Description
The correspondence between maximal orders in a quaternion algebra and supersingular elliptic curves has uncovered new perspectives in the field of isogeny-based cryptography. The KLPT algorithm of Kohel et al. in 2014 introduces an algorithm solving the quaternion isogeny path problem in polynomial time. Studying this problem has applications both constructive and destructive. It has allowed to reduce the problem of computing isogenies between two curves to the one of endomorphism ring computation. The GPS signature scheme from Galbraith et al. in 2017 was built on this algorithm.<br/> The main algorithm of KLPT solves the problem when the maximal order is special extremal. The paper also proposes a generalized version, but it produces an output with some very characteristic property that prevent from using it in some applications, like a generalization of the GPS signature. In this work, we propose a new method to generalize the algorithm. It produces a shorter solution with the same time complexity and without the problematic property.<br/> lien: https://e-learning.sviesolutions.com/pffi7slpuumw
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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