In modular arithmetic computation, Montgomery modular multiplication, more commonly referred to as Montgomery multiplication, is a method for performing fast modular multiplication. It was introduced in 1985 by the American mathematician Peter L. Montgomery. Montgomery modular multiplication relies … See more Let N denote a positive integer modulus. The quotient ring Z/NZ consists of residue classes modulo N, that is, its elements are sets of the form $${\displaystyle \{a+kN\colon k\in \mathbf {Z} \},}$$ See more Many operations of interest modulo N can be expressed equally well in Montgomery form. Addition, subtraction, negation, comparison for … See more Because Montgomery reduction avoids the correction steps required in conventional division when quotient digit estimates are … See more If a and b are integers in the range [0, N − 1], then their sum is in the range [0, 2N − 2] and their difference is in the range [−N + 1, N − 1], so … See more While the above algorithm is correct, it is slower than multiplication in the standard representation because of the need to multiply by R′ and … See more Most cryptographic applications require numbers that are hundreds or even thousands of bits long. Such numbers are too large to be stored in a single machine word. Typically, the … See more • Barrett reduction See more WebJan 1, 2002 · The upper limit on the precision of the scalable and unified Montgomery multiplier is dictated only by the available memory to store the operands and internal …
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