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Perfectly Hiding Commitment Scheme with TwoRound from Any OneWay Permutation
, 2008
"... Commitment schemes are arguably among the most important and useful primitives in cryptography. According to the computational power of receivers, commitments can be classified into three possible types: computational hiding commitments, statistically hiding commitments and perfect computational com ..."
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Commitment schemes are arguably among the most important and useful primitives in cryptography. According to the computational power of receivers, commitments can be classified into three possible types: computational hiding commitments, statistically hiding commitments and perfect computational commitments. The fist commitment with constant rounds had been constructed from any oneway functions in last centuries, and the second with nonconstant rounds were constructed from any oneway functions in FOCS2006, STOC2006 and STOC2007 respectively, furthermore, the lower bound of round complexity of statistically hiding commitments has been proven to be n/log n rounds under the existence of oneway function. Perfectly hiding commitments implies statistically hiding, hence, it is also infeasible to construct a practically perfectly hiding commitments with constant rounds under the existence of oneway function. In order to construct a perfectly hiding commitments with constant rounds, we have to relax the assumption that oneway functions exist. In this paper, we will construct a practically perfectly hiding commitment with tworound from any oneway permutation. To the best of our knowledge, these are the best results so far.
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"... Interactive hashing, introduced by Naor, Ostrovsky, Venkatesan and Yung (CRYPTO ’92), plays an important role in many cryptographic protocols. In particular, it is a major component in all known constructions of statisticallyhiding commitment schemes and of zeroknowledge arguments based on general ..."
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Interactive hashing, introduced by Naor, Ostrovsky, Venkatesan and Yung (CRYPTO ’92), plays an important role in many cryptographic protocols. In particular, it is a major component in all known constructions of statisticallyhiding commitment schemes and of zeroknowledge arguments based on general oneway permutations and on oneway functions. Interactive hashing with respect to a oneway permutation f, is a twoparty protocol that enables a sender that knows y = f(x) to transfer a random hash z = h(y) to a receiver. The receiver is guaranteed that the sender is committed to y (in the sense that it cannot come up with x and x ′ such that f(x) � = f(x ′ ) but h(f(x)) = h(f(x ′)) = z). The sender is guaranteed that the receiver does not learn any additional information on y. In particular,
Interactive Hashing: An Information Theoretic Tool (Invited Talk)
"... Abstract. Interactive Hashing has featured as an essential ingredient in protocols realizing a large variety of cryptographic tasks, notably Oblivious Transfer in the bounded memory model. In Interactive Hashing, a sender transfers a bit string to a receiver such that two strings are received, the ..."
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Abstract. Interactive Hashing has featured as an essential ingredient in protocols realizing a large variety of cryptographic tasks, notably Oblivious Transfer in the bounded memory model. In Interactive Hashing, a sender transfers a bit string to a receiver such that two strings are received, the original string and a second string that appears to be chosen at random among those distinct from the first. This paper starts by formalizing the notion of Interactive Hashing as a cryptographic primitive, disentangling it from the specifics of its various implementations. To this end, we present an applicationindependent set of information theoretic conditions that all Interactive Hashing protocols must ideally satisfy. We then provide a standard implementation of Interactive Hashing and use it to reduce a very standard version of Oblivious Transfer to another one which appears much weaker. 1