Formal Statement
Let N be a positive integer, R and T be integers such that, and, and let be the multiplicative inverse modulo N of R. The Montgomery reduction of T modulo N with respect to R is defined as the value
A systematic interpretation of Montgomery reduction and the definition of Montgomery multiplication operation is based on the 2nd generalized division algorithm; see Euclidean division#Generalized_division_algorithms.
The algorithm used to calculate this reduction is much more efficient than the classical method of taking a product over the integers and reducing the result modulo N.
Read more about this topic: Montgomery Reduction
Famous quotes containing the words formal and/or statement:
“The bed is now as public as the dinner table and governed by the same rules of formal confrontation.”
—Angela Carter (1940–1992)
“The force of truth that a statement imparts, then, its prominence among the hordes of recorded observations that I may optionally apply to my own life, depends, in addition to the sense that it is argumentatively defensible, on the sense that someone like me, and someone I like, whose voice is audible and who is at least notionally in the same room with me, does or can possibly hold it to be compellingly true.”
—Nicholson Baker (b. 1957)