This paper concerns efficient arithmetic modulo a Mersenne number, an integer of the form 2M − 1. These numbers, and a larger family of numbers called general- ized Mersenne numbers [51], [17], [1], have found many arithmetic applications ranging from number theoretic trans- forms [12] to cryptography.
This paper describes carry-less arithmetic operations modulo an integer 2^M-1 in the thousand-bit range, targeted at single instruction multiple data ...
This paper describes carry-less arithmetic operations modulo an integer 2^M-1 in the thousand-bit range, targeted at single instruction multiple data ...
This paper describes carry-less arithmetic operations modulo an integer 2^M-1 in the thousand-bit range, targeted at single instruction multiple data ...
This paper describes carry-less arithmetic operations modulo an integer 2^M − 1 in the thousand-bit range, targeted at single instruction multiple data ...
Efficient SIMD Arithmetic Modulo a Mersenne Number by Joppe W. Bos, Thorsten Kleinjung, Arjen K. Lenstra, Peter L. Montgomery.
Joppe W. Bos, Thorsten Kleinjung, Arjen K. Lenstra, Peter L. Montgomery: Efficient SIMD Arithmetic Modulo a Mersenne Number.
Jan 5, 2018 · There was some discussion about how multiplication and division are particularly efficient in binary modular arithmetic modulo a Mersenne prime 2 n –1.
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The task of the reduction is to reduce the product modulo p to an m-bit integer which again has a (κ, η, ν)-representation. We provide two reduction algorithms ...
Efficient SIMD Arithmetic Modulo a Mersenne Number pp. 213-221. Automatic Generation of Code for the Evaluation of Constant Expressions at Any Precision with�...