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