January 8, 2002
Practical Aspects of Modern
Cryptography
Montgomery Multiplication
Let A, B, and M be n-block integers represented in
base x with 0
£ M < x n.
Let R = x n. GCD(R,M) = 1.
The Montgomery
Product of A and B modulo M is
the integer ABR–1 mod M.
Let M¢ = –M–1 mod R and
S = ABM¢ mod R.
Fact: (AB+SM)/R º ABR–1 (mod M).