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On the Hardness of the Finite Field Isomorphism Problem

by Antoine Joux - 24.01.2023

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The finite field isomorphism FFI problem was introduced in PKC’18 as an alternative to average-case lattice problems (like LWE, SIS, or NTRU). As an application, it has been used to construct a fully homomorphic encryption scheme and a signature scheme.

In this talk, we explain how the decision variant of the FFI problem can be solved in polynomial time for most finite fields. We first recall the necessary background on the theory of finite fields before applying it to construct a FFI distinguisher and a polynomial-time attack on the semantic security of the fully homomorphic encryption scheme.

The speaker

Previously an engineer at DGA, then deputy scientific director at DCSSI (now ANSSI), part-time professor at the University of Versailles - Saint-Quentin-en-Yvelines and holder of the Cryptology chair at Sorbonne University Foundation, Antoine Joux is currently a permanent researcher at the CISPA Helmholtz Center for Cybersecurity in Saarbrücken, Germany and an honorary professor at the University of Saarbrücken.

His specialty is cryptography, and many of his works focus on cryptanalysis, that is, the study of vulnerabilities in cryptographic systems. Co-laureate of the Gödel Prize in 2013 and Fellow of the IACR (International Association for Cryptologic Research), he received an ERC Advanced Grant (Almacrypt) for the algorithmic study of mathematical problems whose supposed difficulty serves as the foundation for public key cryptography.

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