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Algebraic Curves and Cryptography
 
Edited by: V. Kumar Murty University of Toronto, Toronto, ON, Canada
A co-publication of the AMS and Fields Institute
Algebraic Curves and Cryptography
Hardcover ISBN:  978-0-8218-4311-6
Product Code:  FIC/58
List Price: $93.00
MAA Member Price: $83.70
AMS Member Price: $74.40
eBook ISBN:  978-1-4704-1784-0
Product Code:  FIC/58.E
List Price: $88.00
MAA Member Price: $79.20
AMS Member Price: $70.40
Hardcover ISBN:  978-0-8218-4311-6
eBook: ISBN:  978-1-4704-1784-0
Product Code:  FIC/58.B
List Price: $181.00 $137.00
MAA Member Price: $162.90 $123.30
AMS Member Price: $144.80 $109.60
Algebraic Curves and Cryptography
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Algebraic Curves and Cryptography
Edited by: V. Kumar Murty University of Toronto, Toronto, ON, Canada
A co-publication of the AMS and Fields Institute
Hardcover ISBN:  978-0-8218-4311-6
Product Code:  FIC/58
List Price: $93.00
MAA Member Price: $83.70
AMS Member Price: $74.40
eBook ISBN:  978-1-4704-1784-0
Product Code:  FIC/58.E
List Price: $88.00
MAA Member Price: $79.20
AMS Member Price: $70.40
Hardcover ISBN:  978-0-8218-4311-6
eBook ISBN:  978-1-4704-1784-0
Product Code:  FIC/58.B
List Price: $181.00 $137.00
MAA Member Price: $162.90 $123.30
AMS Member Price: $144.80 $109.60
  • Book Details
     
     
    Fields Institute Communications
    Volume: 582010; 133 pp
    MSC: Primary 11; 14

    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).

    Readership

    Graduate students and research mathematicians interested in cryptography, applications of number theory and algebraic geometry.

  • Table of Contents
     
     
    • Chapters
    • V. Kumar Murty — An overview of algebraic curves and cryptography
    • Nicolas Thériault — Schoof’s point counting algorithm
    • Zubair Ashraf, Ali Juma and Pramathanath Sastry — Report on the Denef-Vercauteren/Kedlaya algorithm
    • Mohammed Radi-Benjelloun — An introduction to Gröbner bases
    • Farzali Izadi — $C_{ab}$ curves and arithmetic on their Jacobians
    • Kenneth Shum — The zeta functions of two Garcia-Stichtenoth towers
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 582010; 133 pp
MSC: Primary 11; 14

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).

Readership

Graduate students and research mathematicians interested in cryptography, applications of number theory and algebraic geometry.

  • Chapters
  • V. Kumar Murty — An overview of algebraic curves and cryptography
  • Nicolas Thériault — Schoof’s point counting algorithm
  • Zubair Ashraf, Ali Juma and Pramathanath Sastry — Report on the Denef-Vercauteren/Kedlaya algorithm
  • Mohammed Radi-Benjelloun — An introduction to Gröbner bases
  • Farzali Izadi — $C_{ab}$ curves and arithmetic on their Jacobians
  • Kenneth Shum — The zeta functions of two Garcia-Stichtenoth towers
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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