An $L (1/3 + \varepsilon)$ Algorithm for the Discrete Logarithm Problem for Low Degree Curves
| hal.structure.identifier | Algorithmic number theory for cryptology [TANC] | |
| dc.contributor.author | ENGE, Andreas | |
| hal.structure.identifier | Curves, Algebra, Computer Arithmetic, and so On [CACAO] | |
| dc.contributor.author | GAUDRY, Pierrick | |
| dc.contributor.editor | Moni Naor | |
| dc.date.issued | 2007 | |
| dc.date.conference | 2007-05-20 | |
| dc.description.abstractEn | The discrete logarithm problem in Jacobians of curves of high genus $g$ over finite fields $\FF_q$ is known to be computable with subexponential complexity $L_{q^g}(1/2, O(1))$. We present an algorithm for a family of plane curves whose degrees in $X$ and $Y$ are low with respect to the curve genus, and suitably unbalanced. The finite base fields are arbitrary, but their sizes should not grow too fast compared to the genus. For this family, the group structure can be computed in subexponential time of $L_{q^g}(1/3, O(1))$, and a discrete logarithm computation takes subexponential time of $L_{q^g}(1/3+\varepsilon, o(1))$ for any positive~$\varepsilon$. These runtime bounds rely on heuristics similar to the ones used in the number field sieve or the function field sieve algorithms. | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.title.en | An $L (1/3 + \varepsilon)$ Algorithm for the Discrete Logarithm Problem for Low Degree Curves | |
| dc.type | Communication dans un congrès avec actes | |
| dc.subject.hal | Informatique [cs]/Cryptographie et sécurité [cs.CR] | |
| dc.subject.hal | Mathématiques [math]/Géométrie algébrique [math.AG] | |
| dc.identifier.arxiv | cs.CR/0703032 | |
| bordeaux.page | 379-393 | |
| bordeaux.volume | 4515 | |
| bordeaux.country | ES | |
| bordeaux.title.proceeding | Eurocrypt 2007 | |
| bordeaux.conference.city | Barcelona | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | inria-00135324 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//inria-00135324v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2007&rft.volume=4515&rft.spage=379-393&rft.epage=379-393&rft.au=ENGE,%20Andreas&GAUDRY,%20Pierrick&rft.genre=proceeding |
Fichier(s) constituant ce document
| Fichiers | Taille | Format | Vue |
|---|---|---|---|
|
Il n'y a pas de fichiers associés à ce document. |
|||