Open Problems in Mathematics and Computational Science

1. Front Matter

   Pages i-viii

   PDF

2. About Open Problems

   • Çetin Kaya Koç

   Pages 1-4

3. The Past, Evolving Present, and Future of the Discrete Logarithm

   • Antoine Joux, Andrew Odlyzko, Cécile Pierrot

   Pages 5-36

4. Isogenies in Theory and Praxis

   • Gerhard Frey

   Pages 37-68

5. Another Look at Security Theorems for 1-Key Nested MACs

   • Neal Koblitz, Alfred Menezes

   Pages 69-89

6. Non-extendable \(\mathbb{F}_{q}\)-Quadratic Perfect Nonlinear Maps

   • Ferruh Özbudak, Alexander Pott

   Pages 91-110

7. Open Problems for Polynomials over Finite Fields and Applications

   • Daniel Panario

   Pages 111-126

8. Generating Good Span n Sequences Using Orthogonal Functions in Nonlinear Feedback Shift Registers

   • Kalikinkar Mandal, Guang Gong

   Pages 127-162

9. Open Problems on the Cross-correlation of m-Sequences

   • Tor Helleseth

   Pages 163-179

10. Open Problems on With-Carry Sequence Generators

    • Andrew Klapper

    Pages 181-201

11. Open Problems on Binary Bent Functions

    • Claude Carlet

    Pages 203-241

12. On Semi-bent Functions and Related Plateaued Functions Over the Galois Field \(\mathbb{F}_{2^{n}}\)

    • Sihem Mesnager

    Pages 243-273

13. True Random Number Generators

    • Mario Stipčević, Çetin Kaya Koç

    Pages 275-315

14. How to Sign Paper Contracts? Conjectures and Evidence Related to Equitable and Efficient Collaborative Task Scheduling

    • Eric Brier, David Naccache, Li-yao Xia

    Pages 317-340

15. Theoretical Parallel Computing Models for GPU Computing

    • Koji Nakano

    Pages 341-359

16. Membrane Computing: Basics and Frontiers

    • Gheorghe Păun

    Pages 361-385

17. A Panorama of Post-quantum Cryptography

    • Paulo S. L. M. Barreto, Felipe Piazza Biasi, Ricardo Dahab, Julio César López-Hernández, Eduardo M. de Morais, Ana D. Salina de Oliveira et al.

    Pages 387-439

This book presents interesting, important unsolved problems in the mathematical and computational sciences. The contributing authors are leading researchers in their fields and they explain outstanding challenges in their domains, first by offering basic definitions, explaining the context, and summarizing related algorithms, theorems, and proofs, and then by suggesting creative solutions.

 

The authors feel a strong motivation to excite deep research and discussion in the mathematical and computational sciences community, and the book will be of value to postgraduate students and researchers in the areas of theoretical computer science, discrete mathematics, engineering, and cryptology.

• Coding theory
• Cryptanalysis
• Discrete mathematics
• Number theory
• Random number generators (RNGs);

“This is a worthwhile collection, especially for young researchers.” (J. H. Davenport, Computing Reviews, October, 2015)

• Dept. of Computer Science, University of California, Santa Barbara, Santa Barbara, USA

  Çetin Kaya Koç

Prof. Çetin Kaya Koç is a research professor in the Dept. of Computer Science and the College of Creative Studies at the University of California, Santa Barbara. He received his Ph.D. in Electrical and Computer Engineering from UCSB in 1988, and was an assistant professor at the University of Houston, and a full professor at Oregon State University. He cofounded the Workshop on Cryptographic Hardware and Embedded Systems, and he is the founding Editor-in-Chief of the Journal of Cryptographic Hardware. His research interests are in cryptographic hardware and embedded systems, secure hardware design, side-channel attacks and countermeasures, algorithms, and architectures for computer arithmetic and finite fields. He was elected as an IEEE Fellow for his contributions to cryptographic engineering.

Policies and ethics