High Performance Modular Multiplication for SIDH

Abstract

The latest research indicates that quantum computers will be realized in the near future. In theory, the computation speed of a quantum computer is much faster than current computers, which will pose a serious threat to current cryptosystems. Post-quantum cryptography (PQC) is a class of cryptography based on underlying mathematical problems that are considered infeasible to crack even with access to a quantum computer. The supersingular isogeny Diffie–Hellman (SIDH) key exchange protocol is a new post-quantum cryptosystem, which offers advantages in reduced secret key length and attack resistance. SIDH is the basis of the supersingular isogeny key encapsulation (SIKE) protocol, which is in the second round of the U.S. National Institute of Standards and Technology (NIST) PQC standardization process. In this article, we propose a new modular multiplication algorithm and a new interleaved hardware architecture for SIDH. Performance results for the proposed modular multiplier using four parameter sets for the prime, $p$ that correspond to the SIKE Round 2 parameter sets show significant advantages in speed.