International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Constructions and Bounds for Unconditionally Secure Commitment Schemes

C. Blundo
B. Masucci
D.R. Stinson
R. Wei
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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''.
  title={Constructions and Bounds for Unconditionally Secure Commitment Schemes},
  booktitle={IACR Eprint archive},
  keywords={cryptographic protocols / bit commitment, combinatorial cryptography},
  note={preprint 11207 received 7 Sep 2000},
  author={C. Blundo and B. Masucci and D.R. Stinson and R. Wei},