Cryptography in privacy-preserving applications.

Tsang Pak Kong.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 95-107).Abstracts in English and Chinese.Abstract --- p.iiAcknowledgement --- p.ivChapter 1 --- Introduction --- p.1Chapter 1.1 --- Privacy --- p.1Chapter 1.2 --- Cryptography --- p.5Chapter 1.2.1 --- History of Cryptography --- p.5Chapter 1.2.2 --- Cryptography Today --- p.6Chapter 1.2.3 --- Cryptography For Privacy --- p.7Chapter 1.3 --- Thesis Organization --- p.8Chapter 2 --- Background --- p.10Chapter 2.1 --- Notations --- p.10Chapter 2.2 --- Complexity Theory --- p.11Chapter 2.2.1 --- Order Notation --- p.11Chapter 2.2.2 --- Algorithms and Protocols --- p.11Chapter 2.2.3 --- Relations and Languages --- p.13Chapter 2.3 --- Algebra and Number Theory --- p.14Chapter 2.3.1 --- Groups --- p.14Chapter 2.3.2 --- Intractable Problems --- p.16Chapter 2.4 --- Cryptographic Primitives --- p.18Chapter 2.4.1 --- Public-Key Encryption --- p.18Chapter 2.4.2 --- Identification Protocols --- p.21Chapter 2.4.3 --- Digital Signatures --- p.22Chapter 2.4.4 --- Hash Functions --- p.24Chapter 2.4.5 --- Zero-Knowledge Proof of Knowledge --- p.26Chapter 2.4.6 --- Accumulators --- p.32Chapter 2.4.7 --- Public Key Infrastructure --- p.34Chapter 2.5 --- Zero Knowledge Proof of Knowledge Protocols in Groups of Unknown Order --- p.36Chapter 2.5.1 --- The Algebraic Setting --- p.36Chapter 2.5.2 --- Proving the Knowledge of Several Discrete Logarithms . --- p.37Chapter 2.5.3 --- Proving the Knowledge of a Representation --- p.38Chapter 2.5.4 --- Proving the Knowledge of d Out of n Equalities of Discrete Logarithms --- p.39Chapter 2.6 --- Conclusion --- p.42Chapter 3 --- Related Works --- p.43Chapter 3.1 --- Introduction --- p.43Chapter 3.2 --- Group-Oriented Signatures without Spontaneity and/or Anonymity --- p.44Chapter 3.3 --- SAG Signatures --- p.46Chapter 3.4 --- Conclusion --- p.49Chapter 4 --- Linkable Ring Signatures --- p.50Chapter 4.1 --- Introduction --- p.50Chapter 4.2 --- New Notions --- p.52Chapter 4.2.1 --- Accusatory Linking --- p.52Chapter 4.2.2 --- Non-slanderability --- p.53Chapter 4.2.3 --- Linkability in Threshold Ring Signatures --- p.54Chapter 4.2.4 --- Event-Oriented Linking --- p.55Chapter 4.3 --- Security Model --- p.56Chapter 4.3.1 --- Syntax --- p.56Chapter 4.3.2 --- Notions of Security --- p.58Chapter 4.4 --- Conclusion --- p.63Chapter 5 --- Short Linkable Ring Signatures --- p.64Chapter 5.1 --- Introduction --- p.64Chapter 5.2 --- The Construction --- p.65Chapter 5.3 --- Security Analysis --- p.68Chapter 5.3.1 --- Security Theorems --- p.68Chapter 5.3.2 --- Proofs --- p.68Chapter 5.4 --- Discussion --- p.70Chapter 5.5 --- Conclusion --- p.71Chapter 6 --- Separable Linkable Threshold Ring Signatures --- p.72Chapter 6.1 --- Introduction --- p.72Chapter 6.2 --- The Construction --- p.74Chapter 6.3 --- Security Analysis --- p.76Chapter 6.3.1 --- Security Theorems --- p.76Chapter 6.3.2 --- Proofs --- p.77Chapter 6.4 --- Discussion --- p.79Chapter 6.5 --- Conclusion --- p.80Chapter 7 --- Applications --- p.82Chapter 7.1 --- Offline Anonymous Electronic Cash --- p.83Chapter 7.1.1 --- Introduction --- p.83Chapter 7.1.2 --- Construction --- p.84Chapter 7.2 --- Electronic Voting --- p.85Chapter 7.2.1 --- Introduction --- p.85Chapter 7.2.2 --- Construction . --- p.87Chapter 7.2.3 --- Discussions --- p.88Chapter 7.3 --- Anonymous Attestation --- p.89Chapter 7.3.1 --- Introduction --- p.89Chapter 7.3.2 --- Construction --- p.90Chapter 7.4 --- Conclusion --- p.91Chapter 8 --- Conclusion --- p.92A Paper Derivation --- p.94Bibliography --- p.9

Democratic Group Signatures with Threshold Traceability

Recently, democratic group signatures(DGSs) particularly catch our attention due to their great flexibilities, \emph{i.e}., \emph{no group manager}, \emph{anonymity}, and \emph{individual traceability}. In existing DGS schemes, individual traceability says that any member in the group can reveal the actual signer\u27s identity from a given signature. In this paper, we formally describe the definition of DGS, revisit its security notions by strengthening the requirement for the property of traceability, and present a concrete DGS construction with $(t, n)$-\emph{threshold traceability} which combines the concepts of group signatures and of threshold cryptography. The idea behind the $(t, n)$-threshold traceability is to distribute between $n$ group members the capability of tracing the actual signer such that any subset of not less than $t$ members can jointly reconstruct a secret and reveal the identity of the signer while preserving security even in the presence of an active adversary which can corrupt up to $t-1$ group members

Blacklistable Anonymous Credentials: Blocking Misbehaving Users without TTPs (Extended Version)

Several credential systems have been proposed in which users can authenticate to services anonymously. Since anonymity can give users the license to misbehave, some variants allow the selective deanonymization (or linking) of misbehaving users upon a complaint to a trusted third party (TTP). The ability of the TTP to revoke a user\u27s privacy at any time, however, is too strong a punishment for misbehavior. To limit the scope of deanonymization, systems such as ``e-cash\u27\u27 have been proposed in which users are deanonymized under only certain types of well-defined misbehavior such as ``double spending.\u27\u27 While useful in some applications, it is not possible to generalize such techniques to more subjective definitions of misbehavior. We present the first anonymous credential system in which services can ``blacklist\u27\u27 misbehaving users without contacting a TTP. Since blacklisted users remain anonymous, misbehaviors can be judged subjectively without users fearing arbitrary deanonymization by a TTP

Identity-Committable Signatures and Their Extension to Group-Oriented Ring Signatures

The identity of Deep Throat , a pseudonym of the information source in the Watergate scandal, remained mysterious for more than three decades. In 2005, an ex-FBI official claimed that he was the anonymous source. Nevertheless, some are still inconvinced. In this paper, we introduce a new notion of identity-committable signatures (ICS) to ensure the anonymity of Deep Throat inside a group. A member of an organization can sign a message on behalf of himself (regular signature) or the organization (identity-committed signature). In the latter case, the signer\u27s identity is hidden from anyone, and can be opened by himself only. We describe the requirements of ICS and give the formal definition of it. Then we extend the notion of ICS to group-oriented ring signatures (GRS) which further allow the signer to hide his identity behind multiple groups. We believe a GRS scheme is more efficient and practical than a ring signature scheme for leaking secrets. Finally, we provide concrete constructions of ICS and GRS with information-theoretic anonymity, that is, the identity of the signer is fully-protected

PPAA: Peer-to-Peer Anonymous Authentication (Extended Version)

In the pursuit of authentication schemes that balance user privacy and accountability, numerous anonymous credential systems have been constructed. However, existing systems assume a client-server architecture in which only the clients, but not the servers, care about their privacy. In peer-to-peer (P2P) systems where both clients and servers are peer users with privacy concerns, no existing system correctly strikes that balance between privacy and accountability. In this paper, we provide this missing piece: a credential system in which peers are {\em pseudonymous} to one another (that is, two who interact more than once can recognize each other via pseudonyms) but are otherwise anonymous and unlinkable across different peers. Such a credential system finds applications in, e.g., Vehicular Ad-hoc Networks (VANets) and P2P networks. We formalize the security requirements of our proposed credential system, provide a construction for it, and prove the security of our construction. Our solution is efficient: its complexities are independent of the number of users in the system

On the Portability of Generalized Schnorr Proofs

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Thring Signatures and their Applications to Spender-Ambiguous Digital Currencies

We present threshold ring multi-signatures (thring signatures) for collaborative computation of ring signatures. We discuss a game of existential forgery for thring signatures and the uses of thring signatures in digital currencies, including spender-ambiguous cross-chain atomic swaps for confidential amounts without a trusted set-up. We present an implementation of thring signatures inspired by the works of [13], [20], [14], [1], [18], and [15] we call linkable spontaneous threshold anonymous group (LSTAG) signatures, and we prove the implementation existentially unforgeable under the plain public key and random oracle models