Description
The NTRU problem is an algorithmic problem over structured lattices that was introduced by Hoffstein, Pipher, and Silverman more than 20 years ago, and which has been used to construct various cryptographic primitives. However, its relation to other lattice problems is still not well understood.<br/> In this talk, we will describe different variants of the NTRU problem, and study how they compare to each other (and to other more classical lattice problems) in terms of reductions. More precisely, we will show that a search variant of the NTRU problem is at least as hard as the shortest vector problem (SVP) in ideal lattices; and that the decisional variant of NTRU is at least as hard as another search variant of NTRU. Unfortunately, the two search variants of NTRU that are considered in these reductions do not match, meaning that we cannot combine the reductions in order to obtain a reduction from the ideal shortest vector problem to the decisional NTRU problem. This is a joint work with Damien Stehlé.<br/> lien: https://univ-rennes1-fr.zoom.us/j/97066341266?pwd=RUthOFV5cm1uT0ZCQVh6QUcrb1drQT09
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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