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

Benjamin Smith

##### 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.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. MINOR revision.Proceedings of WAIFI 2018
Keywords
key exchangeelliptic-curve cryptographyisogeniespost-quantum cryptosystems
Contact author(s)
smith @ lix polytechnique fr
History
Short URL
https://ia.cr/2018/882

CC BY

BibTeX

@misc{cryptoeprint:2018/882,
author = {Benjamin Smith},
title = {Pre- and post-quantum Diffie--Hellman from groups, actions, and isogenies},
howpublished = {Cryptology ePrint Archive, Paper 2018/882},
year = {2018},
note = {\url{https://eprint.iacr.org/2018/882}},
url = {https://eprint.iacr.org/2018/882}
}

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