Description
S-Boxes are essential objects in the conception of blockciphers. Typically, an S-Box is simply a permutation (bijective function) on n bits, with n small (usually 4 or 8). Its role in a blockcipher is to bring nonlinearity to the cipher, thus an S-Box must be highly nonlinear. Several parameters of a function are used to measure nonlinearity, among which the most important are differential uniformity and nonlinearity. Although we know a few permutations with good differential uniformity and nonlinearity any number of bits, implementing such S-Boxes has a high cost in general. Therefore, an important problem in symmetric cryptography is to find S-Boxes with good cryptographic parameters (differential uniformity, nonlinearity) with a low implementation cost (which implies a structure). In this presentation, we will address this problem by analyzing a few structures (Feistel, MISTY, Butterfly) which yield a low implementation cost while allowing for some cryptographically strong S-Boxes.
Prochains exposés
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Verification of Rust Cryptographic Implementations with Aeneas
Orateur : Aymeric Fromherz - Inria
From secure communications to online banking, cryptography is the cornerstone of most modern secure applications. Unfortunately, cryptographic design and implementation is notoriously error-prone, with a long history of design flaws, implementation bugs, and high-profile attacks. To address this issue, several projects proposed the use of formal verification techniques to statically ensure the[…] -
On the average hardness of SIVP for module lattices of fixed rank
Orateur : Radu Toma - Sorbonne Université
In joint work with Koen de Boer, Aurel Page, and Benjamin Wesolowski, we study the hardness of the approximate Shortest Independent Vectors Problem (SIVP) for random module lattices. We use here a natural notion of randomness as defined originally by Siegel through Haar measures. By proving a reduction, we show it is essentially as hard as the problem for arbitrary instances. While this was[…] -
Endomorphisms via Splittings
Orateur : Min-Yi Shen - No Affiliation
One of the fundamental hardness assumptions underlying isogeny-based cryptography is the problem of finding a non-trivial endomorphism of a given supersingular elliptic curve. In this talk, we show that the problem is related to the problem of finding a splitting of a principally polarised superspecial abelian surface. In particular, we provide formal security reductions and a proof-of-concept[…]-
Cryptography
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