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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: 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.

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