New multiplier design based on squared law algorithms and table look-ups

A multiplier design based on look-up tables and squared law algorithms is presented. This multiplier can compute the full precision product of two integer numbers or their product modulo 2^N, modulo 2^N-1, or modulo 2^N+1. The design is based on decomposing the two numbers into smaller sizes, performing the cyclic convolution on these smaller numbers, and then finally reconstructing the desired product. The algorithms use no multiplications and instead rely only on squaring operations, additions, and subtractions. A comparative analysis of ROM requirements and hardware complexities for performing the multiplication operation using various look-up techniques is presented