## An efficient system for non-transferable anonymous credentials with optional anonymity revocation (2001)

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@INPROCEEDINGS{Lysyanskaya01anefficient,

author = {Anna Lysyanskaya},

title = {An efficient system for non-transferable anonymous credentials with optional anonymity revocation},

booktitle = {},

year = {2001},

pages = {93--118},

publisher = {Springer}

}

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### Abstract

Abstract. A credential system is a system in which users can obtain credentials from organizations and demonstrate possession of these credentials. Such a system is anonymous when transactions carried out by the same user cannot be linked. An anonymous credential system is of significant practical relevance because it is the best means of providing privacy for users. In this paper we propose a practical anonymous credential system that is based on the strong RSA assumption and the decisional Diffie-Hellman assumption modulo a safe prime product and is considerably superior to existing ones: (1) We give the first practical solution that allows a user to unlinkably demonstrate possession of a credential as many times as necessary without involving the issuing organization. (2) To prevent misuse of anonymity, our scheme is the first to offer optional anonymity revocation for particular transactions. (3) Our scheme offers separability: all organizations can choose their cryptographic keys independently of each other. Moreover, we suggest more effective means of preventing users from sharing their credentials, by introducing allor-nothing sharing: a user who allows a friend to use one of her credentials once, gives him the ability to use all of her credentials, i.e., taking over her identity. This is implemented by a new primitive, called circular encryption, which is of independent interest, and can be realized from any semantically secure cryptosystem in the random oracle model.

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Citation Context ...roof can be found in the full version of this paper [12]). Theorem 4. If G is semantically secure, G ′ is circular-secure. As a basis for our circular encryption scheme, we use the ElGamal encryption =-=[27]-=- in some G = 〈g〉. It is easy to see that the ElGamal cryptosystem is semantically secure under the decisional Diffie-Hellman assumption. Let P = g x be a public key. The resulting circular encryption ... |

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Citation Context ...these schemes need to share the same discrete logarithm group. The concept of revocable anonymity is found in electronic payment systems (e.g., [9, 37]) and group signature and identity escrow (e.g., =-=[2, 14, 20, 33]-=- schemes. Prior to our work, the problem of constructing a practical system with multiple-use credentials eluded researchers for some time [8, 21, 25, 34]. We solve it by extending ideas found in the ... |

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Citation Context ...rieve the identity of the user. In the sequel we describe how the protocols for proving possession of a credential must be adapted such that local revocation is possible using Cramer-Shoup encryption =-=[22]-=-. We then discuss global revocation. We remark that it can be decided at the time when the possession of a credential is proved whether local and/or global revocation shall be possible for the transac... |

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Citation Context ...s problem, an application that allows the individual to control the dissemination of personal information is needed. An anonymous credential system (also called pseudonym system), introduced by Chaum =-=[18]-=-, is the best known idea for such a system. In this paper, we propose a new efficient anonymous credential system, considerably superior to previously proposed ones. The communication and computation ... |

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Citation Context ...].sOur contribution. In Section 2 we present our definitions for a credential system with the basic properties. Although not conceptually new and inspired by the literature on multi-party computation =-=[15, 16]-=- and reactive systems [36], these definitions are of interest, as our treatment is more formal than the one usually encountered in the literature on credential and electronic cash systems. We omit for... |

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Citation Context ...these schemes need to share the same discrete logarithm group. The concept of revocable anonymity is found in electronic payment systems (e.g., [9, 37]) and group signature and identity escrow (e.g., =-=[2, 14, 20, 33]-=- schemes. Prior to our work, the problem of constructing a practical system with multiple-use credentials eluded researchers for some time [8, 21, 25, 34]. We solve it by extending ideas found in the ... |

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Citation Context ... v, z) := (P r2 r1, g r2 , H(r1) ⊕ m). Decryption works by computing H(u/v x )⊕z. We denote this encryption scheme by CElG. 6.2 Verifiable Encryption with a Committed Public Key Verifiable encryption =-=[1, 10]-=-, is a protocol between a prover and a verifier such that as a result of the protocol, on input public key E and value v, the verifier obtains an encryption e of some value s under E such that (s, v) ... |

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Citation Context ...these schemes need to share the same discrete logarithm group. The concept of revocable anonymity is found in electronic payment systems (e.g., [9, 37]) and group signature and identity escrow (e.g., =-=[2, 14, 20, 33]-=- schemes. Prior to our work, the problem of constructing a practical system with multiple-use credentials eluded researchers for some time [8, 21, 25, 34]. We solve it by extending ideas found in the ... |

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Citation Context ... double-users is required. This could for instance be achieved using revocation as described in the previous section, or using similar techniques that are used in for anonymous off-line e-cash (e.g., =-=[7]-=-). We now describe how the latter can be done such that using a one-show credential twice would expose the user’s secret keys connected with the corresponding pseudonym. Together with (any kind of) no... |

213 |
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Citation Context ...user, apart from the fact of the user’s ownership of some set of credentials, even if it cooperates with other organizations. In particular, two pseudonyms belonging to the same user cannot be linked =-=[8, 18, 19, 21, 25, 34]-=-. Finally, it is desirable that the system be efficient. Besides requiring that it be based on efficient protocols, we also require that each interaction involve as few entities as possible, and the r... |

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Citation Context ...ting a practical system with multiple-use credentials eluded researchers for some time [8, 21, 25, 34]. We solve it by extending ideas found in the constructions of strong-RSA-based signature schemes =-=[23, 30]-=- and group signature schemes [2].sOur contribution. In Section 2 we present our definitions for a credential system with the basic properties. Although not conceptually new and inspired by the literat... |

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Citation Context ...n 2 we present our definitions for a credential system with the basic properties. Although not conceptually new and inspired by the literature on multi-party computation [15, 16] and reactive systems =-=[36]-=-, these definitions are of interest, as our treatment is more formal than the one usually encountered in the literature on credential and electronic cash systems. We omit formal definitions for a cred... |

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Citation Context ...bility: when using RSA moduli of length 1024 bits, establishing a pseudonym is somewhat less efficient: it takes about 200 exponentiations in Z ∗ n for both parties, but batch-verification techniques =-=[4]-=- could be applied to reduce this, and organizations have to store about 25K bits per user (here computation complexity could be traded against storage). All-or-nothing non-transferability is based on ... |

132 |
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Citation Context ...oup of quadratic residues modulo a composite n, i.e., G = QRn. This choice for the underlying group has some consequences. First, the protocols are proofs of knowledge under the strong RSA assumption =-=[29]-=-. Second, the largest possible value of the challenge c must be smaller that the smallest factor of G’s order. Third, soundness needs special attention in the case that the verifier is not equipped wi... |

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Citation Context ...ting a practical system with multiple-use credentials eluded researchers for some time [8, 21, 25, 34]. We solve it by extending ideas found in the constructions of strong-RSA-based signature schemes =-=[23, 30]-=- and group signature schemes [2].sOur contribution. In Section 2 we present our definitions for a credential system with the basic properties. Although not conceptually new and inspired by the literat... |

117 | Pseudonym systems
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Citation Context ...ntroducing almost no overhead to realizing privacy in a credential system. ⋆ This research was carried out while the author was visiting IBM Zürich Research Laboratory.sAn anonymous credential system =-=[18, 19, 21, 25, 34]-=- consists of users and organizations. Organizations know the users only by pseudonyms. Different pseudonyms of the same user cannot be linked. Yet, an organization can issue a credential to a pseudony... |

106 | Efficient concurrent zero-knowledge in the auxiliary string model
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Citation Context ...hat are concurrent zero-knowledge. They are characterized by remaining zero-knowledge even if several instances of the same protocol are run arbitrarily interleaved. In the public key model, Damg˚ard =-=[24]-=- shows a general technique for making the so-called Σ-protocols (these include all the proofs of knowledge used here) composable under concurrent composition without incurring a penalty in communicati... |

93 | Key-Privacy in PublicKey Encryption
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Citation Context ...pendently of and concurrently with our work, Black et al. [5] proposed symmetric encryption schemes for key-dependent messages (which is what we call circular symmetric encryption) and Bellare et al. =-=[3]-=- studied key-private encryption (which is what we call key-oblivious encryption).s6.1 Circular Encryption Definition 2. Let n, m ∈ poly(k). A semantically secure encryption scheme G = (E, D) is circul... |

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82 |
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Citation Context ... problems: First, the approach requires that each user encrypts each of her secret keys Di under one of her public keys Ej, thereby creating “circular encryptions”. However, the canonical definitions =-=[35]-=- of secure encryption do not provide security for such encryptions. Moreover, it is not known whether circular security is possible under general assumptions. Nevertheless, we introduce in this sectio... |

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Citation Context ...that all the users and the certification authorities in these schemes need to share the same discrete logarithm group. The concept of revocable anonymity is found in electronic payment systems (e.g., =-=[9, 37]-=-) and group signature and identity escrow (e.g., [2, 14, 20, 33] schemes. Prior to our work, the problem of constructing a practical system with multiple-use credentials eluded researchers for some ti... |

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Citation Context ...].sOur contribution. In Section 2 we present our definitions for a credential system with the basic properties. Although not conceptually new and inspired by the literature on multi-party computation =-=[15, 16]-=- and reactive systems [36], these definitions are of interest, as our treatment is more formal than the one usually encountered in the literature on credential and electronic cash systems. We omit for... |

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Citation Context |

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Citation Context ...that all the users and the certification authorities in these schemes need to share the same discrete logarithm group. The concept of revocable anonymity is found in electronic payment systems (e.g., =-=[9, 37]-=-) and group signature and identity escrow (e.g., [2, 14, 20, 33] schemes. Prior to our work, the problem of constructing a practical system with multiple-use credentials eluded researchers for some ti... |

51 |
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Citation Context ...ntroducing almost no overhead to realizing privacy in a credential system. ⋆ This research was carried out while the author was visiting IBM Zürich Research Laboratory.sAn anonymous credential system =-=[18, 19, 21, 25, 34]-=- consists of users and organizations. Organizations know the users only by pseudonyms. Different pseudonyms of the same user cannot be linked. Yet, an organization can issue a credential to a pseudony... |

47 | M.: Effcient group signature schemes for large groups - Camenisch, Stadler - 1997 |

44 |
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Citation Context ...ntroducing almost no overhead to realizing privacy in a credential system. ⋆ This research was carried out while the author was visiting IBM Zürich Research Laboratory.sAn anonymous credential system =-=[18, 19, 21, 25, 34]-=- consists of users and organizations. Organizations know the users only by pseudonyms. Different pseudonyms of the same user cannot be linked. Yet, an organization can issue a credential to a pseudony... |

41 | Chaum and Eugène van Heyst. Group signatures - David - 1991 |

34 |
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Citation Context ...d non-transferability. That is, sharing a credential implies also sharing a particular, valuable secret key from outside the system (e.g., the secret key that gives access to the user’s bank account) =-=[26, 32, 34]-=-. However, such a valuable key does not always exist. Thus we introduce an alternative, novel way of achieving this: all-or-nothing non-transferability. Here, sharing just one pseudonym or credential ... |

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Citation Context ...ion of this and show that our circular encryption scheme satisfies it. Third, the encryption must be verifiable. To this end we review the verifiable encryption protocol due to Camenisch and Damg˚ard =-=[10]-=- and adapt it to suit our needs. Specifically, we want to enable verification without revealing the public key. We provide a verification method involving a committed public key, so that by inspecting... |

8 | Fast batch veri for modular exponentiation and digital signatures - Bellare, Garay, et al. - 1998 |

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6 |
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Citation Context ...itted public key, so that by inspecting this verifiable encryption, an adversary would not be able to discover the underlying public key. Independently of and concurrently with our work, Black et al. =-=[5]-=- proposed symmetric encryption schemes for key-dependent messages (which is what we call circular symmetric encryption) and Bellare et al. [3] studied key-private encryption (which is what we call key... |

3 |
Self-delegation with controlled propagation—or—What if you lose your laptop
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Citation Context ...d non-transferability. That is, sharing a credential implies also sharing a particular, valuable secret key from outside the system (e.g., the secret key that gives access to the user’s bank account) =-=[26, 32, 34]-=-. However, such a valuable key does not always exist. Thus we introduce an alternative, novel way of achieving this: all-or-nothing non-transferability. Here, sharing just one pseudonym or credential ... |