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Theses

Supersingular Group Actions and Post-quantum Key Exchange

Mathilde Chenu 1
1 GRACE - Geometry, arithmetic, algorithms, codes and encryption
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : Alice and Bob want to exchange information and make sure that an eavesdropper will not be able to listen to them, even with a quantum computer. To that aim they use cryptography and in particular a key-exchange protocol. These type of protocols rely on number theory and algebraic geometry. However current protocols are not quantum resistant, which is the reason why new cryptographic tools must be developed. One of these tools rely on isogenies, i.e. homomorphisms between elliptic curves. In this thesis the first contribution is an implementation of an isogeny-based key-exchange protocol resistant against side-channel attacks (timing and power consumption analysis, fault injection). We also generalize this protocol to a larger set of elliptic curves.
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Submitted on : Wednesday, January 5, 2022 - 3:02:15 PM
Last modification on : Friday, January 21, 2022 - 3:13:24 AM
Long-term archiving on: : Wednesday, April 6, 2022 - 6:21:13 PM

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  • HAL Id : tel-03508143, version 1

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Mathilde Chenu. Supersingular Group Actions and Post-quantum Key Exchange. Cryptography and Security [cs.CR]. Ecole Polytechnique, 2021. English. ⟨tel-03508143⟩

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