Highly-Efficient Universally-Composable Commitments Based on the DDH Assumption

  • Yehuda Lindell
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6632)


Universal composability (a.k.a. UC security) provides very strong security guarantees for protocols that run in complex real-world environments. In particular, security is guaranteed to hold when the protocol is run concurrently many times with other secure and possibly insecure protocols. Commitment schemes are a basic building block in many cryptographic constructions, and as such universally composable commitments are of great importance in constructing UC-secure protocols. In this paper, we construct highly efficient UC-secure commitments from the standard DDH assumption, in the common reference string model. Our commitment stage is non-interactive, has a common reference string with O(1) group elements, and has complexity of O(1) exponentiations for committing to a group element (to be more exact, the effective cost is that of \(23\frac{1}{3}\) exponentiations overall, for both the commit and decommit stages). We present a construction that is secure in the presence of static adversaries, and a construction that is secure in the presence of adaptive adversaries with erasures, where the latter construction has an effective additional cost of just \(5\frac{1}{3}\) exponentiations.

Copyright information

© International Association for Cryptologic Research 2011

Authors and Affiliations

  • Yehuda Lindell
    • 1
  1. 1.Department of Computer ScienceBar-Ilang UniversityIsrael

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