Cryptography and Computational Number Theory

✍ Scribed by Kwok-Yan Lam, Igor Shparlinski, Huaxiong Wang, Chaoping Xing (eds.)

• Publisher: Springer
• Year: 2001
• Tongue: English
• Leaves: 374
• Series: Progress in Computer Science and Applied Logic 20
• Category: Library

✦ Synopsis

This volume contains the refereed proceedings of the Workshop on Cryptography and Computational Number Theory, CCNT'99, which has been held in Singapore during the week of November 22-26, 1999. The workshop was organized by the Centre for Systems Security of the Na­ tional University of Singapore. We gratefully acknowledge the financial support from the Singapore National Science and Technology Board under the grant num­ ber RP960668/M. The idea for this workshop grew out of the recognition of the recent, rapid development in various areas of cryptography and computational number the­ ory. The event followed the concept of the research programs at such well-known research institutions as the Newton Institute (UK), Oberwolfach and Dagstuhl (Germany), and Luminy (France). Accordingly, there were only invited lectures at the workshop with plenty of time for informal discussions. It was hoped and successfully achieved that the meeting would encourage and stimulate further research in information and computer security as well as in the design and implementation of number theoretic cryptosystems and other related areas. Another goal of the meeting was to stimulate collaboration and more active interaction between mathematicians, computer scientists, practical cryptographers and engineers in academia, industry and government.

✦ Table of Contents

Cover......Page 1
Front matter......Page 2
1. On the Dimension and the Number of Parameters of a Unirational Variety......Page 10
2. On Elements of High Order in Finite Fields......Page 17
3. Counting the Number of Points on Affine Diagonal Curves......Page 21
4. Small Values of the Carmichael Function and Cryptographic Applications......Page 31
5. Density Estimates Related to Gauß Periods......Page 39
6. The Distribution of the Coefficients of Primitive Polynomials over Finite Fields......Page 48
7. The Distribution of the Quadratic Symbol in Function Fields and a Faster Mathematical Stream Cipher......Page 63
8. Rational Groups of Elliptic Curves Suitable for Cryptography......Page 73
9. Effective Determination of the Proportion of Split Primes in Number Fields......Page 85
10. Algorithms for Generating, Testing and Proving Primes: A Survey......Page 97
11. Elliptic Curve Factorization Using a “Partially Oblivious” Function......Page 127
12. The Hermite-Serret Algorithm and 12......Page 133
13. Applications of Algebraic Curves to Constructions of Sequences......Page 141
14. Designated 2-Verifier Proofs and their Application to Electronic Commerce......Page 151
15. A Survey of Divide and Conquer Attacks on Certain Irregularly Clocked Stream Ciphers......Page 166
16. New Results on the Randomness of Visual Cryptography Schemes......Page 187
17. Authentication-Myths and Misconceptions......Page 202
18. A Survey of Hard Core Functions......Page 225
19. On the Security of Diffie-Hellman Bits......Page 254
20. Polynomial Rings and Efficient Public Key Authentication II......Page 266
21. Security of Biased Sources for Cryptographic Keys......Page 284
22. Achieving Optimal Fairness from Biased Coinflips......Page 300
23. The Dark Side of the Hidden Number Problem: Lattice Attacks on DSA......Page 317
24. Distribution of Modular Sums and the Security of the Server Aided Exponentiation......Page 327
25. A General Construction for Fail-Stop Signature using Authentication Codes......Page 339
26. Robust Additive Secret Sharing Schemes over Z......Page 353
27. RSA Public Key Validation......Page 365