Study on elliptic curve public key cryptosystems with application of pseudorandom number generator.

by Yuen Ching Wah.Thesis (M.Phil.)--Chinese University of Hong Kong, 1998.Includes bibliographical references (leaves 61-[63]).Abstract also in Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Why use cryptography? --- p.1Chapter 1.2 --- Why is authentication important ？ --- p.2Chapter 1.3 --- What is the relationship between authentication and digital sig- nature? --- p.3Chapter 1.4 --- Why is random number important? --- p.3Chapter 2 --- Background --- p.5Chapter 2.1 --- Cryptography --- p.5Chapter 2.1.1 --- Symmetric key cryptography --- p.5Chapter 2.1.2 --- Asymmetric key cryptography --- p.7Chapter 2.1.3 --- Authentication --- p.8Chapter 2.2 --- Elliptic curve cryptography --- p.9Chapter 2.2.1 --- Mathematical background for Elliptic curve cryptography --- p.10Chapter 2.3 --- Pseudorandom number generator --- p.12Chapter 2.3.1 --- Linear Congruential Generator --- p.13Chapter 2.3.2 --- Inversive Congruential Generator --- p.13Chapter 2.3.3 --- PN-sequence generator --- p.14Chapter 2.4 --- Digital Signature Scheme --- p.14Chapter 2.5 --- Babai's lattice vector algorithm --- p.16Chapter 2.5.1 --- First Algorithm: Rounding Off --- p.17Chapter 2.5.2 --- Second Algorithm: Nearest Plane --- p.17Chapter 3 --- Several Digital Signature Schemes --- p.18Chapter 3.1 --- DSA --- p.19Chapter 3.2 --- Nyberg-Rueppel Digital Signature --- p.21Chapter 3.3 --- EC.DSA --- p.23Chapter 3.4 --- EC-Nyberg-Rueppel Digital Signature Scheme --- p.26Chapter 4 --- Miscellaneous Digital Signature Schemes and their PRNG --- p.29Chapter 4.1 --- DSA with LCG --- p.30Chapter 4.2 --- DSA with PN-sequence --- p.33Chapter 4.2.1 --- Solution --- p.35Chapter 4.3 --- DSA with ICG --- p.39Chapter 4.3.1 --- Solution --- p.40Chapter 4.4 --- EC_DSA with PN-sequence --- p.43Chapter 4.4.1 --- Solution --- p.44Chapter 4.5 --- EC一DSA with LCG --- p.45Chapter 4.5.1 --- Solution --- p.46Chapter 4.6 --- EC-DSA with ICG --- p.46Chapter 4.6.1 --- Solution --- p.47Chapter 4.7 --- Nyberg-Rueppel Digital Signature with PN-sequence --- p.48Chapter 4.7.1 --- Solution --- p.49Chapter 4.8 --- Nyberg-Rueppel Digital Signature with LCG --- p.50Chapter 4.8.1 --- Solution --- p.50Chapter 4.9 --- Nyberg-Rueppel Digital Signature with ICG --- p.51Chapter 4.9.1 --- Solution --- p.52Chapter 4.10 --- EC- Nyberg-Rueppel Digital Signature with LCG --- p.53Chapter 4.10.1 --- Solution --- p.54Chapter 4.11 --- EC- Nyberg-Rueppel Digital Signature with PN-sequence --- p.55Chapter 4.11.1 --- Solution --- p.56Chapter 4.12 --- EC-Nyberg-Rueppel Digital Signature with ICG --- p.56Chapter 4.12.1 --- Solution --- p.57Chapter 5 --- Conclusion --- p.59Bibliography --- p.6