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Open Problems in Mathematics and Computational Science

  • Book
  • © 2014

Overview

Editors:
  1. Çetin Kaya Koç

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

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  • Aims to motivate the mathematical and computational sciences community to discuss open problems
  • Presents interesting, creative approaches to problem-solving
  • Authors among the leading researchers in their fields

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter 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
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Keywords

About this book

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.

Reviews

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

Editors and Affiliations

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

    Çetin Kaya Koç

About the editor

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.

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