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An interactive identification scheme based on discrete logarithms and factoring

Abstract

We describe a modification of an interactive identification scheme of Schnorr intended for use by smart cards. Schnorr's original scheme had its security based on the difficulty of computing discrete logarithms in a subgroup of GF(p) given some side information. We prove that our modification will be witness hiding, which is a more rigid security condition than Schnorr proved for his scheme, if factoring a large integer with some side information is computationally infeasible. In addition, even if the large integer can be factored, then our scheme is still as secure as Schnorr's scheme. For this enhanced security we require only slightly more communication and about a factor of a 3.6 increase in computational power, but the requirements remain quite modest, so that the scheme is well suited for use in smart cards.

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Additional information

A preliminary version of this paper was presented at Eurocrypt '90, May 21–24, Århus, Denmark, and has appeared in the proceedings, pp. 63–71. This work was performed under U.S. Department of Energy contract number DE-AC04-76DP00789.

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Brickell, E.F., McCurley, K.S. An interactive identification scheme based on discrete logarithms and factoring. J. Cryptology 5, 29–39 (1992). https://doi.org/10.1007/BF00191319

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Key words

  • Interactive identification
  • Digital signatures
  • Witness hiding