Hardware Architecture for Supersingular Isogeny Diffie-Hellman and Key Encapsulation Using a Fast Montgomery Multiplier

Public key cryptography lies among the most important bases of security protocols. The classic instances of these cryptosystems are no longer secure when a large-scale quantum computer emerges. These cryptosystems must be replaced by post-quantum ones, such as isogeny-based cryptographic schemes. Supersingular isogeny Diffie-Hellman (SIDH) and key encapsulation (SIKE) are two of the most important such schemes. To improve the performance of these protocols, we have designed several modular multipliers. These multipliers have been implemented for all the prime fields used in SIKE round 3, on a Virtex-7 FPGA, showing a time and area-time product improvement of up to 60.1% and 64.5%, respectively. These multipliers are also suitable for applications such as RSA, as shown by implementations for 512-bit, 1024-bit, and 2048-bit generic moduli on a Virtex-7 FPGA. Our fastest multiplier has been used in the implementation of SIDH and SIKE round 3. Employing six instances of this multiplier, SIDH completes after 7.33, 8.93, 13.39, and 18.67 milliseconds and the encapsulation and the decapsulation of SIKE is performed in 7.13, 8.68, 13.08, and 18.16 milliseconds over p(434), p(503), p(610), p(751), respectively, which yields a least improvement factor of 1.23.