Chapter 6 - Modular Reduction

Abstract

Modular reduction arises quite often within public key cryptography algorithms and various number theoretic algorithms, such as factoring. Modular reduction algorithms are the third class of algorithms of the "multipliers" set. Modular reductions are normally used to create finite groups, rings, or fields. The most common usage for performance driven modular reductions is in modular exponentiation algorithms; that is, to compute d = ab(mod c) as fast as possible. This operation is used in the RSA and Diffie-Hellman public key algorithms. Modular multiplication and squaring also appears as a fundamental operation in elliptic curve cryptographic algorithms. Furthermore, the chapter explains the Barrett reduction; it was inspired by fast division algorithms that multiply by the reciprocal to emulate division.