Paper 2017/437 Original: eprint.iacr.org/2017/437 ↗

Slothful reduction

Abstract

In the implementation of many public key schemes, there is a need to implement modular arithmetic. Typically this consists of addition, subtraction, multiplication and (occasionally) division with respect to a prime modulus. To resist certain side-channel attacks it helps if implementations are ``constant time''. As the calculations proceed there is potentially a need to reduce the result of an operation to its remainder modulo the prime modulus. However often this reduction can be delayed, a process known as ``lazy reduction''. The idea is that results do not have to be fully reduced at each step, that full reduction takes place only occasionally, hence providing a performance benefit. Here we extend the idea to determine the circumstances under which reduction can be delayed to the very end of a particular public key operation.