## Cryptology ePrint Archive: Report 2016/1046

Efficient Finite field multiplication for isogeny based post quantum cryptography

Angshuman karmakar and Sujoy Sinha Roy and Frederik Vercauteren and Ingrid Verbauwhede

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 $p = 2 \cdot 2^a \cdot 3^b - 1$ with b 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.

Category / Keywords: public-key cryptography /

Original Publication (with minor differences): International Workshop on the Arithmetic of Finite Fields-2016