## H.: Resettable Zero-Knowledge in the Weak PublicKey Model (2003)

Venue: | In: Advances in Cryptology { Eurocrypt '03. Volume 2045 of Lecture |

Citations: | 3 - 1 self |

### BibTeX

@INPROCEEDINGS{Zhao03h.:resettable,

author = {Yunlei Zhao and Xiaotie Deng and C. H. Lee and Hong Zhu},

title = {H.: Resettable Zero-Knowledge in the Weak PublicKey Model},

booktitle = {In: Advances in Cryptology { Eurocrypt '03. Volume 2045 of Lecture},

year = {2003},

pages = {123--140},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

Abstract. A new public-key model for resettable zero-knowledge (rZK) protocols, which is an extension and generalization of the upperbounded public-key (UPK) model introduced by Micali and Reyzin [EuroCrypt’01, pp. 373–393], is introduced and is named weak public-key (WPK) model. The motivations and applications of the WPK model are justified in the distributed smart-card/server setting and it seems more preferable in practice, especially in E-commerce over Internet. In this WPK model a 3-round (optimal) black-box resettable zero-knowledge argument with concurrent soundness for NP is presented assuming the security of RSA with large exponents against subexponential-time adversaries. Our result improves Micali and Reyzin’s result of resettable zero-knowledge argument with concurrent soundness for NP in the UPK model. Note that although Micali and Reyzin ’ protocol satisfies concurrent soundness in the UPK model, but it does not satisfy even sequential soundness in our WPK model. Our protocol works in a somewhat “parallel repetition ” manner to reduce the error probability and the black-box zero-knowledge simulator works in strict polynomial time rather than expected polynomial time. The critical tools used are: verifiable random functions introduced by Micali, Rabin and Vadhan [FOCS’99, pp. 120-130], zap presented by Dwork and Naor [FOCS’00, pp. 283–293] and complexity leveraging introduced by Canetti, Goldreich, Goldwasser and Micali [STOC’00, pp. 235–244]. 1

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Citation Context ...del, which underlies any public key cryptosystem or digital signature. Resettable zero-knowledge protocols also shed hope on finding ID schemes secure against resetting attack. Feige, Fiat and Shamir =-=[16,14]-=- introduced a paradigm for ID schemes based on the notion of zero-knowledge proof of knowledge. In essence, a prover identifies himself by convincing the verifier of knowing a given secret. Almost all... |

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Citation Context ... R ←− {0, 1} NIσLen(n) ; Π R ←− NIP(σ, x, y) :(σ, Π)]. The value α is called the NIZK constant. Non-interactive zero-knowledge proof systems for NP can be constructed based on any one-way permutation =-=[15]-=- and one-way permutations can be constructed in turn under RSA assumption [18]. An efficient implementation based on any one-way permutation can be found in [21]. For more recent advances in NIZK read... |

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Citation Context ...ndard complexity assumptions, non-constant-round resettable zeroknowledge proof for NP was constructed in [8,22] by properly modifying the concurrent zero-knowledge protocol of Richardson and Killian =-=[28]-=-. Unfortunately, there are no constant-round rZK protocols in the standard model, at least for the black-box case, as shown by Canetti, Killian, Petrank and Rosen [9]. To get constant-round resettable... |

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Citation Context ...nd Micali [STOC’00, pp. 235–244]. 1 Introduction The strongest notion of zero-knowledge to date, resettable zero-knowledge (rZK), was recently put forward by Canetti, Goldreich, Goldwasser and Micali =-=[8]-=-. Roughly speaking, an rZK protocol is an interactive system in which a verifier learns nothing (except for the verity of a given statement) even if he can interact with the prover polynomial many tim... |

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Citation Context ...way permutation can be found in [21]. For more recent advances in NIZK readers are referred to [10]. 2.1 Verifiable Random Functions A family of verifiable random functions (VRF), first introduced in =-=[26]-=-, is essentially a pseudorandom function family with an additional property that the correct value of a function on an input can not only be computed by the owner of the seed, but also be proven to be... |

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Citation Context ...versaries [26]. Very recently, a new construction of VRF was provided by Lysyanskaya on an assumption about groups in which decisional Diffie-Hellman is easy, but computational Diffie-Hellman is hard =-=[23]-=-. We remark that up to now the first application of VRF, as suggested by Micali and Reyzin, is the simple construction of an rZK argument with one-time soundness for NP in the BPK model [24]. Our resu... |

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Citation Context ...We remark that this result does not hold for black-box zero-knowledge in the standard model. Indeed, expected polynomial time is necessary for blackbox zero-knowledge simulation in the standard model =-=[6]-=- and the first non-blackbox zero-knowledge argument for NP with strict polynomial time simulation was presented in [1]. (2). Concurrent Soundness We first note that a computational power unbounded pro... |

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(Show Context)
Citation Context ...zero-knowledge argument with concurrent soundness for NP in the WPK model. 2 Preliminaries In this section, we present some main tools used in this paper. However, one critical tool, zap presented in =-=[11]-=-, is absent from this section and is provided in Section 3 together with the definition of resettable witness indistinguishability. We remark that all these tools can be constructed assuming the secur... |

43 | Concurrent and Resettable ZeroKnowledge in Poly-logarithmic Rounds
- Kilian, Petrank
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(Show Context)
Citation Context ...urrent zero-knowledge introduced by Dwork, Naor and Sahai [12]. 1.1 Previous Results Under standard complexity assumptions, non-constant-round resettable zeroknowledge proof for NP was constructed in =-=[8,22]-=- by properly modifying the concurrent zero-knowledge protocol of Richardson and Killian [28]. Unfortunately, there are no constant-round rZK protocols in the standard model, at least for the black-box... |

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(Show Context)
Citation Context ... al. have proven that for a 3-round argument system if the verifier has secret information regarding historical transcripts then parallel repetition does not guarantee to reduce the error probability =-=[5]-=-. Note, however, that in our argument protocol the verifier indeed has secret information, the SK. The following proof uses a standard reduction technique. That is, if the above protocol does not sati... |

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(Show Context)
Citation Context ...troduced an appealingly simple model, the bare public-key (BPK) model, and presented a 5-round rZK argument for NP in this model. The round complexity was further reduced to four by Micali and Reyzin =-=[24]-=-. A protocol in the BPK model simply assumes that all verifiers have deposited a public key in a public file before any interaction among the users. This public file is accessible to all users at all ... |

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(Show Context)
Citation Context ...r, up to the emergence of rZK all the previous Fiat-Shamir like ID schemes fail to secure whenever the prover is resettable. Using constant-round rZK protocols in the BPK model above, Bellare, et al. =-=[3]-=- provided identification protocols secure against resetting attack. Unfortunately, there is a main disadvantage of this rZK-based solution since it only preserves the identity prover’s security but do... |

26 | An Efficient Noninteractive Zero-Knowledge Proof System for NP with General Assumptions
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(Show Context)
Citation Context ...ucted based on any one-way permutation [15] and one-way permutations can be constructed in turn under RSA assumption [18]. An efficient implementation based on any one-way permutation can be found in =-=[21]-=-. For more recent advances in NIZK readers are referred to [10]. 2.1 Verifiable Random Functions A family of verifiable random functions (VRF), first introduced in [26], is essentially a pseudorandom ... |

18 | Min-round resettable zero-knowledge in the public-key model
- Micali, Reyzin
- 2001
(Show Context)
Citation Context ... secret key and VRFPKid along with the p(n) random strings, (RV1 ,RV2 , ··· ,RV p(n) )id, is its public key. We remark that in comparison with the key generation stage of Micali and Reyzin’s protocol =-=[25]-=-, the key generation stage of our protocol is greatly simplified.s134 Y. Zhao et al. 4.4 The Full Protocol Common input. An element x ∈ L∩{0, 1} n . Denote by RL the corresponding NP-relation for L. S... |

12 | Linear Zero-Knowledge - A Note on Efficient Zero-Knowledge Proofs and Arguments
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(Show Context)
Citation Context ... for a language outside of BPP requires at least three rounds (using an earlier result of Goldreich and Kraczwyck [20]). For efficient 4-round zero-knowledge protocols for NP, readers are referred to =-=[7]-=-. We also note that 2-round public-coin black-box and concurrent zero-knowledge protocols for NP do exist under the assumption that the prover is resource bounded[13]. Here, resource bounded prover me... |

10 |
Foundation of Cryptography-Basic Tools
- Goldreich
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(Show Context)
Citation Context ...r every v, u and m, ifPr[Csv(1k ,v)=m] and Pr[Csu(1k ,u)=m] are both positive then u = v and sv = su. A one-round perfect-binding commitment scheme can be constructed based on any one-way permutation =-=[17]-=-. Definition 2 (Pseudorandom Functions PRF [19]). A pseudorandom function family is a keyed family of efficiently computable functions, such thats128 Y. Zhao et al. a function picked at random from th... |

9 | 2-round zero knowledge and proof auditors
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(Show Context)
Citation Context ...ls for NP, readers are referred to [7]. We also note that 2-round public-coin black-box and concurrent zero-knowledge protocols for NP do exist under the assumption that the prover is resource bounded=-=[13]-=-. Here, resource bounded prover means that during protocol execution the prover uses certain limited amount of (say, a-priori polynomial bounded) time or non-uniform advice. 1.2 Our Contributions In t... |

7 |
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(Show Context)
Citation Context ...tions can be constructed in turn under RSA assumption [18]. An efficient implementation based on any one-way permutation can be found in [21]. For more recent advances in NIZK readers are referred to =-=[10]-=-. 2.1 Verifiable Random Functions A family of verifiable random functions (VRF), first introduced in [26], is essentially a pseudorandom function family with an additional property that the correct va... |

7 | Zero-Knowledge with Public Keys
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(Show Context)
Citation Context ...ot guarantee to preserve verifier’s security when they are concurrently executed. The various security notions of the verifier in public-key models were first noted and clarified by Micali and Reyzin =-=[24,27]-=-. In public-key models, a verifier V has a secret key SK, corresponding to its public-key PK. A malicious prover P ∗ could potentially gain some knowledge about SK from an interaction with the verifie... |