Improved Zero-Knowledge Proofs of Knowledge for the ISIS Problem, and Applications

  • San Ling
  • Khoa Nguyen
  • Damien Stehlé
  • Huaxiong Wang
Conference paper

DOI: 10.1007/978-3-642-36362-7_8

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7778)
Cite this paper as:
Ling S., Nguyen K., Stehlé D., Wang H. (2013) Improved Zero-Knowledge Proofs of Knowledge for the ISIS Problem, and Applications. In: Kurosawa K., Hanaoka G. (eds) Public-Key Cryptography – PKC 2013. Lecture Notes in Computer Science, vol 7778. Springer, Berlin, Heidelberg

Abstract

In all existing efficient proofs of knowledge of a solution to the infinity norm Inhomogeneous Small Integer Solution (ISIS ∞ ) problem, the knowledge extractor outputs a solution vector that is only guaranteed to be \(\widetilde{O}(n)\) times longer than the witness possessed by the prover. As a consequence, in many cryptographic schemes that use these proof systems as building blocks, there exists a gap between the hardness of solving the underlying ISIS ∞  problem and the hardness underlying the security reductions. In this paper, we generalize Stern’s protocol to obtain two statistical zero-knowledge proofs of knowledge for the ISIS ∞  problem that remove this gap. Our result yields the potential of relying on weaker security assumptions for various lattice-based cryptographic constructions. As applications of our proof system, we introduce a concurrently secure identity-based identification scheme based on the worst-case hardness of the \({\rm SIVP}_{{\widetilde{O}}(n^{1.5})}\) problem (in the ℓ2 norm) in general lattices in the random oracle model, and an efficient statistical zero-knowledge proof of plaintext knowledge with small constant gap factor for Regev’s encryption scheme.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • San Ling
    • 1
  • Khoa Nguyen
    • 1
  • Damien Stehlé
    • 2
  • Huaxiong Wang
    • 1
  1. 1.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore
  2. 2.Laboratoire LIP (U. Lyon, CNRS, ENSL, INRIA, UCBL)ÉNS de LyonLyon Cedex 07France

Personalised recommendations