Efficient finite field multiplication for isogeny based post quantum cryptography

Abstract

Isogeny based post-quantum cryptography is one of the most recent addition to the family of quantum resistant cryptosystems. In this paper we propose an efficient modular multiplication algorithm for primes of the form p =2· 2a3b − 1withb even, typically used in such cryptosystem. Our modular multiplication algorithm exploits the special structure present in such primes. We compare the efficiency of our technique with Barrett reduction and Montgomery multiplication. Our C implementation shows that our algorithm is approximately 3 times faster than the normal Barrett reduction.