Efficient SIMD Arithmetic Modulo a Mersenne Number

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

Computer Arithmetic（2011）

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摘要

This paper describes carry-less arithmetic operations modulo an integer 2^M-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.

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关键词

overall throughput,carry-less arithmetic operation,new record,mersenne number,multiple data platform,thousand-bit range,main performance criterion,integer factorization,efficient simd arithmetic modulo,single instruction,elliptic curve method,electronic countermeasures,single instruction multiple data,polynomials,elliptic curves,computer architecture,simd,singular value decomposition,pipelines,registers,parallel processing,public key cryptography

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