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