**Author**: San Ling

**Publisher:**CRC Press

**ISBN:**1420079476

**Size**: 12.43 MB

**Format:**PDF, Docs

**Category :**Computers

**Languages :**en

**Pages :**340

**View:**7708

**Book Description:**The reach of algebraic curves in cryptography goes far beyond elliptic curve or public key cryptography yet these other application areas have not been systematically covered in the literature. Addressing this gap, Algebraic Curves in Cryptography explores the rich uses of algebraic curves in a range of cryptographic applications, such as secret sh

## Computational Aspects Of Algebraic Curves

**Author**:

**Publisher:**

**ISBN:**9814479578

**Size**: 12.88 MB

**Format:**PDF, Docs

**Category :**

**Languages :**en

**Pages :**

**View:**5208

**Book Description:**

## Algebraic Curves And Cryptography

**Author**: Vijaya Kumar Murty

**Publisher:**American Mathematical Soc.

**ISBN:**0821843117

**Size**: 74.78 MB

**Format:**PDF

**Category :**Mathematics

**Languages :**en

**Pages :**133

**View:**3440

**Book Description:**It is by now a well-known paradigm that public-key cryptosystems can be built using finite Abelian groups and that algebraic geometry provides a supply of such groups through Abelian varieties over finite fields. Of special interest are the Abelian varieties that are Jacobians of algebraic curves. All of the articles in this volume are centered on the theme of point counting and explicit arithmetic on the Jacobians of curves over finite fields. The topics covered include Schoof's $\ell$-adic point counting algorithm, the $p$-adic algorithms of Kedlaya and Denef-Vercauteren, explicit arithmetic on the Jacobians of $C_{ab}$ curves and zeta functions. This volume is based on seminars on algebraic curves and cryptography held at the GANITA Lab of the University of Toronto during 2001-2008. The articles are mostly suitable for independent study by graduate students who wish to enter the field, both in terms of introducing basic material as well as guiding them in the literature. The literature in cryptography seems to be growing at an exponential rate. For a new entrant into the subject, navigating through this ocean can seem quite daunting. In this volume, the reader is steered toward a discussion of a few key ideas of the subject, together with some brief guidance for further reading. It is hoped that this approach may render the subject more approachable. Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).|It is by now a well-known paradigm that public-key cryptosystems can be built using finite Abelian groups and that algebraic geometry provides a supply of such groups through Abelian varieties over finite fields. Of special interest are the Abelian varieties that are Jacobians of algebraic curves. All of the articles in this volume are centered on the theme of point counting and explicit arithmetic on the Jacobians of curves over finite fields. The topics covered include Schoof's $\ell$-adic point counting algorithm, the $p$-adic algorithms of Kedlaya and Denef-Vercauteren, explicit arithmetic on the Jacobians of $C_{ab}$ curves and zeta functions. This volume is based on seminars on algebraic curves and cryptography held at the GANITA Lab of the University of Toronto during 2001-2008. The articles are mostly suitable for independent study by graduate students who wish to enter the field, both in terms of introducing basic material as well as guiding them in the literature. The literature in cryptography seems to be growing at an exponential rate. For a new entrant into the subject, navigating through this ocean can seem quite daunting. In this volume, the reader is steered toward a discussion of a few key ideas of the subject, together with some brief guidance for further reading. It is hoped that this approach may render the subject more approachable. Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

## Elliptic Curves In Cryptography

**Author**: I. Blake

**Publisher:**Cambridge University Press

**ISBN:**9780521653749

**Size**: 73.83 MB

**Format:**PDF, ePub, Docs

**Category :**Computers

**Languages :**en

**Pages :**204

**View:**4620

**Book Description:**This book explains the mathematics behind practical implementations of elliptic curve systems.

## Algebraic Curves And Their Applications

**Author**: Lubjana Beshaj

**Publisher:**American Mathematical Soc.

**ISBN:**1470442477

**Size**: 61.46 MB

**Format:**PDF, ePub, Mobi

**Category :**Curves, Algebraic

**Languages :**en

**Pages :**344

**View:**6565

**Book Description:**This volume contains a collection of papers on algebraic curves and their applications. While algebraic curves traditionally have provided a path toward modern algebraic geometry, they also provide many applications in number theory, computer security and cryptography, coding theory, differential equations, and more. Papers cover topics such as the rational torsion points of elliptic curves, arithmetic statistics in the moduli space of curves, combinatorial descriptions of semistable hyperelliptic curves over local fields, heights on weighted projective spaces, automorphism groups of curves, hyperelliptic curves, dessins d'enfants, applications to Painlevé equations, descent on real algebraic varieties, quadratic residue codes based on hyperelliptic curves, and Abelian varieties and cryptography. This book will be a valuable resource for people interested in algebraic curves and their connections to other branches of mathematics.

## Algebraic Aspects Of Cryptography

**Author**: Neal Koblitz

**Publisher:**Springer Science & Business Media

**ISBN:**3662036428

**Size**: 45.61 MB

**Format:**PDF, ePub, Docs

**Category :**Computers

**Languages :**en

**Pages :**206

**View:**6053

**Book Description:**From the reviews: "This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. [...] Overall, this is an excellent expository text, and will be very useful to both the student and researcher." Mathematical Reviews

## Algebraic Curves And Finite Fields

**Author**: Harald Niederreiter

**Publisher:**Walter de Gruyter GmbH & Co KG

**ISBN:**3110379554

**Size**: 28.14 MB

**Format:**PDF

**Category :**Mathematics

**Languages :**en

**Pages :**251

**View:**7602

**Book Description:**Algebra and number theory have always been counted among the most beautiful and fundamental mathematical areas with deep proofs and elegant results. However, for a long time they were not considered of any substantial importance for real-life applications. This has dramatically changed with the appearance of new topics such as modern cryptography, coding theory, and wireless communication. Nowadays we find applications of algebra and number theory frequently in our daily life. We mention security and error detection for internet banking, check digit systems and the bar code, GPS and radar systems, pricing options at a stock market, and noise suppression on mobile phones as most common examples. This book collects the results of the workshops "Applications of algebraic curves" and "Applications of finite fields" of the RICAM Special Semester 2013. These workshops brought together the most prominent researchers in the area of finite fields and their applications around the world. They address old and new problems on curves and other aspects of finite fields, with emphasis on their diverse applications to many areas of pure and applied mathematics.

## An Algebraic Approach To Elliptic And Hyperelliptic Curve Cryptography

**Author**: Sofía Garzón Mora

**Publisher:**

**ISBN:**

**Size**: 65.73 MB

**Format:**PDF, ePub, Docs

**Category :**

**Languages :**en

**Pages :**

**View:**5433

**Book Description:**During the past decades, cryptographic methods have radically improved as well as the mathematical tools employed in them. In this work we introduce elliptic curves as building blocks of cryptosystems and review their properties from a theoretical viewpoint. Moreover, we analyze the Discrete Logarithm Problem on groups of points on elliptic curves, and algorithms for its solution are implemented and compared. Furthermore, hyperelliptic curves are included as a generalization of elliptic curves for use in cryptography. The Jacobian is then described as an analogue of the group of points on elliptic curves for the case of higher genus curves. Two algorithms are also implemented and compared for the solution of the Discrete Logarithm Problem on the Jacobian of a general hyperelliptic curve. Finally, we find some conditions for curves to be employed in real system applications.

## Computing In The Jacobian Of A C34 Curve

**Author**: Soondug Kim

**Publisher:**

**ISBN:**

**Size**: 56.89 MB

**Format:**PDF

**Category :**Curves, Algebraic

**Languages :**en

**Pages :**63

**View:**5476

**Book Description:**

## Elliptic Curves

**Author**: Lawrence C. Washington

**Publisher:**CRC Press

**ISBN:**9780203484029

**Size**: 35.19 MB

**Format:**PDF, Docs

**Category :**Computers

**Languages :**en

**Pages :**440

**View:**4940

**Book Description:**Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem. However, most books on the subject assume a rather high level of mathematical sophistication, and few are truly accessible to