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內容簡介

　　利用有限Abel群構建公鑰密碼系統(tǒng)現(xiàn)在已經成為著名的范例，而代數(shù)幾何學通過有限域上的Abel簇提供了一些這樣的群，特別令人感興趣的是Abel簇為代數(shù)曲線的Jacobi簇的情形?！洞鷶?shù)曲線與密碼學（影印版英文版）》中的所有文章都聚焦于有限域上曲線的Jacobi簇的點計數(shù)和顯式算法這一主題。這些文章的論題包括Schoof的l進點計數(shù)算法、Kedlaya和Denef-Vercauteren的p進算法、Cab曲線和zeta函數(shù)的Jacobi簇的顯式算法?！洞鷶?shù)曲線與密碼學（影印版英文版）》的文章大部分都適合希望進入這一領域的研究生獨立學習，這些文章既介紹了基礎性材料，又能引導讀者深入到文獻中去。密碼學的文獻看上去是呈指數(shù)型增長的，對于一個入門者來說，穿越這片海洋令人望而卻步?！洞鷶?shù)曲線與密碼學（影印版英文版）》會將讀者引向關于這一數(shù)學分支的若干新思想的討論，并給出進一步閱讀的簡明指引?！洞鷶?shù)曲線與密碼學（影印版英文版）》適合對密碼學以及數(shù)論和代數(shù)幾何的應用感興趣的研究生和研究人員閱讀。

作者簡介

暫缺《代數(shù)曲線與密碼學（影印版）》作者簡介

圖書目錄

Chapter 1 An Overview of Algebraic Curves and Cryptography
V． KUMAR MURTY
1．1 Introduction
1．2 The basic paradigm
1．3 The Diffie-Hellman decision problem
1．4 Constraints on the group
1．5 Abelian varieties over finite fields
1．6 Elliptic curves
1．7 Statistical results
1．8 Abelian varieties of higher dimension
1．9 Outline of contents
Chapter 2 School's Point Counting Algorithm
NICOLAS THERIAULT
2．1 Preliminaries
2．2 Division polynomials
2．3 Schoof's algorithm
2．4 Implementation
2．5 Improvements by Atkin and Elkies
2．6 Computing the modular equations
2．7 Computing Pl
2．8 Computing the factor
2．9 Parallelization
Chapter 3 Report on the Denef-Vercauteren/Kedlaya Algorithm
ZUBAIRASHRAFALIJUMAANDPRAMATHANATHSASTRY
3．1 Background
3．2 Generalities
3．3 Main strategy
3．4 Monsky-Washnitzer cohomology
3．5 Hyperelliptic curves
3．6 Data structures
3．7 Algorithm for lifting the curve to characteristic zero
3．8 Inversion
3．9 The 2-power Frobenius on K
3．10 The characteristic polynomial of Frobenius
3．11 Multiplication
3．12 Running times
3．13 Parallelization
Chapter 4 An Introduction to Gr5bner Bases
MOHAMMEDRADI-BENJELLOUN
4．1 Introduction
4．2 GrSbner bases
Chapter 5 Cab Curves and Arithmetic on Their Jacobians
FARZALI IZADI
5．1 Introduction
5．2 Preliminaries
5．3 The Cab curves
5．4 Addition algorithm for Jacobian group in divisor representation
5．5 Addition algorithm for Jacobian group in ideal representation
Chapter 6 The Zeta Functions of Two Garcia-Stichtenoth Towers
KENNETH W． SHUM6．1 Introduction
6．2 Background on zeta functions
6．3 The first Garcia-Stichtenoth tower
6．4 The second Garcia-Stichtenoth tower
6．5 Conclusion
Appendix： Counting points over P0 in GS1
Bibliography
Index