Lower bounds for discrete logarithms and related problems

  • Authors:
  • Victor Shoup

  • Affiliations:
  • IBM Research-Zürich, Rüschlikon, Switzerland

  • Venue:
  • EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
  • Year:
  • 1997

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Abstract

This paper considers the computational complexity of the discrete logarithm and related problems in the context of "generic algorithms"--that is, algorithms which do not exploit any special properties of the encodings of group elements, other than the property that each group element is encoded as a unique binary string. Lower bounds on the complexity of these problems are proved that match the known upper bounds: any generic algorithm must perform Ω(p1/2) group operations, where p is the largest prime dividing the order of the group. Also, a new method for correcting a faulty Diffie-Hellman oracle is presented.