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
-
Dual attacks in code-based (and lattice-based) cryptography
Speaker : Charles Meyer-Hilfiger - Inria Rennes
The hardness of the decoding problem and its generalization, the learning with errors problem, are respectively at the heart of the security of the Post-Quantum code-based scheme HQC and the lattice-based scheme Kyber. Both schemes are to be/now NIST standards. These problems have been actively studied for decades, and the complexity of the state-of-the-art algorithms to solve them is crucially[…]-
Cryptography
-
-
Design of fast AES-based Universal Hash Functions and MACs
Speaker : Augustin Bariant - ANSSI
Ultra-fast AES round-based software cryptographic authentication/encryption primitives have recently seen important developments, fuelled by the authenticated encryption competition CAESAR and the prospect of future high-profile applications such as post-5G telecommunication technology security standards. In particular, Universal Hash Functions (UHF) are crucial primitives used as core components[…]-
Cryptography
-
-
Lie algebras and the security of cryptosystems based on classical varieties in disguise
Speaker : Mingjie Chen - KU Leuven
In 2006, de Graaf et al. proposed a strategy based on Lie algebras for finding a linear transformation in the projective linear group that connects two linearly equivalent projective varieties defined over the rational numbers. Their method succeeds for several families of “classical” varieties, such as Veronese varieties, which are known to have large automorphism groups. In this talk, we[…]-
Cryptography
-
-
Some applications of linear programming to Dilithium
Speaker : Paco AZEVEDO OLIVEIRA - Thales & UVSQ
Dilithium is a signature algorithm, considered post-quantum, and recently standardized under the name ML-DSA by NIST. Due to its security and performance, it is recommended in most use cases. During this presentation, I will outline the main ideas behind two studies, conducted in collaboration with Andersson Calle-Vierra, Benoît Cogliati, and Louis Goubin, which provide a better understanding of[…]