## Cryptology ePrint Archive: Report 2020/1385

An Alternative Approach for SIDH Arithmetic

Cyril Bouvier and Laurent Imbert

Abstract: In this paper, we present new algorithms for the field arithmetic of supersingular isogeny Diffie-Hellman; one of the fifteen remaining candidates in the NIST post-quantum standardization process. Our approach uses a polynomial representation of the field elements together with mechanisms to keep the coefficients within bounds during the arithmetic operations. We present timings and comparisons for SIKEp503 and suggest a novel 736-bit prime that offers a $1.17\times$ speedup compared to SIKEp751 for a similar level of security.

Category / Keywords: public-key cryptography / Supersingular isogeny Diffie-Hellman, Polynomial Modular Number System, Efficient arithmetic