A Zero-Knowledge Identification Scheme Based on an Average-Case NP-Complete Problem

  • P. Caballero-Gil
  • C. Hernández-Goya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2776)


The present work investigates the possibility of designing zero-knowledge identification schemes based on hard-on-average problems. It includes a new two-party identification protocol whose security relies on a problem classified as DistNP-Complete under the average-case analysis, the so-called Distributional Matrix Representability Problem. One of the most critical questions in cryptography is referred to the misunderstanding equivalence between using a difficult problem as basis of a cryptographic application and its security. Problems belonging to NP according to the worst-case analysis are frequently used in cryptography, but when random generated instances are used, in most cases there exist efficient algorithms to solve them that make useless their worst-case difficulty. So, by using the search version of the mentioned distributional problem, the security of the proposed scheme is actually guaranteed. Also, with the proposal of a new zero-knowledge proof based on a problem not used before for this purpose, the set of tools for designing cryptographic protocols is enlarged.


Identification Zero-knowledge Average-case completeness 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • P. Caballero-Gil
    • 1
  • C. Hernández-Goya
    • 1
  1. 1.Dept. Statistics, Operations Research and ComputingUniversity of La LagunaLa Laguna, TenerifeSpain

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