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Efficient SIMD Arithmetic modulo a Mersenne Number

Joppe W. Bos, Thorsten Kleinjung, Arjen K. Lenstra, and Peter L. Montgomery


This paper describes carry-less arithmetic operations modulo an integer 2M-1 in the thousand-bit range, targeted at single instruction multiple data platforms and applications where overall throughput is the main performance criterion. Using an implementation on a cluster of PlayStation 3 game consoles a new record was set for the elliptic curve method for integer factorization.


Publication typeInproceedings
Published inIEEE Symposium on Computer Arithmetic – ARITH-20
PublisherIEEE Computer Society
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