MULTIPLIER WITH LOOK UP TABLES

A method of performing modular multiplication of integers X and Y to produce a result R, where R=X.Y mod N, in a multiplication engine. X is fragmented into a first plurality of words xn each having a first predetermined number of bits, k and Y is fragmented into a second plurality of words yn each having a second predetermined number of bits, m. Multiples of a word xn of X are derived in a pre calculation circuit and subsequently used to derive products of the word xn of X with each of the plurality of words yn of Y. An intermediate result Rjis calculated as a cumulating sum derived from said pre-calculated multiples and the steps repeated for each successive word of X so as to generate successive intermediate results, Rj, for each of the first plurality of words xn. The final result, R is obtained from the last of the intermediate results Rn-1.