Cryptanalysis of a digital signature scheme of W. He.

Wong, Chun Kuen.Thesis (M.Phil.)--Chinese University of Hong Kong, 2002.Includes bibliographical references (leaves 43-45).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Origin of The First Digital Signature Scheme --- p.2Chapter 1.2 --- On the security of digital signature schemes --- p.3Chapter 1.3 --- Organization of the Thesis --- p.4Chapter 2 --- Mathematical Background --- p.6Chapter 2.1 --- Divisibility --- p.6Chapter 2.2 --- Prime --- p.7Chapter 2.3 --- Modular arithmetic --- p.7Chapter 2.4 --- Congruence --- p.7Chapter 2.5 --- Greatest Common Divisor --- p.7Chapter 2.6 --- Integers modulo n --- p.8Chapter 2.7 --- Inverse --- p.8Chapter 2.8 --- Division in Zn --- p.8Chapter 2.9 --- Order of element --- p.8Chapter 2.10 --- Euclidean Algorithm --- p.9Chapter 2.11 --- Extended Euclidean Algorithm --- p.9Chapter 2.12 --- Chinese Remainder Theorem --- p.10Chapter 2.13 --- Relatively Prime --- p.10Chapter 2.14 --- Euler Totient Function --- p.10Chapter 2.15 --- Fermat's Little Theorem --- p.11Chapter 2.16 --- Euler's Theorem --- p.11Chapter 2.17 --- Square root --- p.12Chapter 2.18 --- Quadratic residue --- p.12Chapter 2.19 --- Legendre Symbol --- p.13Chapter 2.20 --- Jacobi Symbol --- p.14Chapter 2.21 --- Blum Integer --- p.15Chapter 2.22 --- The Factoring Problem --- p.16Chapter 2.23 --- The Discrete Logarithm Problem --- p.17Chapter 2.24 --- One-way Hash Function --- p.17Chapter 3 --- Survey of digital signature schemes --- p.19Chapter 3.1 --- The RSA signature scheme --- p.19Chapter 3.1.1 --- Key generation in the RSA signature scheme --- p.20Chapter 3.1.2 --- Signature generation in the RSA signature scheme --- p.20Chapter 3.1.3 --- Signature verification in the RSA signature scheme --- p.20Chapter 3.1.4 --- On the security of the RSA signature scheme --- p.21Chapter 3.2 --- The ElGamal signature scheme --- p.22Chapter 3.2.1 --- Key generation in the ElGamal signature scheme --- p.23Chapter 3.2.2 --- Signature generation in the ElGamal signature scheme --- p.23Chapter 3.2.3 --- Signature verification in the ElGamal signature scheme --- p.23Chapter 3.2.4 --- On the security of the ElGamal signature scheme --- p.24Chapter 3.3 --- The Schnorr signature scheme --- p.26Chapter 3.3.1 --- Key generation in the Schnorr signature scheme --- p.26Chapter 3.3.2 --- Signature generation in the Schnorr signature scheme --- p.26Chapter 3.3.3 --- Signature verification in the Schnorr signature scheme --- p.27Chapter 3.3.4 --- Discussion --- p.27Chapter 3.4 --- Digital signature schemes based on both the factoring and discrete logarithm problems --- p.27Chapter 3.4.1 --- The Brickell-McCurley signature scheme --- p.28Chapter 3.4.2 --- The Okamoto signature scheme --- p.29Chapter 3.4.3 --- The Harn signature scheme --- p.30Chapter 3.4.4 --- The Shao signature scheme --- p.30Chapter 3.4.5 --- The W. He signature scheme --- p.31Chapter 4 --- Cryptanalysis of the digital signature scheme of W. He --- p.32Chapter 4.1 --- The Digital Signature Scheme of W. He --- p.33Chapter 4.1.1 --- System setup in the W. He Digital Signature Scheme --- p.33Chapter 4.1.2 --- Key generation in the W. He Digital Signature Scheme --- p.34Chapter 4.1.3 --- Signature generation in the W. He Digital Signature Scheme --- p.34Chapter 4.1.4 --- Signature verification in the W. He Digital Signature Scheme --- p.34Chapter 4.2 --- Cryptanalysis of the digital signature scheme of W. He --- p.35Chapter 4.2.1 --- Theorems on the security of the digital signature scheme of W. He --- p.35Chapter 4.2.2 --- Signature Forgery in the digital signature scheme of W. He --- p.37Chapter 4.2.3 --- Remedy --- p.40Chapter 5 --- Conclusions --- p.41Bibliography --- p.4