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This book is dealing with three mathematical areas, namely polynomial matrices over finite fields, linear systems and coding theory. Primeness properties of polynomial matrices provide criteria for the reachability and observability of interconnected linear systems. Since time-discrete linear systems over finite fields and convolutional codes are basically the same objects, these results could be transferred to criteria for non-catastrophicity of convolutional codes. In particular, formulas for the number of pairwise coprime polynomials and for the number of mutually left coprime polynomial matrices are calculated. This leads to the probability that a parallel connected linear system is reachable and that a parallel connected convolutional code is non-catastrophic. Moreover, other networks of linear systems and convolutional codes are considered.
This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm. The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science.
Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and
This book constitutes the thoroughly refereed post-conference proceedings of the 22nd International Workshop on Fast Software Encryption, held in Istanbul, Turkey, March 8-11, 2015. The 28 revised full papers presented were carefully reviewed and selected from 71 initial submissions. The papers are organized in topical sections on block cipher cryptanalysis; understanding attacks; implementation issues; more block cipher cryptanalysis; cryptanalysis of authenticated encryption schemes; proofs; design; lightweight; cryptanalysis of hash functions and stream ciphers; and mass surveillance.
This book constitutes the thoroughly refereed proceedings of the 8th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICACRYPT 2016, held in Fes, Morooco, in April 2016. The 18 papers presented in this book were carefully reviewed and selected from 65 submissions. The aim of Africacrypt 2016 is to provide an international forum for practitioners and researchers from industry, academia and government from all over the world for a wide ranging discussion of all forms of cryptography. Topics of interest are such as lattices; elliptic curves; secret-key cryptanalysis; efficient implementations; secure protocols; and public-key cryptography.
MATRIX is Australia’s international, residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each lasting 1-4 weeks. This book is a scientific record of the five programs held at MATRIX in its first year, 2016: - Higher Structures in Geometry and Physics - Winter of Disconnectedness - Approximation and Optimisation - Refining C*-Algebraic Invariants for Dynamics using KK-theory - Interactions between Topological Recursion, Modularity, Quantum Invariants and Low- dimensional Topology The MATRIX Scientific Committee selected these programs based on their scientific excellence and the participation rate of high-profile international participants. Each program included ample unstructured time to encourage collaborative research; some of the longer programs also included an embedded conference or lecture series. The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on selected topics related to the MATRIX program; the remaining contributions are predominantly lecture notes based on talks or activities at MATRIX.
This book constitutes the thoroughly refereed post-proceedings of the 7th International Conference on Finite Fields and Applications, Fq7, held in Toulouse, France, in May 2004. The 19 revised full papers presented were carefully selected from around 60 presentations at the conference during two rounds of reviewing and revision. Among the topics addressed are Weierstrass semigroups, Galois rings, hyperelliptic curves, polynomial irreducibility, pseudorandom number sequences, permutation polynomials, random polynomials, matrices, function fields, ramified towers, BCH codes, cyclic codes, primitive polynomials, covering sequences, cyclic decompositions.
The three volume-set, LNCS 9814, LNCS 9815, and LNCS 9816, constitutes the refereed proceedings of the 36th Annual International Cryptology Conference, CRYPTO 2016, held in Santa Barbara, CA, USA, in August 2016. The 70 revised full papers presented were carefully reviewed and selected from 274 submissions. The papers are organized in the following topical sections: provable security for symmetric cryptography; asymmetric cryptography and cryptanalysis; cryptography in theory and practice; compromised systems; symmetric cryptanalysis; algorithmic number theory; symmetric primitives; asymmetric cryptography; symmetric cryptography; cryptanalytic tools; hardware-oriented cryptography; secure computation and protocols; obfuscation; quantum techniques; spooky encryption; IBE, ABE, and functional encryption; automated tools and synthesis; zero knowledge; theory.
This book constitutes the refereed proceedings of the 13th International Workshop on Security, IWSEC 2018, held in Sendai, Japan, in September 2018. The 18 regular papers and 2 short papers presented in this volume were carefully reviewed and selected from 64 submissions. They were organized in topical sections named: Cryptanalysis, Implementation Security, Public-Key Primitives, Security in Practice, Secret Sharing, Symmetric-Key Primitives, and Provable Security.
The three volume-set LNCS 11476, 11477, and 11478 constitute the thoroughly refereed proceedings of the 38th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2019,held in Darmstadt, Germany, in May 2019. The 76 full papers presented were carefully reviewed and selected from 327 submissions. The papers are organized into the following topical sections: ABE and CCA security; succinct arguments and secure messaging; obfuscation; block ciphers; differential privacy; bounds for symmetric cryptography; non-malleability; blockchain and consensus; homomorphic primitives; standards; searchable encryption and ORAM; proofs of work and space; secure computation; quantum, secure computation and NIZK, lattice-based cryptography; foundations; efficient secure computation; signatures; information-theoretic cryptography; and cryptanalysis.