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

Serge Fehr and Max Fillinger

##### 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.

Available format(s)
Publication info
Preprint. MINOR revision.
Keywords
bit commitmenttwo provers
Contact author(s)
max fillinger @ cwi nl
History
Short URL
https://ia.cr/2016/113

CC BY

BibTeX

@misc{cryptoeprint:2016/113,
author = {Serge Fehr and Max Fillinger},
title = {On the Composition of Two-Prover Commitments, and Applications to Multi-Round Relativistic Commitments},
howpublished = {Cryptology ePrint Archive, Paper 2016/113},
year = {2016},
note = {\url{https://eprint.iacr.org/2016/113}},
url = {https://eprint.iacr.org/2016/113}
}

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