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Constructions and Bounds for Unconditionally Secure Commitment Schemes
Authors: C. Blundo, B. Masucci, D. R. Stinson, R. WeiAbstract:
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’'.
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