Titlebook: Open Problems in Mathematics and Computational Science; ?etin Kaya Ko? Book 2014 Springer International Publishing Switzerland 2014 Coding

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About Open Problems,ng the Bosphorus Straits to discuss several difficult problems they and others in similar fields are tackling. The motivation of the . was to enable and encourage the academic community, particularly young researchers and Ph.D. candidates, to hear about unsolved, open problems in mathematical and co

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The Past, Evolving Present, and Future of the Discrete Logarithm,discrete logarithms are hard to compute. This intractability hypothesis is also the foundation for the security of a large variety of other public key systems and protocols..Since the introduction of the Diffie–Hellman key exchange more than three decades ago, there have been substantial algorithmic

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Isogenies in Theory and Praxis,. This is a wide and deep territory with a huge amount of research activity and exciting results ranging from the highlights of pure mathematics like the proof of Fermat’s last theorem to stunning applications to public-key cryptography. Necessarily we have to be rather superficial, and thus special

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Another Look at Security Theorems for 1-Key Nested MACs, proof has some advantages over earlier proofs: it is in the uniform model, it uses a weaker related-key assumption, and it covers a broad class of MACs in a single theorem. However, we also explain why our theorem is of doubtful value in assessing the real-world security of these MAC schemes. In ad

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Open Problems for Polynomials over Finite Fields and Applications,of polynomials. The open problems in that part of the survey are of a more theoretical nature. Then, we center on classes of low-weight (irreducible) polynomials. The conjectures here are more practically oriented. Finally, we give brief descriptions of a selection of open problems from several area

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Generating Good Span , Sequences Using Orthogonal Functions in Nonlinear Feedback Shift Registers, and has the following randomness properties: period 2. ? 1, balance, and ideal .-tuple distribution. A span . sequence may have a high linear span. However, how to find a nonlinear feedback function that generates such a sequence constitutes a long-standing challenging problem for about 5 decades s

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Open Problems on the Cross-correlation of ,-Sequences,ngth linear sequences (or .-sequences) are popular in sequence designs due to their long period and excellent pseudorandom properties. In code-division multiple-access (CDMA) applications, there is a demand for large families of sequences having good correlation properties. The best families of sequ

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Open Problems on With-Carry Sequence Generators,edback shift registers (LFSRs) to generate such sequences, either directly or as components in more complex structures. Much of the analysis of such sequences is done using the algebra of polynomials and power series over finite fields. The subjects of this chapter are feedback with carry shift regi

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On Semi-bent Functions and Related Plateaued Functions Over the Galois Field ,,arious cryptographic characteristics. They are defined in terms of the Walsh–Hadamard spectrum. Plateaued functions bring together various nonlinear characteristics and include two important classes of Boolean functions defined in even dimension: the well-known bent functions and the semi-bent funct