Cryptography and Computational Number Theory

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

• Publisher: Springer
• Year: 2001
• Tongue: English
• Leaves: 375
• 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

Front Matter....Pages i-viii
Front Matter....Pages 1-1
On the Dimension and the Number of Parameters of a Unirational Variety....Pages 3-9
On Elements of High Order in Finite Fields....Pages 11-14
Counting the Number of Points on Affine Diagonal Curves....Pages 15-24
Small Values of the Carmichael Function and Cryptographic Applications....Pages 25-32
Density Estimates Related to Gauß Periods....Pages 33-41
The Distribution of the Coefficients of Primitive Polynomials over Finite Fields....Pages 43-57
The Distribution of the Quadratic Symbol in Function Fields and a Faster Mathematical Stream Cipher....Pages 59-68
Rational Groups of Elliptic Curves Suitable for Cryptography....Pages 69-80
Effective Determination of the Proportion of Split Primes in Number Fields....Pages 81-92
Algorithms for Generating, Testing and Proving Primes: A Survey....Pages 93-122
Elliptic Curve Factorization Using a “Partially Oblivious” Function....Pages 123-128
The Hermite-Serret Algorithm and 12 2 + 33 2 ....Pages 129-136
Applications of Algebraic Curves to Constructions of Sequences....Pages 137-146
Front Matter....Pages 147-147
Designated 2-Verifier Proofs and their Application to Electronic Commerce....Pages 149-163
A Survey of Divide and Conquer Attacks on Certain Irregularly Clocked Stream Ciphers....Pages 165-185
New Results on the Randomness of Visual Cryptography Schemes....Pages 187-201
Authentication-Myths and Misconceptions....Pages 203-225
A Survey of Hard Core Functions....Pages 227-255
On the Security of Diffie-Hellman Bits....Pages 257-268
Polynomial Rings and Efficient Public Key Authentication II....Pages 269-286
Front Matter....Pages 147-147
Security of Biased Sources for Cryptographic Keys....Pages 287-302
Achieving Optimal Fairness from Biased Coinflips....Pages 303-319
The Dark Side of the Hidden Number Problem: Lattice Attacks on DSA....Pages 321-330
Distribution of Modular Sums and the Security of the Server Aided Exponentiation....Pages 331-342
A General Construction for Fail-Stop Signature using Authentication Codes....Pages 343-356
Robust Additive Secret Sharing Schemes over Z m ....Pages 357-368
RSA Public Key Validation....Pages 369-378

✦ Subjects

Data Encryption; Number Theory