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An Improved Protocol for Demonstrating Possession of Discrete Logarithms and Some Generalizations

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 304)

Abstract

A new protocol is presented that allows A to convince B that she knows a solution to the Discrete Log Problem—i.e. that she knows an x such that α xβ (mod N) holds—without revealing anything about x to B. Protocols are given both for N prime and for N composite.

We also give protocols for extensions of the Discrete Log problem allowing A to show possession of:
  • multiple discrete logarithms to the same base at the same time, i.e. knowing x 1, . . . , x K such that \( \alpha ^{x_1 } \equiv \beta _1 ,...,\alpha ^{x_K } \equiv \beta _K \);

  • several discrete logarithms to different bases at the same time, i.e. knowing x 1, . . . , x K such that the product \( \alpha _1^{x_1 } \alpha _2^{x_2 } \cdot \cdot \cdot \alpha _K^{x_K } \equiv \beta \);

  • a discrete logarithm that is the simultaneous solution of several different instances, i.e. knowing x such that α 1 x ≡β1,...α K x ≡βK.

We can prove that the sequential versions of these protocols do not reveal any “knowledge” about the discrete logarithm(s) in a well-defined sense, provided that A knows (a multiple of) the order of α.

Keywords

Elliptic Curve Discrete Logarithm Cryptographic Protocol Random Tape Probabilistic Polynomial Time Algorithm 
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

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  1. 1.Centre for Mathematics and Computer ScienceAmsterdamThe Netherlands

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