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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Non-interactive zero-knowledge proof ： ウィキペディア英語版 Non-interactive zero-knowledge proof Non-interactive zero-knowledge proofs are a variant of zero-knowledge proofs in which no interaction is necessary between prover and verifier. Blum, Feldman, and Micali 〔Manuel Blum, Paul Feldman, and Silvio Micali. Non-Interactive Zero-Knowledge and Its Applications. Proceedings of the twentieth annual ACM symposium on Theory of computing (STOC 1988). 103–112. 1988〕 showed that a common reference string shared between the prover and the verifier is enough to achieve computational zero-knowledge without requiring interaction. Goldreich and Oren〔Oded Goldreich and Yair Oren. Definitions and Properties of Zero-Knowledge Proof Systems. Journal of Cryptology. Vol 7(1). 1–32. 1994 ((PS) )〕 gave impossibility results for one shot zero-knowledge protocols in the standard model. In 2003, Goldwasser and Kalai published an instance of identification scheme for which any hash function will yield an insecure digital signature scheme.〔Shafi Goldwasser and Yael Kalai. On the (In)security of the Fiat–Shamir Paradigm. Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS'03). 2003〕 These results are not contradictory, as the impossibility result of Goldreich and Oren does not hold in the common reference string model or the random oracle model. Non-interactive zero-knowledge proofs however show a separation between the cryptographic tasks that can be achieved in the standard model and those that can be achieved in 'more powerful' extended models. The model influences the properties that can be obtained from a zero-knowledge protocol. Pass〔Rafael Pass. On Deniability in the Common Reference String and Random Oracle Model. Advances in Cryptology – CRYPTO 2003. 316–337. 2003 ((PS) )〕 showed that in the common reference string model non-interactive zero-knowledge protocols do not preserve all of the properties of interactive zero-knowledge protocols, e.g. they do not preserve deniability. Non-interactive zero-knowledge proofs can also be obtained in the random oracle model using the Fiat–Shamir heuristic. ==Definition== Originally,〔 non-interactive zero-knowledge was only defined as a single theorem proof system. In such a system each proof requires its own fresh common reference string. A common reference string in general is not a random string. It may, for instance, consist of randomly chosen group elements that all protocol parties use. Although the group elements are random, the reference string is not as it contains a certain structure (e.g., group elements) that is distinguishable from randomness. Subsequently, Feige, Lapidot, and Shamir〔Uriel Feige, Dror Lapidot, Adi Shamir: Multiple Non-Interactive Zero Knowledge Proofs Under General Assumptions. SIAM J. Comput. 29(1): 1–28 (1999)〕 introduced multi-theorem zero-knowledge proofs as a more versatile notion for non-interactive zero knowledge proofs. In this model the prover and the verifier are in possession of a reference string sampled from a distribution ''D'' by a trusted setup $\backslash sigma\; \backslash gets\; \backslash mathrm(1^k)$. To prove statement $y\backslash in\; L$ with witness ''w'', the prover runs $\backslash pi\; \backslash gets\; \backslash mathrm(\backslash sigma,y,w)$ and sends the proof $\backslash pi$ to the verifier. The verifier accepts if $\backslash mathrm(\backslash sigma,y,\backslash pi)=\backslash mathrm$, and rejects otherwise. To account for the fact that $\backslash sigma$ may influence the statements that are being proven, the witness relation can be generalized to $(y,w)\; \backslash in\; R\_\backslash sigma$ parameterized by $\backslash sigma$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Non-interactive zero-knowledge proof」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.