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On the Composition of Two-Prover Commitments, and Applications to Multi-round Relativistic Commitments

  • Serge FehrEmail author
  • Max FillingerEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9666)

Abstract

We consider the related notions of two-prover and of relativistic commitment schemes. In recent work, Lunghi et al. proposed a new relativistic commitment scheme with a multi-round sustain phase that keeps the binding property alive as long as the sustain phase is running. They prove security of their scheme against classical attacks; however, the proven bound on the error parameter is very weak: it blows up double exponentially in the number of rounds.

In this work, we give a new analysis of the multi-round scheme of Lunghi et al., and we show a linear growth of the error parameter instead (also considering classical attacks only). Our analysis is based on a new composition theorem for two-prover commitment schemes. The proof of our composition theorem is based on a better understanding of the binding property of two-prover commitments that we provide in the form of new definitions and relations among them. As an additional consequence of these new insights, our analysis is actually with respect to a strictly stronger notion of security than considered by Lunghi et al.

Notes

Acknowledgments

We would like to thank Jędrzej Kaniewski for helpful discussions regarding [10], and for commenting on an earlier version of our work.

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Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  1. 1.Centrum Wiskunde and Informatica (CWI)AmsterdamThe Netherlands

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