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Hybrid Commitments and their Applications to Zero-Knowledge Proof Systems
Full text linkWe introduce the notion of hybrid trapdoor commitment schemes. Intuitively a hybrid trapdoor commitment scheme is a primitive which can be either an unconditionally binding commitment scheme or a trapdoor commitment scheme depending on the distribution of commitment parameters. Moreover, such two possible distributions are computationally indistinguishable. Hybrid trapdoor commitments are related but different with respect to mixed commitments (introduced by Damgard and Nielsen at Crypto 2002). In particular hybrid trapdoor commitments can either be polynomially trapdoor commitments or unconditionally binding commitments, while mixed commitments can be either trapdoor commitments or extractable commitments. In this paper we show that strong notions (e.g., simulation sound, multi-trapdoor) of hybrid trapdoor commitments admit constructions based on the sole assumption that one-way functions exist as well as efficient constructions based on standard number-theoretic assumptions. To further stress the difference between hybrid and mixed commitments, we remark here that mixed commitments seem to require stronger theoretical assumptions (and the known number-theoretic constructions are less efficient). Our main result, is to show how to construct concurrent and simulation-sound zero-knowledge proof systems (in contrast to the arguments recently presented in [I. Damgard 2000; P. MacKenzie, K. Yang 2004; R. Gennaro, 2004]) in the common reference string model. We crucially use hybrid trapdoor commitments since we present general constructions based on the sole assumption that one-way functions exist and very efficient constructions based on number-theoretic assumptions
Delayed-input cryptographic protocols
No full textThe delayed-input witness-indistinguishable proof of knowledge of Lapidot and Shamir (LS) [CRYPTO 1989] is a powerful tool for designing round-efficient cryptographic protocols. Since LS was designed for the language of Hamiltonian graphs, when used as subprotocol it usually requires expensive NP reductions. We first overview how LS works, how it can be used to obtain round-efficient protocols as shown by Ostrovsky and Visconti [ECCC 2012] and why it suffers of intrinsic efficiency limitations. Then we will overview some recent advances on delayed-input cryptographic protocols and their applications. We will in particular consider the efficient witness-indistinguishable proofs of knowledge of Ciampi, Persiano, Scafuro, Siniscalchi and Visconti [TCC 2016a, Eurocrypt 2016], and the round-efficient non-malleable commitments of Ciampi, Ostrovsky, Siniscalchi and Visconti [Crypto 2016, Eprint 2016]
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