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
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