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:
“Two clergymen disputing whether ordination would be valid without the imposition of both hands, the more formal one said, “Do you think the Holy Dove could fly down with only one wing?””
—Horace Walpole (1717–1797)
“He that writes to himself writes to an eternal public. That statement only is fit to be made public, which you have come at in attempting to satisfy your own curiosity.”
—Ralph Waldo Emerson (1803–1882)