Fast algorithm for modular reduction

Abstract

The paper presents an algorithm for computing the residue R = X mod M. The algorithm is based on a sign estimation technique that estimates the sign of a number represented by a carry-sum pair produced by a carry save adder. Given the (n + k)-bit X and the n-bit M, the modular reduction algorithm computes the n-bit residue R in O(k + log n) time, and is particularly useful when the operand size is large. We also present a variant of the algorithm that performs modular multiplication by interleaving the shift-and-add and the modular reduction steps. The modular multiplication algorithm can be used to obtain efficient VLSI implementations of exponentiation cryptosystems.