Cryptography and Computational Number Theory

1. Front Matter

   Pages i-viii

   PDF

2. Computational Number Theory

   1. Front Matter

      Pages 1-1

      PDF

   2. On the Dimension and the Number of Parameters of a Unirational Variety

      • Cesar Alonso, Jaime Gutierrez, Rosario Rubio

      Pages 3-9

   3. On Elements of High Order in Finite Fields

      • Alessandro Conflitti

      Pages 11-14

   4. Counting the Number of Points on Affine Diagonal Curves

      • Cunsheng Ding, David R. Kohel, San Ling

      Pages 15-24

   5. Small Values of the Carmichael Function and Cryptographic Applications

      • John B. Friedlander, Carl Pomerance, Igor E. Shparlinski

      Pages 25-32

   6. Density Estimates Related to Gauß Periods

      • Joachim von zur Gathen, Francesco Pappalardi

      Pages 33-41

   7. The Distribution of the Coefficients of Primitive Polynomials over Finite Fields

      • Wenbao Han

      Pages 43-57

   8. The Distribution of the Quadratic Symbol in Function Fields and a Faster Mathematical Stream Cipher

      • Jeffrey Hoffstein, Daniel Lieman

      Pages 59-68

   9. Rational Groups of Elliptic Curves Suitable for Cryptography

      • David R. Kohel

      Pages 69-80

   10. Effective Determination of the Proportion of Split Primes in Number Fields

       • Kwok Yan Lam, Francesco Sica

       Pages 81-92

   11. Algorithms for Generating, Testing and Proving Primes: A Survey

       • Preda Mihăilescu

       Pages 93-122

   12. Elliptic Curve Factorization Using a “Partially Oblivious” Function

       • René Peralta

       Pages 123-128

   13. The Hermite-Serret Algorithm and 122 + 332

       • Alf van der Poorten

       Pages 129-136

   14. Applications of Algebraic Curves to Constructions of Sequences

       • Chaoping Xing

       Pages 137-146

3. Cryptography

   1. Front Matter

      Pages 147-147

      PDF

   2. Designated 2-Verifier Proofs and their Application to Electronic Commerce

      • Nikos Alexandris, Vassilis Chrissikopoulos, Mike Burmester, Yvo Desmedt

      Pages 149-163

   3. A Survey of Divide and Conquer Attacks on Certain Irregularly Clocked Stream Ciphers

      • Ed Dawson, Leonie Simpson, Jovan Golić

      Pages 165-185

   4. New Results on the Randomness of Visual Cryptography Schemes

      • Annalisa De Bonis, Alfredo De Santis

      Pages 187-201

   5. Authentication-Myths and Misconceptions

      • Dieter Gollmann

      Pages 203-225

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.

• Computer Science
• computational number theory
• cryptography
• cryptosystems
• information
• number theory
• theoretical computer science

• Department of Computer Science, National University of Singapore, Singapore

  Kwok-Yan Lam

• Department of Computing, Macquarie University, Australia

  Igor Shparlinski

• Department of Computer Science, University of Wollongong, Australia

  Huaxiong Wang

• Department of Mathematics, National University of Singapore, Singapore

  Chaoping Xing

Policies and ethics