Description
I will report on some first attempts to do isogeny-based cryptography in genus 2. More precisely, we will use isogeny graphs of superspecial principally polarized abelian surfaces over GF(p^2) for constructing variants of Charles, Goren and Lauter's hash function and of Jao and De Feo's SIDH key exchange protocol, both of which use supersingular elliptic curves over GF(p^2). This will be largely based on joint work with Thomas Decru and Benjamin Smith.<br/> lien: http://desktop.visio.renater.fr/scopia?ID=722850***3761&autojoin
Next sessions
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Verification of Rust Cryptographic Implementations with Aeneas
Speaker : 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
Speaker : 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
Speaker : 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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