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 new statement will comprise the skepticisms, as well as the faiths of society, and out of unbeliefs a creed shall be formed. For, skepticisms are not gratuitous or lawless, but are limitations of the affirmative statement, and the new philosophy must take them in, and make affirmations outside of them, just as much as must include the oldest beliefs.”
—Ralph Waldo Emerson (1803–1882)