Abstract: A system, method and computer-readable medium provide secure communication between a first and a second computer system based on supersingular isogeny elliptic curve cryptography. The first computer system and the second computer system each determine kernels KA and KB including computing mP+nQ by accessing a lookup table stored in a memory that contains a range of doubles of an end point of the respective kernels, where P and Q are points on the public elliptic curve and m and n are integers. The first computer system and the second computer system compute secret isogenies by determining a respective kernel KBA and KAB using mixed-base multiplicands with a single inversion, including computing the respective kernel KBA and KAB by converting the multiplicands to base 32, and computing scalar multiplications using the base 32 multiplicands.

Abstract: A system, method and computer-readable medium provide secure communication between a first and a second computer system based on supersingular isogeny elliptic curve cryptography. The first computer system and the second computer system each determine kernels KA and KB including computing mP+nQ by accessing a lookup table stored in a memory that contains a range of doubles of an end point of the respective kernels, where P and Q are points on the public elliptic curve and m and n are integers. The first computer system and the second computer system compute secret isogenies by determining a respective kernel KBA and KAB using mixed-base multiplicands with a single inversion, including computing the respective kernel KBA and KAB by converting the multiplicands to base 32, and computing scalar multiplications using the base 32 multiplicands.