الصفحة 1
الصفحة 1
Number Theory ; Vol. II : Analytic and Modern Tools
The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects.
Number Theory ; Vol. I : Tools and Diophantine Equations
The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects.
Number Fields and Function Fields – Two Parallel Worlds
These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives.
Multivariate Public Key Cryptosystems
Multivariate public key cryptosystems (MPKC) is a fast-developing new area in cryptography. In the past 10 years, MPKC schemes have increasingly been seen as a possible alternative to number theoretic-based cryptosystems such as RSA, as they are generally more efficient in terms of computational effort. As quantum computers are developed, MPKC will become a necessary alternative. Multivariate Public Key Cryptosystems systematically presents the subject matter for a broad audience. Information security experts in industry can use the book as a guide for understanding what is needed to implement these cryptosystems for practical applications, and researchers in both computer science and mathematics will find this book a good starting point for exploring this new field. It is also suitable as a textbook for advanced-level students.
Information security practice and experience ; Vol. 3903 ; 2nd International Conference, ISPEC 2006, Hangzhou, China, April 11-14, 2006, Proceedings
Contains the Research Track proceedings of the Second Information Security Practice and Experience Conference 2006 (ISPEC 2006), which took place in Hangzhou, China, April 11–14, 2006. The inaugural ISPEC 2005 was held exactly one year earlier in Singapore. As applications of information security technologies become pervasive, issues pertaining to their deployment and operations are becoming increasingly imp- tant. ISPEC is an annual conference that brings together researchers and pr- titioners to provide a con?uence of new information security technologies, their applications and their integration with IT systems in various vertical sectors. ISPEC 2006 received 307 submissions.
Information security practice and experience ; 4th International Conference, ISPEC 2008 Sydney, Australia, April 21-23, 2008 Proceedings
The 4 th Information Security Practice and Experience Conference (ISPEC2008) was held at Crowne Plaza, Darling Harbour, Sydney, Australia, during April 21-23, 2008. The previous three conferences were held in Singapore in 2005, Hangzhou, China in 2006 and Hong Kong, China in 2007. As with the previous three conference proceedings, the proceedings of ISPEC 2008 were published in the LNCS series by Springer. The conference received 95 submissions, out of which the Program Committee selected 29 papers for presentation at the conference. These papers are included in the proceedings. The accepted papers cover a range of topics in mathem- ics, computer science and security applications.
Information security and privacy ; Vol. 3574 : 10th Australasian Conference, ACISP 2005, Brisbane, Australia, July 4-6, 2005, Proceedings
Constitutes the refereed proceedings of the 10th Australasian Conference on Information Security and Privacy, ACISP 2005, held in Brisbane, Australia in July 2005. The papers are organized in topical sections on network security, cryptanalysis, group communication, elliptic curve cryptography, mobile security, side channel attacks, and more.
Handbook of mathematics
This guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. In the newer editions emphasis was laid on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing. For the 5th edition, the chapters "Computer Algebra Systems" and "Dynamical Systems and Chaos" were fundamentally revised, updated and expanded. In the chapter "Algebra and Discrete Mathematics" a section on "Finite Fields and Shift Registers" was added.
Galois Theory
Classical Galois theory is a subject generally acknowledged to be one of the most central and beautiful areas in pure mathematics. This text develops the subject systematically and from the beginning, requiring of the reader only basic facts about polynomials and a good knowledge of linear algebra.The book discusses Galois theory in considerable generality, treating fields of characteristic zero and of positive characteristic with consideration of both separable and inseparable extensions, but with a particular emphasis on algebraic extensions of the field of rational numbers. While most of the book is concerned with finite extensions, it concludes with a discussion of the algebraic closure and of infinite Galois extensions.
Fields and Galois Theory
The pioneering work of Abel and Galois in the early nineteenth century demonstrated that the long-standing quest for a solution of quintic equations by radicals was fruitless: no formula can be found. The techniques they used were, in the end, more important than the resolution of a somewhat esoteric problem, for they were the genesis of modern abstract algebra. This book provides a gentle introduction to Galois theory suitable for third- and fourth-year undergraduates and beginning graduates. The approach is unashamedly unhistorical: it uses the language and techniques of abstract algebra to express complex arguments in contemporary terms. Thus the insolubility of the quintic by radicals is linked to the fact that the alternating group of degree 5 is simple - which is assuredly not the way Galois would have expressed the connection.
Field Theory ; 2nd ed.
This book presents the basic theory of fields, starting more or less from the beginning. It is suitable for a graduate course in field theory, or independent study.There are new exercises, a new chapter on Galois theory from an historical perspective, and additional topics sprinkled throughout the text, including a proof of the Fundamental Theorem of Algebra, a discussion of casus irreducibilis, Berlekamp's algorithm for factoring polynomials over Zp and natural and accessory irrationalities.
Field Arithmetic ; 3rd ed.
Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements.
Field Arithmetic ; 2nd ed.
Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements.Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)?
Fault Diagnosis and Tolerance in Cryptography ; 3rd International Workshop, FDTC 2006, Yokohama, Japan, October 10, 2006, Proceedings
The sophistication of the underlying cryptographic algorithms, the high complexity of the implementations, and the easy access and low cost of cryptographic devices resulted in increased concerns regarding the reliability and security of crypto-devices. The effectiveness of side channel attacks on cryptographic devices, like timing and power-based attacks, has been known for some time. Several recent investigations have demonstrated the need to develop methodologies and techniques for designing robust cryptographic systems (both hardware and software) to protect them against both accidental faults and maliciously injected faults with the purpose of extracting the secret key. This trend has been particularly motivated by the fact that the equipment needed to carry out a successful side channel attack based on fault injection is easily accessible at a relatively low cost (for example, laser beam technology), and that the skills needed to use it are quite common.
Error-Correcting Linear Codes : Classification by Isometry and Applications
This text offers a thorough introduction to the mathematical concepts behind the theory of error-correcting linear codes. Care is taken to introduce the necessary algebraic concepts, for instance the theory of finite fields, the polynomial rings over such fields and the ubiquitous concept of group actions that allows the classification of codes by isometry. The book provides in-depth coverage of important topics like cyclic codes and the coding theory used in compact disc players. The final four chapters cover advanced and algorithmic topics like the classification of linear codes by isometry, the enumeration of isometry classes, random generation of codes, the use of lattice basis reduction to compute minimum distances, the explicit construction of codes with given parameters, as well as the systematic evaluation of representatives of all isometry classes of codes.
Cryptography Arithmetic : Algorithms and Hardware Architectures
Modern cryptosystems, used in numerous applications that require secrecy or privacy - electronic mail, financial transactions, medical-record keeping, government affairs, social media etc. - are based on sophisticated mathematics and algorithms that in implementation involve much computer arithmetic. And for speed it is necessary that the arithmetic be realized at the hardware (chip) level. This book is an introduction to the implementation of cryptosystems at that level.
Cryptographic hardware and embedded systems - CHES 2005 ; 7th International Workshop, Edinburgh, UK, August 29 - September 1, 2005, Proceedings
Constitutes the refereed proceedings of the 7th International Workshop on Cryptographic Hardware and Embedded Systems, CHES 2005, held in Edinburgh, UK in August/September 2005. The papers in this book are organized in topical sections on side channels, arithmetic for cryptanalysis, special purpose hardware, hardware attacks and more.
Cryptographic Algorithms on Reconfigurable Hardware
This book covers the study of computational methods, computer arithmetic algorithms, and design improvement techniques needed to implement efficient cryptographic algorithms in FPGA reconfigurable hardware platforms. The concepts and techniques reviewed in this book will make special emphasis on the practical aspects of reconfigurable hardware design, explaining the basic mathematics related and giving a comprehensive description of state-of-the-art implementation techniques. The authors show how high-speed cryptographic algorithms implementations can be achieved on reconfigurable hardware devices without posing prohibited high requirements for hardware resources. The material in this book will be of interest to engineering professionals, programmers, hardware designers, and graduate students interested in the development of security and cryptographic mechanisms at a beginning/intermediate level.
Coding and Cryptography ; International Workshop, WCC 2005, Bergen, Norway, March 14-18, 2005, Revised Selected Papers
This volume contains refereed papers devotedtocodingandcrypto graphy.These papers arethe full versionsof a selectionof the best extended abstractsaccepted for presentation at the International Workshop on Coding and Cryptography (WCC 2005) held in Bergen, Norway, March 14–18, 2005. Each of the 118 - tended abstracts originallysubmitted to the workshop were reviewed by at least two members of the Program Committee. As a result of this screening process, 58 papers were selected for presentation, of which 52 were eventually presented at the workshop together with four invited talks.
Aritmetica, crittografia e codici = Arithmetic, cryptography and codes
The basic techniques of algebra and number theory useful in recent applications to cryptography and codes are developed, with the aim of being elementary and self-sufficient. The emphasis is on computational problems. This part of the volume can be useful as a textbook for a first course in algebra for mathematicians, computer scientists or engineers. Important applications of algebra and geometry to cryptography and codes are then illustrated. Both, cryptography and codes have significant applications in daily life which are illustrated here. Cryptography is developed in detail in much of its classic and current aspects, and both private and public key cryptography are developed. Cryptography with the use of elliptic curves on finite fields is also illustrated. A chapter introducing the subject is dedicated to linear codes.
