An $L (1/3)$ Discrete Logarithm Algorithm for Low Degree Curves
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ENGE, Andreas | |
| hal.structure.identifier | Cryptology, Arithmetic: Hardware and Software [CARAMEL] | |
| dc.contributor.author | GAUDRY, Pierrick | |
| hal.structure.identifier | Cryptology, Arithmetic: Hardware and Software [CARAMEL] | |
| dc.contributor.author | THOMÉ, Emmanuel | |
| dc.date.accessioned | 2024-04-04T02:30:30Z | |
| dc.date.available | 2024-04-04T02:30:30Z | |
| dc.date.created | 2009 | |
| dc.date.issued | 2011 | |
| dc.identifier.issn | 0933-2790 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190249 | |
| dc.description.abstractEn | We present an algorithm for solving the discrete logarithm problem in Jacobians of families of plane curves whose degrees in $X$ and $Y$ are low with respect to their genera. The finite base fields $\FF_q$ are arbitrary, but their sizes should not grow too fast compared to the genus. For such families, the group structure and discrete logarithms can be computed in subexponential time of $L_{q^g}(1/3, O(1))$. The runtime bounds rely on heuristics similar to the ones used in the number field sieve or the function field sieve. | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.subject.en | discrete logarithm | |
| dc.subject.en | algebraic curve | |
| dc.subject.en | subexponentiality | |
| dc.subject.en | function field sieve | |
| dc.title.en | An $L (1/3)$ Discrete Logarithm Algorithm for Low Degree Curves | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s00145-010-9057-y | |
| dc.subject.hal | Informatique [cs]/Cryptographie et sécurité [cs.CR] | |
| dc.subject.hal | Mathématiques [math]/Géométrie algébrique [math.AG] | |
| dc.identifier.arxiv | 0905.2177 | |
| bordeaux.journal | Journal of Cryptology | |
| bordeaux.page | 24-41 | |
| bordeaux.volume | 24 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | inria-00383941 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//inria-00383941v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Cryptology&rft.date=2011&rft.volume=24&rft.spage=24-41&rft.epage=24-41&rft.eissn=0933-2790&rft.issn=0933-2790&rft.au=ENGE,%20Andreas&GAUDRY,%20Pierrick&THOM%C3%89,%20Emmanuel&rft.genre=article |
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