A Simpler Sieving Device: Combining ECM and TWIRL

A Simpler Sieving Device: Combining ECM and TWIRL (2006)

Cached

Download Links

Other Repositories/Bibliography

DBLP

by Willi Geiselmann , Fabian Januszewski , Hubert Köpfer , Jan Pelzl , Rainer Steinwandt

Venue:	In Proceedings of ICISC 2006
Citations:	1 - 1 self

BibTeX

@INPROCEEDINGS{Geiselmann06asimpler,
    author = {Willi Geiselmann and Fabian Januszewski and Hubert Köpfer and Jan Pelzl and Rainer Steinwandt},
    title = {A Simpler Sieving Device: Combining ECM and TWIRL},
    booktitle = {In Proceedings of ICISC 2006},
    year = {2006},
    publisher = {Springer}
}

Bookmark

OpenURL

Abstract

A main obstacle in manufacturing the TWIRL device for realizing the sieving step of the Number Field Sieve is the sophisticated chip layout. Especially the logic for logging and recovering large prime factors found during sieving adds significantly to the layout complexity. We describe a device building on the Elliptic Curve Method (ECM) that for parameters of interest allows to replace the complete logging part in TWIRL by an o#-wafer postprocessing. The postprocessing is done in real time, leaving the total sieving time basically unchanged.

Citations

2057	Handbook of Applied Cryptography - Menezes, Oorschot, et al. - 1997
337	Modular multiplication without trial division - Montgomery - 1985
199	Factoring integers with elliptic curves - Lenstra - 1987
108	The development of the number field sieve - Lenstra, Lenstra - 1993
32	A tale of two sieves - Pomerance - 1996
28	Finding suitable curves for the elliptic curve method of factorization - Atkin, Morain - 1993
27	A scalable architecture for modular multiplication based on Montgomery’s algorithm - Tenca, Koç
17	Factorization of the tenth and eleventh Fermat numbers - Brent - 1997
12	Hardware for solving sparse systems of linear equations over GF(2), proc - Geiselmann, Steinwandt - 2003
8	Tromer, Analysis of Bernstein's factorization circuit - Lenstra, Shamir, et al. - 2002
6	Circuits for Integer Factorization: a Proposal. At the time of writing available electronically at http://cr.yp.to/papers/nfscircuit.pdf - Bernstein - 2001
6	Scalable Hardware for Sparse Systems of Linear Equations, with Applications to Integer Factorization - Geiselmann, Shamir, et al. - 2005
6	A Monte Carlo method for factorization, Nordisk Tidskr. Informationsbehandling (BIT - Pollard - 1975
4	Pelzl, Christine Priplata, Colin Stahlke, SHARK: A Realizable Special Hardware Sieving Device for Factoring 1024-Bit - Franke, Kleinjung, et al.
3	Improved RoutingBased Linear Algebra for the Number Field Sieve - Geiselmann, Köpfer, et al. - 2005
1	Atkin and François Morain. Finding suitable curves for the elliptic curve method of factorization - L - 1993
1	Geiselmann and Rainer Steinwandt. Hardware for Solving Sparse Systems of Linear Equations over GF(2 - Willi - 2003
1	Geiselmann and Rainer Steinwandt. Yet Another Sieving Device - Willi - 2004
1	Ein dedizierter Faktorisierungsalgorithmus auf Basis elliptischer Kurven, 2005. Diplomarbeit, Universität Karlsruhe (Germany), Fakultät für Informatik, Institut für Algorithmen und Kognitive Systeme - Januszewski
1	The RSA Challenge Numbers. http://www.rsasecurity.com/rsalabs/ node.asp?id=2093 - Laboratories
1	Shamir and Eran Tromer. Factoring Large Numbers with the TWIRL Device - Adi - 2003