Pre- and post-quantum Diffie-Hellman from groups, actions, and isogenies release_3cs76dmgvbebpfgcrcgdgevba4

by Benjamin Smith

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2018  

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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Date   2018-09-13
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arXiv  1809.04803v1
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