3 edition of **Elliptic curves, modular forms and cryptography** found in the catalog.

Elliptic curves, modular forms and cryptography

Advanced Instructional Workshop on Algebraic Number Theory (2000 Harish-Chandra Research Institute)

- 262 Want to read
- 38 Currently reading

Published
**2003**
by Hindustan Book Agency in New Delhi
.

Written in English

**Edition Notes**

Includes bibliographical references.

Statement | edited by A.K. Bhandari ... [et. al.]. |

Contributions | Bhandari, A. K. |

The Physical Object | |
---|---|

Pagination | viii, 345 p. : |

Number of Pages | 345 |

ID Numbers | |

Open Library | OL3443631M |

ISBN 10 | 8185931429 |

LC Control Number | 2005320523 |

The theme of the workshop was algebraic number theory with special emphasis on elliptic curves. The volume is in three parts, the first part contains articles in the field of elliptic curves, the second contains articles on modular forms. The third part presents some basics on cryptography, as well as some advanced topics. Although the formal definition of an elliptic curve is fairly technical and requires some background in algebraic geometry, it is possible to describe some features of elliptic curves over the real numbers using only introductory algebra and geometry.. In this context, an elliptic curve is a plane curve defined by an equation of the form = + + where a and b are real numbers.

Neil I. Koblitz, “Introduction to Elliptic Curves and Modular Forms“, Graduate Texts in Mathematics (Book 97), Springer; 2nd edition (Ap ). (My own) Alvaro Lozano-Robledo, “Elliptic Curves, Modular Forms, and their L-Functions“, American Mathematical Society (February 8, ).Author: Alvaro Lozano-Robledo. We make reference to material in the five books listed below. In addition, there are citations and links to other references. [Washington] = Washington, Lawrence C. Elliptic Curves: Number Theory and Cryptography. Chapman & Hall / CRC, ISBN: (Errata (PDF)) [Preview with Google Books]. Online version.

Summary. Elliptic curve cryptography (ECC) was proposed by Victor Miller and Neal Koblitz in the mid s. An elliptic curve is the set of solutions (x,y) to an equation of the form y^2 = x^3 + Ax + B, together with an extra point O which is called the point at applications to cryptography we consider finite fields of q elements, which I will write as F_q or GF(q). “This course is an introduction to elliptic curves and modular forms. These play a cen-tral role in modern arithmetical geometry and even in applications to cryptography. On the elliptic curve side, we shall cover elliptic curves over ﬁnite ﬁelds, over the complex num-bers, and over the rationals.

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Buy Elliptic Curves, Modular Forms and Cryptography: Proceedings of the Advanced Instructional Workshop on Algebraic Number Theory on FREE SHIPPING on qualified orders Elliptic Curves, Modular Forms and Cryptography: Proceedings of the Advanced Instructional Workshop on Algebraic Number Theory: Ashwani K.

Bhandari, D.S. Nagaraj, B. Elliptic Curves, Modular Forms and Cryptography Proceedings of the Advanced Instructional Workshop on Algebraic Number Theory. Search within book. Front Matter.

Pages i-viii. PDF. Elliptic Curves. Front Matter. Pages PDF. An overview. Elliptic Curves and Cryptography. Balasubramanian. Pages About this book. And in this objective Lozano-Robledo succeeds admirably.

The book is full of examples and exercises of such appeal that a properly disposed rookie should go after nigh-on all of them; to boot, the author's narrative is compact and smooth.

Elliptic Curves, Modular Forms, and Their L-Functions is a marvelous addition to the by: 9. Elliptic Curves, Modular Forms and Cryptography Proceedings of the Advanced Instructional Workshop on Algebraic Number Theory. Editors: Bhandari, A.K., Nagaraj, D.S Brand: Hindustan Book Agency. Buy Introduction to Elliptic Curves and Modular Forms on FREE SHIPPING on qualified orders/5(6).

The theory modular forms and cryptography book elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Cited by: The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory.

This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Price: $ Elliptic Curves, Modular Forms and Cryptography Proceedings of the Advanced Instructional Workshop on Aigebraic Number Theory Volumes containing conference proceedings, workshop lectures, and collection of invited articles in any area of mathematics are published in this series.

About this Textbook This textbook covers the basic properties of elliptic curves and modular forms, with emphasis on certain connections with number theory.

The ancient "congruent number problem" is the central motivating example for most of the book. 4 D. Zagier The modular group takes its name from the fact that the points of the quotient space Γ1\H are moduli (= parameters) for the isomorphism classes of elliptic curves over C.

To each point z∈ H one can associate the lattice Λ z = Z.z+ Z.1 ⊂C and the quotient space E z = C/Λ z, which is an elliptic curve, i.e., it is at the same time a complex curve and an abelian Size: 1MB.

about modular forms, and explore the relationship between lattice functions and modular forms. We conclude by giving a small glimpse of the relationship between modular forms and elliptic curves.

1 Introduction In this paper, we focus on the fundamentals of modular forms. We rst give a de nition of a modular form through a careful series of.

a modular curve of the form X 0(N). Any such elliptic curve has the property that its Hasse-Weil zeta function has an analytic continuation and satisﬁes a functional equation of the standard type.

If an elliptic curve over Qwith a given j-invariant is modular then it is easy to see that all elliptic curves withCited by: The theory of elliptic curves and modular forms is one subject where the most diverse branches of Mathematics like complex analysis, algebraic geometry, representation theory and number theory come together.

Our point of view will be number theoretic. A well-known feature of number theory is theFile Size: KB. This will give you a very solid and rather modern introduction into the subject algebraic curves, and to elliptic curves in particular. Afterwards you can go back to chaps.

II and III and read the theory of schemes and the machinery of sheaf cohomology, if you wish to further pursue algebraic geometry. † Elliptic curves with points in Fp are ﬂnite groups. † Elliptic Curve Discrete Logarithm Prob-lem (ECDLP) is the discrete logarithm problem for the group of points on an elliptic curve over a ﬂnite ﬂeld.

† The best known algorithm to solve the ECDLP is exponential, which is why elliptic curve groups are used for Size: KB. of elliptic curves, modular forms and their L-functions, with an em- sible for undergraduates and emphasizes the cryptography applications of elliptic curves.

Stein’s book [Ste08]alsohas There are several graduate-level texts on elliptic curves. Sil-verman’s book [Sil86] is. E(Q), the set of rational points on an elliptic curve, as well as the Birch and Swinnerton-Dyer conjecture.

The appendix ends with a brief discussion of elliptic curves over C, elliptic functions, and the characterizationofE(C)asacomplextorus. Appendix B has solutions to the File Size: KB. Guide to Elliptic Curve Cryptography Darrel Hankerson Alfred Menezes Scott Vanstone Springer.

Guide to Elliptic Curve Cryptography Use in connection with any form of information storage and reltrieval, electronic adaption, compute r software, or by similar or dissimilar methodology now known 01 Modular reduction (one bit at a time.

uate course on elliptic curve cryptography. I was so pleased with the outcome that I encouraged Andreas to publish the manuscript. I ﬁrmly believe that this book is a very good starting point for anyone who wants to pursue the theory of elliptic curves over ﬁnite ﬁelds and their applications to cryptography.

Vanstone, April 5Cited by: In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth theory of modular forms therefore belongs to complex analysis but the main importance of the theory has traditionally been in its connections with number theory.

In this article we shall see how elliptic curves are used in cryptography. When public-key cryptography was introduced to the research community by Diffe and Hellman in [4], it represented an exciting innovation in cryptography and a surprising applications of number by: 6.Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide equivalent security.

Elliptic curves are applicable for key agreement, digital signatures, pseudo-random generators and other tasks.A modular elliptic curve is an elliptic curve E that admits a parametrisation X 0 (N) → E by a modular is not the same as a modular curve that happens to be an elliptic curve, something that could be called an elliptic modular curve.

The modularity theorem, also known as the Taniyama–Shimura conjecture, asserts that every elliptic curve defined over the rational numbers is modular.