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Algorithmic Number Theory
  • Language: en
  • Pages: 461

Algorithmic Number Theory

This book constitutes the refereed proceedings of the 6th International Algorithmic Number Theory Symposium, ANTS 2004, held in Burlington, VT, USA, in June 2004. The 30 revised full papers presented together with 3 invited papers were carefully reviewed and selected for inclusion in the book. Among the topics addressed are zeta functions, elliptic curves, hyperelliptic curves, GCD algorithms, number field computations, complexity, primality testing, Weil and Tate pairings, cryptographic algorithms, function field sieve, algebraic function field mapping, quartic fields, cubic number fields, lattices, discrete logarithms, and public key cryptosystems.

Advances on Superelliptic Curves and Their Applications
  • Language: en
  • Pages: 387

Advances on Superelliptic Curves and Their Applications

  • Type: Book
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  • Published: 2015-07-16
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  • Publisher: IOS Press

This book had its origins in the NATO Advanced Study Institute (ASI) held in Ohrid, Macedonia, in 2014. The focus of this ASI was the arithmetic of superelliptic curves and their application in different scientific areas, including whether all the applications of hyperelliptic curves, such as cryptography, mathematical physics, quantum computation and diophantine geometry, can be carried over to the superelliptic curves. Additional papers have been added which provide some background for readers who were not at the conference, with the intention of making the book logically more complete and easier to read, but familiarity with the basic facts of algebraic geometry, commutative algebra and number theory are assumed. The book is divided into three sections. The first part deals with superelliptic curves with regard to complex numbers, the automorphisms group and the corresponding Hurwitz loci. The second part of the book focuses on the arithmetic of the subject, while the third addresses some of the applications of superelliptic curves.

Arithmetic of Finite Fields
  • Language: en
  • Pages: 353

Arithmetic of Finite Fields

This book constitutes the thoroughly refereed post-workshop proceedings of the 8th International Workshop on the Arithmetic of Finite Field, WAIFI 2022, held in Chengdu, China, in August – September 2022. The 19 revised full papers and 3 invited talks presented were carefully reviewed and selected from 25 submissions. The papers are organized in topical sections: structures in finite fields; efficient finite field arithmetic; coding theory; cryptography; sequences.

Cryptology and Network Security
  • Language: en
  • Pages: 634

Cryptology and Network Security

This book constitutes the refereed proceedings of the 19th International Conference on Cryptology and Network Security, CANS 2020, held in Vienna, Austria, in December 2020.* The 30 full papers were carefully reviewed and selected from 118 submissions. The papers focus on topics such as cybersecurity; credentials; elliptic curves; payment systems; privacy-enhancing tools; lightweight cryptography; and codes and lattices. *The conference was held virtually due to the COVID-19 pandemic.

Arithmetic of Finite Fields
  • Language: en
  • Pages: 214

Arithmetic of Finite Fields

This book constitutes the refereed proceedings of the Second International Workshop on the Arithmetic of Finite Fields, WAIFI 2008, held in Siena, Italy, in July 2008. The 16 revised full papers presented were carefully reviewed and selected from 34 submissions. The papers are organized in topical sections on structures in finite fields, efficient finite field arithmetic, efficient implementation and architectures, classification and construction of mappings over finite fields, and codes and cryptography.

Information Security Applications
  • Language: en
  • Pages: 409

Information Security Applications

  • Type: Book
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  • Published: 2017-03-29
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  • Publisher: Springer

This book constitutes the thoroughly refereed post-workshop proceedings of the 17th International Workshop on Information Security Applications, WISA 2016, held on Jeju Island, Korea, in August 2016. The 31 revised full papers including two invited talks presented in this volume were carefully reviewed and selected from 61 submissions. The papers are organized in topical sections such as network security, threat analysis, application security, cryptographic. Protocols, cryptanalysis, cryptographic implementations, authentication using bio and ML, authentication, ICT Convergent security

Handbook of Elliptic and Hyperelliptic Curve Cryptography
  • Language: en
  • Pages: 843

Handbook of Elliptic and Hyperelliptic Curve Cryptography

  • Type: Book
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  • Published: 2005-07-19
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  • Publisher: CRC Press

The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases. Therefore curve-based cryptosystems require much smaller key sizes than RSA to attain the same security level. This makes them particularly attractive for implementations on memory-restricted devices like smart cards and in high-security applications. The Handbook of Elliptic and Hyperelliptic Curve Cryptography introduces the theory and algorithms involved in curve-based cryptography. After a very d...

Arithmetic of Finite Fields
  • Language: en
  • Pages: 273

Arithmetic of Finite Fields

This book constitutes the thoroughly refereed post-workshop proceedings of the 8th International Workshop on the Arithmetic of Finite Field, WAIFI 2020, held in Rennes, France in July 2020. Due to the COVID-19, the workshop was held online. The 12 revised full papers and 3 invited talks presented were carefully reviewed and selected from 22 submissions. The papers are organized in topical sections on invited talks, Finite Field Arithmetic, Coding Theory, Network Security and much more.

Guide to Pairing-Based Cryptography
  • Language: en
  • Pages: 587

Guide to Pairing-Based Cryptography

  • Type: Book
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  • Published: 2017-01-06
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  • Publisher: CRC Press

This book is devoted to efficient pairing computations and implementations, useful tools for cryptographers working on topics like identity-based cryptography and the simplification of existing protocols like signature schemes. As well as exploring the basic mathematical background of finite fields and elliptic curves, Guide to Pairing-Based Cryptography offers an overview of the most recent developments in optimizations for pairing implementation. Each chapter includes a presentation of the problem it discusses, the mathematical formulation, a discussion of implementation issues, solutions accompanied by code or pseudocode, several numerical results, and references to further reading and notes. Intended as a self-contained handbook, this book is an invaluable resource for computer scientists, applied mathematicians and security professionals interested in cryptography.

Number Theory
  • Language: en
  • Pages: 619

Number Theory

This book deals with several aspects of what is now called "explicit number theory." The central theme 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 of its most basic aspects. The local aspect, global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject.