Hidden Structures and Quantum Cryptanalysis

Xavier Bonnetain

Published Nov 15, 2019• 1 citation

Abstract

In this thesis, we study the security of cryptographic systems against an adversary who has access to a quantum computer. In quantum computing, we studied the hidden period and hidden shift problems, which are among the few known problems that have some applications in cryptogaphy and for which the best known quantum algorithm is more than polynomially faster than the best known classical algorithm. We proposed some improvements, new tradeoffs between classical and quantum time and memory, and extended their scope of applications to cases where only a classical oracle is available. In cryptanalysis, in symmetric cryptography, we proposed some attacks against symmetric constructions based on hidden shifts, and generalized many attacks using hidden periods to cases where the construction is only accessible classically. We proposed a quantum cryptanalysis of the different versions of the authenticated cipher AEZ and some quantum versions of multiple slide attacks, which are a classical family of cryptanalyses. This rewriting of attacks in the formalism of hidden periods has allowed us to propose a new classical attack against multiple variants of the cipher MiMC. In asymmetric cryptography, we proposed a concrete and asymptotic quantum security analysis of some isogeny-based key exchanges. Finally, we studied quantum security in some cases where these hidden structure problems do not apply, with in particular the first quantum security analysis of AES, the most used symmetric cipher to date.

DOI: 10.70675/376c5157z8acez485dzab89z9e1bfa697ee9

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