The BMM symmetrising trace conjecture for the exceptional 2-reflection groups of rank 2

We prove the symmetrising trace conjecture of Brou\'e, Malle and Michel for the generic Hecke algebra associated to the exceptional irreducible complex reflection group $G_{13}$. Our result completes the proof of the conjecture for the exceptional 2-reflection groups of rank 2.Comment: 17 page

Zero-Sum Distinguishers for Iterated Permutations and Application to Keccak-f and Hamsi-256

International audienceThe zero-sum distinguishers introduced by Aumasson and Meier are investigated. First, the minimal size of a zero-sum is established. Then, we analyze the impacts of the linear and the nonlinear layers in an iterated permutation on the construction of zero-sum partitions. Finally, these techniques are applied to the Keccak-f permutation and to Hamsi-256. We exhibit several zero-sum partitions for 20 rounds (out of 24) of Keccak-f and some zero-sum partitions of size 2^{19} and 2^{10} for the finalization permutation in Hamsi-256

On the influence of the algebraic degree of F−1F^{−1} on the algebraic degree of G∘FG \circ F

We present a study on the algebraic degree of iterated permutations seen as multivari- ate polynomials. Our main result shows that this degree depends on the algebraic degree of the inverse of the permutation which is iterated. This result is also extended to non-injective balanced vectorial functions where the relevant quantity is the minimal degree of the inverse of a permutation expanding the function. This property has consequences in symmetric cryptography since several attacks or distinguishers exploit a low algebraic degree, like higher-order differential attacks, cube attacks and cube testers, or algebraic attacks. Here, we present some applications of this improved bound to a higher-degree variant of the block cipher KN , to the block cipher Rijndael-256 and to the inner permutations of the hash functions ECHO and JH

A zero-sum property for the KECCAK-f permutation with 18 rounds

International audienceA new type of distinguishing property, named the zero-sum property has been recently presented by Aumasson and Meier. It has been applied to the inner permutation of the hash function Keccak and it has led to a distinguishing property for the Keccak-f permutation up to 16 rounds, out of 24 in total. Here, we additionally exploit some spectral properties of the Keccak-f permutation and we improve the previously known upper bounds on the degree of the inverse permutation after a certain number of rounds. This result enables us to extend the zero-sum property to 18 rounds of the Keccak-f permutation, which was the number of rounds in the previous version of Keccak submitted to the SHA-3 competition

A General Proof Framework for Recent AES Distinguishers

In this paper, a new framework is developed for proving and adapting the recently proposed multiple-of-8 property and mixture-differential distinguishers. The above properties are formulated as immediate consequences of an equivalence relation on the input pairs, under which the difference at the output of the round function is invariant. This approach provides a further understanding of these newly developed distinguishers. For example, it clearly shows that the branch number of the linear layer does not influence the validity of the property, on the contrary of what was previously believed. We further provide an extension of the mixture-differential distinguishers and multiple-of-8 property to any SPN and to a larger class of subspaces. These adapted properties can then be exhibited in a systematic way for other ciphers than the AES. We illustrate this with the examples of Midori, Klein, LED and Skinny

Related-Key Differential Analysis of the AES

The Advanced Encryption Standard (AES) is considered to be the most important and widely deployed symmetric primitive. While the cipher was designed to be immune against differential and other classical attacks, this immunity does not hold in the related-key setting, and various related-key attacks have appeared over time. This work presents tools and algorithms to search for related-key distinguishers and attacks of differential nature against the AES. First, we propose two entirely different approaches to find optimal truncated differential characteristics and bounds on the minimum number of active S-boxes for all variants of the AES. In the first approach, we propose a simple MILP model that handles better linear inconsistencies with respect to the AES system of equations and that compares particularly well to previous tool-based approaches to solve this problem. The main advantage of this tool is that it can easily be used as the core algorithm to search for any attack on AES exploiting related-key differentials. Then, we design a fast and low-memory algorithm based on dynamic programming that has a very simple to understand complexity analysis and does not depend on any generic solver. This second algorithm provides us useful insight on the related-key differential search problem for AES and shows that the search space is not as big as one would expect. Finally, we build on the top of our MILP model a fully automated tool to search for the best differential MITM attacks against the AES. We apply our tool on AES-256 and find an attack on 13 rounds with only two related keys. This attack can be seen as the best known cryptanalysis against this variant if only 2 related keys are permitted

Side-channel Analysis of Gr{\o}stl and Skein

International audienceIn this work, a detailed study of two finalists of the SHA-3 competition from the side-channel analysis point of view is provided. For both functions when used as a MAC, this paper presents detected strategies for performing a power analysis. Besides the classical HMAC mode, two additionally proposed constructions, the envelope MAC for Grøstl and the Skein-MAC for Skein are analyzed. Consequently, examples of software countermeasures thwarting first-order DPA or CPA are given. For the validation of our choices, HMAC-Grøstl, HMAC-Skein as well as the countermeasures were implemented on a 32-bit ARM-based smart card, and power analysis attacks were mounted in practice on both unprotected and protected implementations. Finally, the performance difference between both versions is discussed

Differential analysis of the ternary hash function Troika

Troika is a sponge-based hash function designed by Kölbl, Tischhauser, Bogdanov and Derbez in 2019. Its specificity is that it is defined over $\mathbb{F}_3$ in order to be used inside IOTA’s distributed ledger but could also serve in all settings requiring the generation of ternary randomness. To be used in practice, Troika needs to be proven secure against state-of-the-art cryptanalysis. However, there are today almost no analysis tools for ternary designs. In this article we take a step in this direction by analyzing the propagation of differential trails of Troika and by providing bounds on the weight of its trails. For this, we adapt a well-known framework for trail search designed for KECCAK and provide new advanced techniques to handle the search on $\mathbb{F}_3$. Our work demonstrates that providing analysis tools for non-binary designs is a highly non-trivial research direction that needs to be enhanced in order to better understand the real security offered by such non-conventional primitives

Развитие компенсаторных механизмов у старших дошкольников с нарушением слуха в процессе подготовки их к школе

Выпускная квалифицированная работа посвящена проблеме развитию компенсаторных механизмов у детей старшего дошкольного возраста с нарушением слуха в процессе подготовке к школьному обучению. При проведении констатирующего и контрольного эксперимента были использованы методики: определение ведущих мотивов учения, “Дерево, “Назови фигуру”, “Цвета”, “Формы”, “Определи, какой предмет”, “Волшебный мешочек”. “Перенос позы”, которые направлены на выявление эмоционального фона воспитанников, а также на уровень компенсаторных функций (зрительная и тактильная). Коррекционная работа была проведена, как на индивидуальных, так и на фронтальных занятиях, задействованы ведущие компенсаторные анализаторы и в ведущей деятельности детей дошкольного возраста

Differential Equivalences on SBoxes

International audienc