Factorization with genus 2 curves

Romain Cosset 1
1 CARAMEL - Cryptology, Arithmetic: Hardware and Software
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [10 references]  Display  Hide  Download

https://hal.inria.fr/inria-00384128
Contributor : Romain Cosset <>
Submitted on : Thursday, May 14, 2009 - 2:29:54 PM
Last modification on : Tuesday, December 18, 2018 - 4:18:25 PM
Long-term archiving on : Monday, October 15, 2012 - 10:25:45 AM

File

cosset.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Romain Cosset. Factorization with genus 2 curves. Mathematics of Computation / Mathematics of Computation, American Mathematical Society, 2010, 79, pp.1191-1208. ⟨10.1090/S0025-5718-09-02295-9⟩. ⟨inria-00384128⟩

Share

Metrics

Record views

454

Files downloads

251