Classical and Quantum Generic Attacks on 6-round Feistel Schemes

In this paper, we describe new quantum generic attacks on 6 rounds balanced Feistel networks with internal functions or internal permutations. In order to obtain our new quantum attacks, we revisit a result of Childs and Eisenberg that extends Ambainis\u27 collision finding algorithm to the subset finding problem. In more details, we continue their work by carefully analyzing the time complexity of their algorithm. We also use four points structures attacks instead of two points structures attacks that leads to a complexity of $\mathcal{O}(2^{8n/5})$ instead of $\mathcal{O}(2^{2n})$. Moreover, we have also found a classical (i.e. non quantum) improved attack on $6$ rounds with internal permutations. The complexity here will be in $\mathcal{O}(2^{2n})$ instead of $\mathcal{O}(2^{3n})$ previously known

Extended Generalized Feistel Networks using Matrix Representation

International audienceWhile Generalized Feistel Networks have been widely studied in the literature as a building block of a block cipher, we propose in this paper a unified vision to easily represent them through a matrix representation. We then propose a new class of such schemes called Extended Generalized Feistel Networks well suited for cryptographic applications. We instantiate those proposals into two particular constructions and we finally analyze their security

Measuring Performances of a White-Box Approach in the IoT Context

The internet of things (IoT) refers to all the smart objects that are connected to other objects, devices or servers and that are able to collect and share data, in order to "learn" and improve their functionalities. Smart objects suffer from lack of memory and computational power, since they are usually lightweight. Moreover, their security is weakened by the fact that smart objects can be placed in unprotected environments, where adversaries are able to play with the symmetric-key algorithm used and the device on which the cryptographic operations are executed. In this paper, we focus on a family of white-box symmetric ciphers substitution-permutation network (SPN)box, extending and improving our previous paper on the topic presented at WIDECOM2019. We highlight the importance of white-box cryptography in the IoT context, but also the need to have a fast black-box implementation (server-side) of the cipher. We show that, modifying an internal layer of SPNbox, we are able to increase the key length and to improve the performance of the implementation. We measure these improvements (a) on 32/64-bit architectures and (b) in the IoT context by encrypting/decrypting 10,000 payloads of lightweight messaging protocol Message Queuing Telemetry Transport (MQTT)

Elastic Block Ciphers: Method, Security and Instantiations

We introduce the concept of an elastic block cipher which refers to stretching the supported block size of a block cipher to any length up to twice the original block size while incurring a computational workload that is proportional to the block size. Our method uses the round function of an existing block cipher as a black box and inserts it into a substitution- permutation network. Our method is designed to enable us to form a reduction between the elastic and the original versions of the cipher. Using this reduction, we prove that the elastic version of a cipher is secure against key-recovery attacks if the original cipher is secure against such attacks. We note that while reduction-based proofs of security are a cornerstone of cryptographic analysis, they are typical when complete components are used as sub-components in a larger design. We are not aware of the use of such techniques in the case of concrete block cipher designs. We demonstrate the general applicability of the elastic block cipher method by constructing examples from existing block ciphers: AES, Camellia, MISTY1, and RC6. We compare the performance of the elastic versions to that of the original versions and evaluate the elastic versions using statistical tests measuring the randomness of the ciphertext. We also use our examples to demonstrate the concept of a generic key schedule for block ciphers

Differential Attacks on Generalized Feistel Schemes

While generic attacks on classical Feistel schemes and unbalanced Feistel schemes have been studied a lot, generic attacks on several generalized Feistel schemes like type-1, type-2 and type-3 and Alternating Feistel schemes, as defined in~\cite{HR}, have not been systematically investigated. This is the aim of this paper. We give our best Known Plaintext Attacks and non-adaptive Chosen Plaintext Attacks on these schemes and we determine the maximum number of rounds that we can attack. It is interesting to have generic attacks since there are well known block cipher networks that use generalized Feistel schemes: CAST-256 (type-1), RC-6 (type-2), MARS (type-3) and BEAR/LION (alternating). Also, Type-1 and Type-2 Feistel schemes are respectively used in the construction of the hash functions $Lesamnta$ and $SHAvite-3_{512}$

Simplified MITM modeling for permutations: New (quantum) attacks

Meet-in-the-middle (MITM) is a general paradigm where internal states are computed along two independent paths (’forwards’ and ’backwards’) that are then matched. Over time, MITM attacks improved using more refined techniques and exploiting additional freedoms and structure, which makes it more involved to find and optimize such attacks. This has led to the use of detailed attack models for generic solvers to automatically search for improved attacks, notably a MILP model developed by Bao et al. at EUROCRYPT 2021. In this paper, we study a simpler MILP modeling combining a greatly reduced attack representation as input to the generic solver, together with a theoretical analysis that, for any solution, proves the existence and complexity of a detailed attack. This modeling allows to find both classical and quantum attacks on a broad class of cryptographic permutations. First, Present-like constructions, with the permutations from the Spongent hash functions: we improve the MITM step in distinguishers by up to 3 rounds. Second, AES-like designs: despite being much simpler than Bao et al.’s, our model allows to recover the best previous results. The only limitation is that we do not use degrees of freedom from the key schedule. Third, we show that the model can be extended to target more permutations, like Feistel networks. In this context we give new Guess-and-determine attacks on reduced Simpira v2 and Sparkle. Finally, using our model, we find several new quantum preimage and pseudo-preimage attacks (e.g. Haraka v2, Simpira v2 . . . ) targeting the same number of rounds as the classical attacks

4-point Attacks with Standard Deviation Analysis on A-Feistel Schemes

A usual way to construct block ciphers is to apply several rounds of a given structure. Many kinds of attacks are mounted against block ciphers. Among them, differential and linear attacks are widely used. In~\cite{V98,V03}, it is shown that ciphers that achieve perfect pairwise decorrelation are secure against linear and differential attacks. It is possible to obtain such schemes by introducing at least one random affine permutation as a round function in the design of the scheme. In this paper, we study attacks on schemes based on classical Feistel schemes where we introduce one or two affine permutations. Since these schemes resist against linear and differential attacks, we will study stronger attacks based on specific equations on 4-tuples of cleartext/ciphertext messages. We give the number of messages needed to distinguish a permutation produced by such schemes from a random permutation, depending on the number of rounds used in the schemes, the number and the position of the random affine permutations introduced in the schemes

NaSHA

We propose the NaSHA-(m, k, r) family of cryptographic hash functions, based on quasigroup transformations. We use huge quasigroups defined by extended Feistel networks from small bijections and a novel design principle: the quasigroup used in every iteration of the compression function is different and depends on the processed message block. We present in all details of the implementations of NaSHA-(m, 2, 6) where m in {224, 256, 384, 512}

Generic Attacks on Alternating Unbalanced Feistel Schemes

\begin{abstract} Generic attacks against classical (balanced) Feistel schemes, unbalanced Feistel schemes with contracting functions and unbalanced Feistel schemes with expanding functions have been studied in \cite {P01}, \cite{Jut}, \cite{PNB06}, \cite{PNB07}. In this paper we study schemes where we use alternatively contracting random functions and expanding random functions. We name these schemes ``Alternating Unbalanced Feistel Schemes\u27\u27. They allow constructing pseudo-random permutations from $kn$ bits to $kn$ bits where $k \geq 3$. At each round, we use either a random function from $n$ bits to $(k-1)n$ bits or a random function from $(k-1)n$ bits to $n$ bits. We describe the best generic attacks we have found. We present``known plaintext attacks\u27\u27 (KPA) and ``non-adaptive chosen plaintext attacks\u27\u27 (CPA-1). Let $d$ be the number of rounds. We show that if $d \leq k$, there are CPA-1 with 2 messages and KPA with $m$ the number of messages about $2^{\frac {(d-1)n}{4}}$. For $d \geq k+1$ we have to distinguish $k$ even and $k$ odd. For $k$ even, we have $m=2$ in CPA-1 and $m \simeq 2^{\frac {kn}{4}}$ in KPA. When $k$ is odd, we show that there exist CPA-1 for $d \leq 2k-1$ and KPA for $d \leq 2k+3$ with less than $2^{kn}$ messages and computations. Beyond these values, we give KPA against generators of permutations. \end{abstract

Generic Attacks on Misty Schemes -5 rounds is not enough-

Misty schemes are classic cryptographic schemes used to construct pseudo-random permutations from $2n$ bits to $2n$ bits by using $d$ pseudo-random permutations from $n$ bits to $n$ bits. These $d$ permutations will be called the ``internal\u27\u27 permutations, and $d$ is the number of rounds of the Misty scheme. Misty schemes are important from a practical point of view since for example, the Kasumi algorithm based on Misty schemes has been adopted as the standard blockcipher in the third generation mobile systems. In this paper we describe the best known ``generic\u27\u27 attacks on Misty schemes, i.e. attacks when the internal permutations do not have special properties, or are randomly chosen. We describe known plaintext attacks (KPA), non-adaptive chosen plaintext attacks (CPA-1) and adaptive chosen plaintext and ciphertext attacks (CPCA-2) against these schemes. Some of these attacks were previously known, some are new. One important result of this paper is that we will show that when $d=5$ rounds, there exist such attacks with a complexity strictly less than $2^{2n}$. Consequently, at least 6 rounds are necessary to avoid these generic attacks on Misty schemes. When $d \geq 6$ we also describe some attacks on Misty generators, i.e. attacks where more than one Misty permutation is required