An L(1/3) Discrete Logarithm Algorithm for Low Degree Curves

An L(1/3) Discrete Logarithm Algorithm for Low Degree Curves

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 are arbitrary, but their sizes should not grow too fast compared to the genus. For such families, the grou...

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Veröffentlicht in:Journal of cryptology 2011, Vol.24 (1), p.24-41
Hauptverfasser: Enge, Andreas, Gaudry, Pierrick, Thomé, Emmanuel
Format: Artikel
Sprache:eng
Schlagworte:
Algebraic Geometry
Algorithms
Applied sciences
Coding and Information Theory
Combinatorics
Communications Engineering
Computational Mathematics and Numerical Analysis
Computer Science
Cryptography
Cryptography and Security
Curves
Exact sciences and technology
Information, signal and communications theory
Jacobians
Logarithms
Mathematics
Networks
Number theory
Probability Theory and Stochastic Processes
Signal and communications theory
Telecommunications and information theory
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Beschreibung
Zusammenfassung: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 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 . The runtime bounds rely on heuristics similar to the ones used in the number field sieve or the function field sieve.
ISSN:0933-2790
1432-1378
DOI:10.1007/s00145-010-9057-y