You are given two numbers a and b. You need to find the multiplication of a and b under modulo M (M as 109+7). Example 1: Input: a = 92233720368547758 b = 92233720368547758 Output: 484266119 ...

Abstract: In this paper, we investigate statistical properties of modular multiplication modulo a power of two. In fact, we obtain the distribution of every single bit of modular multiplication.

We extend the work of Richard Crandall et al. to demonstrate how the Discrete Weighted Transform (DWT) can be applied to speed up multiplication modulo any number of ...

Abstract: We present faster algorithms for the residue multiplication modulo 521-bit Mersenne prime on 32- and 64-bit platforms by using Toeplitz matrix-vector product. The total arithmetic cost of ...