A Practical (Non-interactive) Publicly Verifiable Secret Sharing Scheme

  • Mahabir Prasad Jhanwar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6672)

Abstract

A publicly verifiable secret sharing (PVSS) scheme, proposed by Stadler in [29], is a VSS scheme in which anyone, not only the shareholders, can verify that the secret shares are correctly distributed. PVSS can play essential roles in the systems using VSS. Achieving simultaneously the following two features for PVSS is a challenging job:
  • Efficient non-interactive public verification.

  • Proving security for the public verifiability in the standard model.

In this paper we propose a (t, n)-threshold PVSS scheme which satisfies both of these properties. Efficiency of the non-interactive public verification step of the proposed scheme is optimal (in terms of computations of bilinear maps (pairing)) while comparing with the earlier solution by [18]. In public verification step of [18], one needs to compute 2n many pairings, where n is the number of shareholders, whereas in our scheme the number of pairing computations is 4 only. This count is irrespective of the number of shareholders. We also provide a formal proof for the semantic security (IND) of our scheme based on the hardness of a problem that we call the (n,t)-multi-sequence of exponents Diffie-Hellman problem (MSE-DDH). This problem falls under the general Diffie-Hellman exponent problem framework [5].

Keywords

Secret sharing non-interactive PVSS general Diffie-Hellman exponent problem 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Mahabir Prasad Jhanwar
    • 1
  1. 1.C R RAO Advanced Institute of Mathematics, Statistics and Computer ScienceUniversity of Hyderabad CampusHyderabadIndia

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