Statistically-hiding commitment from any one-way function
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Non-malleable Statistically Hiding Commitment from Any One-Way Function
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Statistically-Hiding quantum bit commitment from approximable-preimage-size quantum one-way function
TQC'09 Proceedings of the 4th international conference on Theory of Quantum Computation, Communication, and Cryptography
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We show that every language in NP has a statistical zero-knowledge argument system under the (minimal) complexity assumption that one-way functions exist. In such protocols, even a computationally unbounded verifier cannot learn anything other than the fact that the assertion being proven is true, whereas a polynomial-time prover cannot convince the verifier to accept a false assertion except with negligible probability. This resolves an open question posed by Naor, Ostrovsky, Venkatesan, and Yung (CRYPTO '92, J. Cryptology '98). Departing from previous works on this problem, we do not construct standard statistically hiding commitments from any one-way function. Instead, we construct a relaxed variant of commitment schemes called "1-out-of-2-binding commitments," recently introduced by Nguyen and Vadhan (STOC '06).