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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. [1] [2]
Peter Lawrence Montgomery (September 25, 1947 – February 18, 2020) was an American mathematician who worked at the System Development Corporation and Microsoft Research.He is best known for his contributions to computational number theory and mathematical aspects of cryptography, including the Montgomery multiplication method for arithmetic in finite fields, the use of Montgomery curves in ...
A similar algorithm for multiplication by doubling exists. This specific implementation of Montgomery's ladder is not yet protected against cache timing attacks: memory access latencies might still be observable to an attacker, as different variables are accessed depending on the value of bits of the secret exponent. Modern cryptographic ...
Algorithms, such as Montgomery reduction, also exist to allow simple arithmetic operations, such as multiplication and exponentiation modulo m, to be performed efficiently on large numbers. Some operations, like finding a discrete logarithm or a quadratic congruence appear to be as hard as integer factorization and thus are a starting point for ...
Koç's studies on Montgomery multiplication methods contributed to the development of high-speed and efficient algorithms. He explored Montgomery multiplication methods, examining operations and presenting high-speed, space-efficient algorithms for computing MonPro(a, b), analyzing their time and space requirements, and introducing new ...
However, Montgomery multiplication requires a conversion to and from Montgomery domain which means it is expensive when a few modular multiplications are needed. To perform Barrett multiplication with non-constant operands, one can set a {\displaystyle a} as the product of the operands and set b {\displaystyle b} to 1 {\displaystyle 1} .
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