Factorization with genus 2 curves

Author:
Romain Cosset

Journal:
Math. Comp. **79** (2010), 1191-1208

MSC (2000):
Primary 11Y05; Secondary 11Y16, 11Y40

DOI:
https://doi.org/10.1090/S0025-5718-09-02295-9

Published electronically:
August 20, 2009

MathSciNet review:
2600562

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Abstract | References | Similar Articles | Additional Information

Abstract: The elliptic curve method (ECM) is one of the best factorization methods available. It is possible to use hyperelliptic curves instead of elliptic curves but it is in theory slower. We use special hyperelliptic curves and Kummer surfaces to reduce the complexity of the algorithm. Our implementation GMP-HECM is faster than GMP-ECM for factoring large numbers.

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Additional Information

**Romain Cosset**

Affiliation:
LORIA, Campus Scientifique - BP 239, 54506 Vandoeuvre-lès-Nancy, France

Email:
romain.cosset@loria.fr

DOI:
https://doi.org/10.1090/S0025-5718-09-02295-9

Received by editor(s):
February 10, 2009

Received by editor(s) in revised form:
April 4, 2009

Published electronically:
August 20, 2009

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.