Multiple non-interactive zero knowledge proofs based on a single random string

@article{Feige1990MultipleNZ,
  title={Multiple non-interactive zero knowledge proofs based on a single random string},
  author={Uriel Feige and Dror Lapidot and Adi Shamir},
  journal={Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science},
  year={1990},
  pages={308-317 vol.1}
}
  • U. Feige, D. Lapidot, A. Shamir
  • Published 22 October 1990
  • Mathematics, Computer Science
  • Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science
The authors solve the two major open problems associated with noninteractive zero-knowledge proofs: how to enable polynomially many provers to prove in writing polynomially many theorems based on the basis of a single random string, and how to construct such proofs under general (rather than number-theoretic) assumptions. The constructions can be used in cryptographic applications in which the prover is restricted to polynomial time, and they are much simpler than earlier (and less capable… Expand
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This paper construct simulation-so und NIZK proofs for any NPcomplete language which remain secure even after the adversary has seen any number of simulated proofs of its chosing. Expand
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Abstract : We investigate the possibility of disposing of interaction between Prover and Verifier in a zero-knowledge proof if they share beforehand a short random string. Without any assumption, weExpand
Publicly Verifiable Non-Interactive Zero-Knowledge Proofs
In this paper we construct the first publicly verifiable non-interactive zero-knowledge proof for any NP statement under the general assumption that one way permutations exist. If the prover isExpand
Non-Interactive Zero-Knowledge with Preprocessing
TLDR
It is proved that the existence of any secure probabilistic encryption scheme is enough for Non-Interactive Zero-Knowledge in a modified model and the ability to prove a randomly chosen theorem allows to subsequently prove noninteractively and in Zero- knowledge any smaller size theorem whose proof is discovered. Expand
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It is shown that interaction in any zero-knowledge proof can be replaced by sharing a common, short, random string, and this result is used to construct the first public-key cryptosystem secure against chosen ciphertext attack. Expand
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Noninteractive zero knowledge proofs in a network which have the property that anyone in the network can individually check correctness while the proof is zero knowledge to any sufficiently small coalition are shown. Expand
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It is shown that after a preprocessing stage consisting of O(k) executions of oblivious transfer, any polynomial number of NP-theorems of any polysize can be proved noninteractively and in zero knowledge. Expand
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A general algorithmic scheme for constructing polynomial-time deterministic algorithms that stretch a short secret random input into a long sequence of unpredictable pseudo-random bits is presented. Expand
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