Blog blog Explaining X where X = Montgomery form for efficient multiprecision multiplication arithmetic. modular-arithmetic Prerequisites are the following Residue class of modulo N is all \(a\) that satisfy \(a + kN\) where N is a constant and \(k \in \mathbb{Z}\). Montgomery multiplication is a method for performing fast modular multiplication. The algorithm uses the Montgomery forms of \(a\) and \(b\) to efficiently compute the Montgomery form of \(ab \mod N\).