FAST ALGORITHM FOR MODULAR REDUCTION

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 car ry save adder. Given the (n + k)-bit X and the n-bit M the modular red uction algorithm computes the n-bit residue R in O(k + log n) time, an d is particularly useful when the operand size is large. We also prese nt a variant of the algorithm that performs modular multiplication by interleaving the shift-and-add and the modular reduction steps. The mo dular multiplication algorithm can be used to obtain efficient VLSI im plementations of exponentiation cryptosystems.