RIPEMD-160.

The conditional cube attack on round-reduced \textsc{Keccak} keyed modes was proposed by Huang~\emph{et al.} at EUROCRYPT 2017. In their attack, a conditional cube variable was introduced, whose diffusion was significantly reduced by certain key bit conditions. The attack requires a set of cube variables which are not multiplied in the first round while the conditional cube variable is not multiplied with other cube variables (called ordinary cube variables) in the first two rounds. This has an impact on the degree of the output of \textsc{Keccak} and hence gives a distinguisher. Later, the MILP method was applied to find ordinary cube variables. However, for some \textsc{Keccak} based versions with few degrees of freedom, one could not find enough ordinary cube variables, which weakens or even invalidates the conditional cube attack. In this paper, a new conditional cube attack on \textsc{Keccak} is proposed. We remove the limitation that no cube variables multiply with each other in the first round. As a result, some quadratic terms may appear in the first round. We make use of some new bit conditions to prevent the quadratic terms from multiplying with other cube variables in the second round, so that there will be no cubic terms in the first two rounds. Furthermore, we introduce the \emph{kernel quadratic term} and construct a \emph{6-2-2 pattern} to reduce the diffusion of quadratic terms significantly, where the $\theta$ operation even in the second round becomes an identity transformation (CP-kernel property) for the \emph{kernel quadratic term}. Previous conditional cube attacks on \textsc{Keccak} only explored the CP-kernel property of $\theta$ operation in the first round. Therefore, more degrees of freedom are available for ordinary cube variables and fewer bit conditions are used to remove the cubic terms in the second round, which plays a key role in the conditional cube attack on versions with very few degrees of freedom. We also use the MILP method in the search of cube variables and give key-recovery attacks on round-reduced \textsc{Keccak} keyed modes. As a result, we reduce the time complexity of key-recovery attacks on 7-round \textsc{Keccak}-MAC-512 and 7-round \textsc{Ketje Sr} v2 from $2^{111}$, $2^{99}$ to $2^{72}$, $2^{77}$, respectively. Additionally, we have reduced the time complexity of attacks on 9-round \texttt{KMAC256} and 7-round \textsc{Ketje Sr} v1. Besides, practical attacks on 6-round \textsc{Ketje Sr} v1 and v2 are also given in this paper for the first time.

S-boxes, typically the only nonlinear part of a block cipher, are the heart of symmetric cryptographic primitives. They significantly impact the cryptographic strength and the implementation characteristics of an algorithm. Due to their simplicity, quadratic vectorial Boolean functions are preferred when efficient implementations for a variety of applications are of concern. Many characteristics of a function stay invariant under affine equivalence. So far, all 6-bit Boolean functions, 3- and 4-bit permutations have been classified up to affine equivalence. At FSE 2017, Bozoliv et al. presented the first classification of 5-bit quadratic permutations. In this work, we propose an adaptation of their work resulting in a highly efficient algorithm to classify $n \times m$ functions for $n \geq m$. Our algorithm enables for the first time a complete classification of 6-bit quadratic permutations as well as all balanced quadratic functions for $n \leq 6$. These functions can be valuable for new cryptographic algorithm designs with efficient multi-party computation or side-channel analysis resistance as goal. In addition, we provide a second tool for finding decompositions of length two. We demonstrate its use by decomposing existing higher degree S-boxes and constructing new S-boxes with good cryptographic and implementation properties.