Extended NIST Prime Family for Efficient Modular Reduction

Abstract

The FIPS 186-2 standard recommends five prime fields with a modulus so-called NIST primes for elliptic curve cryptosystems. Primes of the special form such as NIST primes have a property yields modular reduction algorithms that are significantly fast. However the number of NIST primes are not large enough. In this paper, we further extend the idea of NIST primes. Then we find more primes can provide fast modular reduction computation that NIST prime family does not support. Our method provides more efficient modular arithmetic than Montgomery algorithm in prime fields that NIST primes does not support.