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Finite Fields

Author: Rudolf Lidl
Publisher: Cambridge University Press
ISBN: 9780521392310
Size: 78.94 MB
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This book is devoted entirely to the theory of finite fields.

Theory And Applications Of Finite Fields

Author: Michel Lavrauw
Publisher: American Mathematical Soc.
ISBN: 0821852981
Size: 50.58 MB
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This volume contains the proceedings of the 10th International Congress on Finite Fields and their Applications (Fq 10), held July 11-15, 2011, in Ghent, Belgium. Research on finite fields and their practical applications continues to flourish. This volume's topics, which include finite geometry, finite semifields, bent functions, polynomial theory, designs, and function fields, show the variety of research in this area and prove the tremendous importance of finite field theory.

Finite Fields

Author: Lidl
Publisher: Cambridge University Press
ISBN: 9780521302401
Size: 23.51 MB
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The theory of finite fields is a branch of modern algebra that has come to the fore in the last fifty years because of its diverse applications in such areas as combinatorics, coding theory and the mathematical study of switching circuits. This book, the first one devoted entirely to this theory, provides comprehensive coverage of the literature on finite fields and their applications. Extensive bibliographical notes at the end of each chapter give a historical survey of the development of the subject. Worked examples and lists of exercises found throughout the book make it useful as a text for advanced level courses.

Arithmetic Of Finite Fields

Author: Sylvain Duquesne
Publisher: Springer
ISBN: 3319552279
Size: 38.16 MB
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This book constitutes the thoroughly refereed post-workshop proceedings of the 6th International Workshop on the Arithmetic of Finite Field, WAIFI 2016, held in Ghent, Belgium, in July 2016. The 14 revised full papers and 3 invited talks presented were carefully reviewed and selected from 38 submissions. The papers are organized in topical sections on invited talks; elliptic curves; applications; irreducible polynomials; applications to cryptography; Boolean functions; cryptography; cryptography and Boolean functions.

Finite Fields With Applications To Coding Theory Cryptography And Related Areas

Author: Gary L. Mullen
Publisher: Springer Science & Business Media
ISBN: 3642594352
Size: 33.25 MB
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The Sixth International Conference on Finite Fields and Applications, Fq6, held in the city of Oaxaca, Mexico, from May 21-25, 2001, continued a series of biennial international conferences on finite fields. This volume documents the steadily increasing interest in this topic. Finite fields are an important tool in discrete mathematics and its applications cover algebraic geometry, coding theory, cryptology, design theory, finite geometries, and scientific computation, among others. An important feature is the interplay between theory and applications which has led to many new perspectives in research on finite fields and other areas. This interplay has been emphasized in this series of conferences and certainly was reflected in Fq6. This volume offers up-to-date original research papers by leading experts in the area.

Security Aspects In Information Technology

Author: Marc Joye
Publisher: Springer Science & Business Media
ISBN: 3642245854
Size: 13.10 MB
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This book constitutes the refereed proceedings of the First International Conference on Security Aspects in Information Technology, High-Performance Computing and Networking held in Haldia, India, in October 2011. The 14 full papers presented together with the abstracts of 2 invited lectures were carefully reviewed and selected from 112 sumbissions. The papers address all current aspects in cryptography, security aspects in high performance computing and in networks as well. The papers are divided in topical sections on embedded security; digital rights management; cryptographic protocols; cryptanalysis/side channel attacks; and cipher primitives.

Formal Languages Automata And Numeration Systems 1

Author: Michel Rigo
Publisher: John Wiley & Sons
ISBN: 1119008220
Size: 68.37 MB
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Formal Languages, Automaton and Numeration Systems presents readers with a review of research related to formal language theory, combinatorics on words or numeration systems, such as Words, DLT (Developments in Language Theory), ICALP, MFCS (Mathematical Foundation of Computer Science), Mons Theoretical Computer Science Days, Numeration, CANT (Combinatorics, Automata and Number Theory). Combinatorics on words deals with problems that can be stated in a non-commutative monoid, such as subword complexity of finite or infinite words, construction and properties of infinite words, unavoidable regularities or patterns. When considering some numeration systems, any integer can be represented as a finite word over an alphabet of digits. This simple observation leads to the study of the relationship between the arithmetical properties of the integers and the syntactical properties of the corresponding representations. One of the most profound results in this direction is given by the celebrated theorem by Cobham. Surprisingly, a recent extension of this result to complex numbers led to the famous Four Exponentials Conjecture. This is just one example of the fruitful relationship between formal language theory (including the theory of automata) and number theory.