[Resource Topic] 2018/882: Pre- and post-quantum Diffie--Hellman from groups, actions, and isogenies

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

Authors: Benjamin Smith


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.

ePrint: https://eprint.iacr.org/2018/882

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