Ebook: Cryptography and Computational Number Theory

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.

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The fields of cryptography and computational number theory have recently witnessed a rapid development, which was the subject of the CCNT workshop in Singapore in November 1999. Its aim was to stimulate further research in information and computer security as well as the design and implementation of number theoretic cryptosystems and other related areas. Another achievement of the meeting was the collaboration of mathematicians, computer scientists, practical cryptographers and engineers in academia, industry and government. The present volume comprises a selection of refereed papers originating from this event, presenting either a survey of some area or original and new results. They concern many different aspects of the field such as theory, techniques, applications and practical experience. It provides a state-of-the-art report on some number theoretical issues of significance to cryptography.

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The fields of cryptography and computational number theory have recently witnessed a rapid development, which was the subject of the CCNT workshop in Singapore in November 1999. Its aim was to stimulate further research in information and computer security as well as the design and implementation of number theoretic cryptosystems and other related areas. Another achievement of the meeting was the collaboration of mathematicians, computer scientists, practical cryptographers and engineers in academia, industry and government. The present volume comprises a selection of refereed papers originating from this event, presenting either a survey of some area or original and new results. They concern many different aspects of the field such as theory, techniques, applications and practical experience. It provides a state-of-the-art report on some number theoretical issues of significance to cryptography.
Content:
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 Gau? 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
Applications of Algebraic Curves to Constructions of Sequences....Pages 129-136
Front Matter....Pages 137-146
Designated 2-Verifier Proofs and their Application to Electronic Commerce....Pages 147-147
A Survey of Divide and Conquer Attacks on Certain Irregularly Clocked Stream Ciphers....Pages 149-163
New Results on the Randomness of Visual Cryptography Schemes....Pages 165-185
Authentication-Myths and Misconceptions....Pages 187-201
A Survey of Hard Core Functions....Pages 203-225
On the Security of Diffie-Hellman Bits....Pages 227-255
Polynomial Rings and Efficient Public Key Authentication II....Pages 257-268
Front Matter....Pages 269-286
Security of Biased Sources for Cryptographic Keys....Pages 147-147
Achieving Optimal Fairness from Biased Coinflips....Pages 287-302
The Dark Side of the Hidden Number Problem: Lattice Attacks on DSA....Pages 303-319
Distribution of Modular Sums and the Security of the Server Aided Exponentiation....Pages 321-330
A General Construction for Fail-Stop Signature using Authentication Codes....Pages 331-342
RSA Public Key Validation....Pages 343-356
....Pages 357-368