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Conference Papers Year : 2018

Pre- and post-quantum Diffie-Hellman from groups, actions, and isogenies

Abstract

Diffie-Hellman key exchange is at the foundations of public-key cryptography, but conventional group-based Diffie-Hellman is vulnerable to Shor's quantum algorithm. A range of "post-quantum Diffie-Hellman" protocols have been proposed to mitigate this threat, including the Couveignes, Rostovtsev-Stolbunov, SIDH, and CSIDH schemes, all based on the combinatorial and number-theoretic structures formed by isogenies of elliptic curves. Pre-and post-quantum Diffie-Hellman schemes resemble each other at the highest level, but the further down we dive, the more differences emerge-differences that are critical when we use Diffie-Hellman as a basic component in more complicated constructions. In this survey we compare and contrast pre-and post-quantum Diffie-Hellman algorithms, highlighting some important subtleties.
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Dates and versions

hal-01872825 , version 1 (12-09-2018)
hal-01872825 , version 2 (19-09-2018)
hal-01872825 , version 3 (13-12-2019)

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Cite

Benjamin Smith. Pre- and post-quantum Diffie-Hellman from groups, actions, and isogenies. Arithmetic of Finite Fields - WAIFI 2018, Jun 2018, Bergen, Norway. pp.36, ⟨10.1007/978-3-030-05153-2_1⟩. ⟨hal-01872825v3⟩
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