A fast modular multiplication algorithm for calculating the product AB modulo N

In this paper, we propose a fast iterative modular multiplication algorithm for calculating the product AB modulo N , where N is a large modulus in number-theoretic cryptosystems, such as RSA cryptosystems. Our algorithm requires ( 3 − 1 4k ) nk + 5 3 4 k − 3 2k − 17 6 additions on average for an n-bit modulus if k carry bits are dealt with in each loop. For a 512-bit modulus, the known fastest modular multiplication algorithm, Chen and Liu’s algorithm, requires 517 additions on average. However, compared to Chen and Liu’s algorithm, our algorithm reduces the number of additions by 26% for a 512-bit modulus.  1999 Elsevier Science B.V. All rights reserved.