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A Subexponential-Time Algorithm for Computing Discrete Logarithms over GF(p2)

  • Taher ElGamal

Abstract

An algorithm for computing discrete logarithms over GF(p 2 ), where p is a prime, is described. The algorithm is proved to have a subexponential running time for 99.8% of the values of p. The algorithm is similar to the Merkle-Adleman algorithm for computing logarithms over GF(p), but it uses quadratic fields as the appropriate algebraic structure. It also makes use of a modification due to Hellman and Reyneri for computing discrete logarithms over GF(p m), for m growing and p fixed.

Keywords

Discrete Logarithm Real Field Discrete Logarithm Problem Quadratic Field Quadratic Residue 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • Taher ElGamal
    • 1
  1. 1.Information Systems LaboratoryStanford UniversityUSA

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