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Constructions and Bounds for Unconditionally Secure Commitment Schemes
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| Abstract: | Commitment schemes have been extensively studied since they were introduced by Blum in 1982. Rivest recently showed how to construct unconditionally secure commitment schemes, assuming the existence of a trusted initializer. In this paper, we present a formal mathematical model for such schemes, and analyze their binding and concealing properties. In particular, we show that such schemes cannot be perfectly concealing: there is necessarily a small probability that Alice can cheat Bob by committing to one value but later revealing a different value. We prove several bounds on Alice's cheating probability, and present constructions of schemes that achieve optimal cheating probabilities. We also show a close link between commitment schemes and the classical ``affine resolvable designs''. |
BibTeX
@misc{eprint-2000-11387,
title={Constructions and Bounds for Unconditionally Secure Commitment Schemes},
booktitle={IACR Eprint archive},
keywords={cryptographic protocols / bit commitment, combinatorial cryptography},
url={http://eprint.iacr.org/2000/043},
note={preprint dstinson@uwaterloo.ca 11207 received 7 Sep 2000},
author={C. Blundo and B. Masucci and D.R. Stinson and R. Wei},
year=2000
}