Montgomery reduction

Abstract

Montgomery Reduction To perform the Montgomery reduction of an input C modulo to a modulo N, particularly within the context of a Montgomery multiplication, includes: (i) performing a multiplication to obtain an approximate product Y based on a value D and the modulus N, in which only a significant part of the approximate product Y is computed and / or approximated using an incomplete execution of the multiplication, in which the value D is deduced from the input C and an auxiliary number N' of the Montgomery reduction, (ii) determining a sum by adding a word or part word of the input C to a word or part word of the approximate product Y, (iii) determining a carry-over in terms of the sum, and (iv) adding the carry-over to the input C or to a value deduced from the input C. Figure for the abstract: Fig. 5