Spontaneous anonymous group cryptography and its applications.

Fung Kar-Yin.Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.Includes bibliographical references (leaves 72-81).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Development of Cryptography --- p.1Chapter 1.2 --- Group Cryptography --- p.3Chapter 1.3 --- Spontaneous Anonymous Group Signature --- p.4Chapter 1.4 --- Blind Signature --- p.5Chapter 1.5 --- Blind SAG Signature --- p.6Chapter 1.6 --- Organization of This Thesis --- p.6Chapter 2 --- Background Study --- p.7Chapter 2.1 --- Six Primitives in Cryptography --- p.7Chapter 2.1.1 --- Symmetric Encryption --- p.8Chapter 2.1.2 --- Asymmetric Encryption --- p.8Chapter 2.1.3 --- Digital Signature --- p.9Chapter 2.1.4 --- Hash Function --- p.9Chapter 2.1.5 --- Digital Certificate --- p.10Chapter 2.1.6 --- Proof of Knowledge --- p.10Chapter 2.2 --- Euler Totient Function --- p.11Chapter 2.3 --- One-Way Function --- p.12Chapter 2.3.1 --- One-Way Trapdoor Function --- p.13Chapter 2.3.2 --- Discrete Logarithm Problem --- p.13Chapter 2.3.3 --- RSA Problem --- p.14Chapter 2.3.4 --- Integer Factorization Problem --- p.15Chapter 2.3.5 --- Quadratic Residuosity Problem --- p.15Chapter 2.3.6 --- Schnorr's ROS assumption --- p.16Chapter 2.4 --- Bilinear Pairing --- p.16Chapter 2.4.1 --- Weil Pairing --- p.18Chapter 2.4.2 --- Tate Pairing --- p.18Chapter 2.5 --- Gap Diffie-Hellman Group --- p.19Chapter 2.5.1 --- GDH --- p.19Chapter 2.5.2 --- Co-GDH --- p.20Chapter 2.6 --- Random Oracle Model --- p.21Chapter 2.6.1 --- Random Permutation --- p.23Chapter 2.6.2 --- Lunchtime Attack --- p.23Chapter 2.6.3 --- Back Patch --- p.23Chapter 2.6.4 --- Rewind Simulation --- p.24Chapter 2.7 --- Generic Group Model --- p.24Chapter 3 --- Digital and Threshold Signatures --- p.26Chapter 3.1 --- Introduction --- p.26Chapter 3.2 --- Notion of Attacks and Security in Signature --- p.28Chapter 3.2.1 --- Types of Signatures --- p.29Chapter 3.3 --- Threshold Signature --- p.31Chapter 3.4 --- Properties in Threshold Signatures --- p.31Chapter 4 --- Blind Signature --- p.33Chapter 4.1 --- Introduction --- p.33Chapter 4.1.1 --- Security Requirements --- p.35Chapter 4.2 --- Transferred Proof of Knowledge --- p.36Chapter 4.3 --- RSA Based Schemes --- p.37Chapter 4.3.1 --- Chaum's RSA Scheme --- p.37Chapter 4.3.2 --- Abe's RSA Scheme --- p.38Chapter 4.4 --- Discrete Logarithm Based Schemes --- p.39Chapter 4.4.1 --- Schnorr Blind Signature --- p.39Chapter 4.4.2 --- Okamoto-Schnorr Blind Signature --- p.40Chapter 4.5 --- Bilinear Mapping Based Schemes --- p.40Chapter 5 --- Spontaneous Anonymous Group Signature --- p.42Chapter 5.1 --- Introduction --- p.42Chapter 5.2 --- Cramer-Damgard-Schoemaker (CDS) SAG Signature --- p.44Chapter 5.2.1 --- (1´ةn)-CDS type SAG Signature --- p.44Chapter 5.2.2 --- "(t, n)-CDS type SAG Signature" --- p.45Chapter 5.3 --- Ring-type SAG Signature Schemes --- p.46Chapter 5.3.1 --- Rivest-Shamir-Tauman --- p.46Chapter 5.3.2 --- Abe's 1-out-of-n Ring Signature --- p.49Chapter 5.4 --- Discussions --- p.51Chapter 6 --- Blind SAG Signature --- p.53Chapter 6.1 --- Introduction --- p.53Chapter 6.2 --- Security Definitions --- p.54Chapter 6.2.1 --- Security Model --- p.55Chapter 6.3 --- "(1,n)-Ring Structured Blind SAG Signature" --- p.57Chapter 6.3.1 --- Signing Protocol --- p.58Chapter 6.3.2 --- Verification Algorithm --- p.58Chapter 6.4 --- CDS-type Blind SAG Signature --- p.59Chapter 6.4.1 --- "(l,n)-CDS-type" --- p.59Chapter 6.5 --- "(t,n)-CDS-type" --- p.60Chapter 6.5.1 --- Signing Protocol --- p.61Chapter 6.5.2 --- Verification Algorithm --- p.61Chapter 6.6 --- Security Analysis --- p.62Chapter 6.7 --- Applications to Credential System --- p.67Chapter 7 --- Conclusion --- p.69A --- p.71Bibliography --- p.8

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