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:
“This is no argument against teaching manners to the young. On the contrary, it is a fine old tradition that ought to be resurrected from its current mothballs and put to work...In fact, children are much more comfortable when they know the guide rules for handling the social amenities. It’s no more fun for a child to be introduced to a strange adult and have no idea what to say or do than it is for a grownup to go to a formal dinner and have no idea what fork to use.”
—Leontine Young (20th century)
“The most distinct and beautiful statement of any truth must take at last the mathematical form.”
—Henry David Thoreau (1817–1862)