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Paper 2014/921

Batch NFS

Daniel J. Bernstein and Tanja Lange

Abstract

This paper shows, assuming standard heuristics regarding the number-field sieve, that a "batch NFS" circuit of area L^{1.181...+o(1)} factors L^{0.5+o(1)} separate B-bit RSA keys in time L^{1.022...+o(1)}. Here L=exp((log 2^B)^{1/3}(log log 2^B)^{2/3}). The circuit's area-time product (price-performance ratio) is just L^{1.704...+o(1)} per key. For comparison, the best area-time product known for a single key is L^{1.976...+o(1)}. This paper also introduces new "early-abort" heuristics implying that "early-abort ECM" improves the performance of batch NFS by a superpolynomial factor, specifically exp((c+o(1))(log 2^B)^{1/6}(log log 2^B)^{5/6}) where c is a positive constant.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Published elsewhere. Minor revision. SAC 2014
Keywords
integer factorizationnumber-field sieveprice-performance ratiobatchingsmooth numberselliptic curvesearly aborts
Contact author(s)
authorcontact-batchnfs @ box cr yp to
History
2014-11-10: received
Short URL
https://ia.cr/2014/921
License
Creative Commons Attribution
CC BY
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