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Algorithmic of curves in the context of bilinear and post-quantum cryptography

Simon Masson 1, 2
1 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms
LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry, Inria Nancy - Grand Est
Abstract : This thesis studies the algorithmic of several cryptographic applications related to elliptic curves and isogenies of elliptic curves. On the one hand, we study the tradeoff between efficiency and security in pairing-based cryptography at the 128-bit security level. The threat of the recent improvements on the discrete logarithm computation over specific finite fields lead us to study new pairing-friendly curves. We give a comparison of efficiency between our new curves and the state-of-the-art curves by estimating the measurement in practice. On the other and, we present isogeny-based cryptography, considered to be post-quantum resistant. We look at a concrete implementation of cryptanalysis based on connecting ideals between maximal orders of quaternion algebras. Finally, we present two constructions of verifiable delay functions based on computations of pairings and isogenies of large smooth degree. These functions are not considered to be post-quantum resistant, but bring several new properties compared to the current constructions. We analyse their security and give a comparison of all the known functions at the 128-bit security level.
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Submitted on : Thursday, December 10, 2020 - 4:11:43 PM
Last modification on : Tuesday, February 2, 2021 - 12:35:10 PM
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  • HAL Id : tel-03052499, version 1

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Simon Masson. Algorithmic of curves in the context of bilinear and post-quantum cryptography. Cryptography and Security [cs.CR]. Université de Lorraine, 2020. English. ⟨NNT : 2020LORR0151⟩. ⟨tel-03052499⟩

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