Description
Finding a short non zero vector in an Euclidean lattice is a well-studied problem which has proven useful to construct many cryptographic primitives. The current best asymptotic algorithm to find a relatively short vector in an arbitrary lattice is the BKZ algorithm. This algorithm recovers a vector which is at most $2^{n^{\alpha}}$ times larger than the shortest non zero vector in time $2^{n^{1-\alpha}}$ for any $\alpha$ between 0 and 1.<br/> In order to gain in efficiency, it is sometimes interesting to use structured lattices instead of general lattices. An example of such structured lattices are ideal lattices. One may then wonder whether, on the security front, it is easier to find short vectors in a structured lattice or not. Until 2016, there was no known algorithm which would perform better on ideal lattices than the BKZ algorithm (either classically or quantumly). In 2016 and 2017, Cramer-Ducas-Peikert-Regev and Cramer-Ducas-Wesolowski proposed a quantum algorithm that finds a $2^{\sqrt n}$ approximation of the shortest non zero vector in polynomial time. However, the BKZ algorithm remained the best algorithm in the classical setting or for approximation factor smaller than $2^{\sqrt n}$ in the quantum setting.<br/> In this talk, I will present an algorithm that extends the one of Cramer et al. and improves upon the BKZ algorithm for ideal lattices, both quantumly and classically. This algorithm is heuristic and non uniform (i.e., it requires an exponential time pre-processing).<br/> lien: http://desktop.visio.renater.fr/scopia?ID=723420***3028&autojoin
Prochains exposés
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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[…] -
Attacks and Remedies for Randomness in AI: Cryptanalysis of PHILOX and THREEFRY
Orateur : Yevhen Perehuda - Ruhr-University Bochum
In this work, we address the critical yet understudied question of the security of the most widely deployed pseudorandom number generators (PRNGs) in AI applications. We show that these generators are vulnerable to practical and low-cost attacks. With this in mind, we conduct an extensive survey of randomness usage in current applications to understand the efficiency requirements imposed in[…]-
Cryptography
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Lightweight (AND, XOR) Implementations of Large-Degree S-boxes
Orateur : Marie Bolzer - LORIA
The problem of finding a minimal circuit to implement a given function is one of the oldest in electronics. In cryptography, the focus is on small functions, especially on S-boxes which are classically the only non-linear functions in iterated block ciphers. In this work, we propose new ad-hoc automatic tools to look for lightweight implementations of non-linear functions on up to 5 variables for[…]-
Cryptography
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Symmetrical primitive
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Implementation of cryptographic algorithm
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Algorithms for post-quantum commutative group actions
Orateur : Marc Houben - Inria Bordeaux
At the historical foundation of isogeny-based cryptography lies a scheme known as CRS; a key exchange protocol based on class group actions on elliptic curves. Along with more efficient variants, such as CSIDH, this framework has emerged as a powerful building block for the construction of advanced post-quantum cryptographic primitives. Unfortunately, all protocols in this line of work are[…] -
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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