@article{7771c165563c4c5da40856a8b93c35a5,

title = "WEAK ZERO-KNOWLEDGE BEYOND THE BLACK-BOX BARRIER",

abstract = "The round complexity of zero-knowledge protocols is a long-standing open question and is yet to be settled under standard assumptions. So far, the question has appeared equally challenging for relaxations such as weak zero-knowledge and witness hiding. Like full-fledged zero-knowledge, protocols satisfying these relaxed notions under standard assumptions have at least four messages. The difficulty in improving round complexity stems from a fundamental barrier: none of these notions can be achieved in three messages via reductions (or simulators) that treat the verifier as a black box. We introduce a new non-black-box technique and use it to obtain the first protocols that cross this barrier under standard assumptions. Our main results are (1) weak zero-knowledge for NP in two messages, assuming quasi-polynomially secure fully homomorphic encryption and other standard primitives (known from quasi-polynomial hardness of learning with errors) as well as subexponentially secure one-way functions; and (2) weak zero-knowledge for NP in three messages under standard polynomial assumptions (following, for example, from fully homomorphic encryption and factoring). We also give, under polynomial assumptions, a two-message witness-hiding protocol for any language L in NP that has a witness encryption scheme. This protocol is also publicly verifiable. Our technique is based on a new homomorphic trapdoor paradigm, which can be seen as a non-black-box analogue of the classic Feige-Lapidot-Shamir trapdoor paradigm.",

keywords = "cryptographic protocols, round complexity, witness hiding, zero-knowledge",

author = "Nir Bitansky and Dakshita Khurana and Omer Paneth",

note = "Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics.",

year = "2023",

month = apr,

doi = "10.1137/20M1319565",

language = "אנגלית",

volume = "52",

pages = "156--199",

journal = "SIAM Journal on Computing",

issn = "0097-5397",

publisher = "Society for Industrial and Applied Mathematics (SIAM)",

number = "2",

}