Curve41417: Karatsuba revisited

Abstract

This paper introduces constant-time ARM Cortex-A8 ECDH software that (1) is faster than the fastest ECDH option in the latest version of OpenSSL but (2) achieves a security level above 2200 using a prime above 2400. For comparison, this OpenSSL ECDH option is not constant-time and has a security level of only 280. The new speeds are achieved in a quite different way from typical prime-field ECC software: they rely on a synergy between Karatsuba’s method and choices of radix smaller than the CPU word size.