Elliptic Curves, Modular Forms and
Cryptography : Proceedings of the Advanced Instructional Workshop on Algebraic
Number Theory/edited by A.K. Bhandari, D.S. Nagaraj, B. Ramakrishnan and T.N.
Venkataramana. New Delhi, Hindustan Book Agency,
2003, viii, 346 p., ISBN 81-85931-42-9.
Contents: Preface. I. Elliptic curves: 1. An overview/D.S. Nagaraj. 2. A quick introduction to algebraic geometry and Elliptic curves/D.S. Nagaraj and B. Sury. 3. Elliptic curves over finite fields/B. Sury. 4. The Nagell-Lutz Theorem/Rajat Tandon. 5. Weak Mordell-Weil Theorem/C.S. Rajan. 6. The Mordell-Weil Theorem/D.S. Nagaraj and B. Sury. 7. Complex multiplication/Eknath Ghate. 8. The main Theorem of complex multiplication/Dipendra Prasad. 9. Approximations of algebraic numbers by rationals: a Theorem of Thue/T.N. Shorey. 10. Siegel’s Theorem: finiteness of integral points/S.D. Adhikari and D.S. Ramana. 11. P-adic Theta functions and Tate curves/Alexander F. Brown. 12. L-adic representation attached to an elliptic curve over a number field/D.S. Nagaraj. 13. Arithmetic on curves/Chandan Singh Dalawat. II. Modular forms: 1. Introduction/B. Ramakrishnan. 2. Elliptic functions/Parvati Shastri. 3. An introduction to modular forms and Hecke operators/M. Manickam and B. Ramakrishnan. 4. L-Functions of modular forms/C.S. Yogananda. 5. On the Eichler-Shimura congruence relation/T.N. Venkataramana. III. Cryptography: 1. Cryptography/Ashwani K. Bhandari. 2. Classical cryptosystems/R. Thangadurai. 3. The public key cryptography/Ashwani K. Bhandari. 4. Primality and factoring/Amora Nongkynrih. 5. Elliptic curves and cryptography/R. Balasubramanian.
From the preface: "The theme of the workshop was Algebraic number theory with special emphasis on Elliptic curves. The theory of Elliptic curves has been the source of new approaches to classical problems in number theory. It has also found applications in cryptography. The workshop also covered some aspects of cryptography.
The volume is in three parts, the first part contains articles in the field of Elliptic curves, the second contains articles on Modular forms. Some basics as well as some advanced topics on cryptography are presented in the third and final part of these proceedings.
Each part contains an introduction, which, in some sense, gives the overall picture of the contents in that part. Most of the articles are presented in a self-contained style and they give a different flavour to the subject. Though some of the contents of a few articles are already contained in some text books, they are presented here (with due references) in order to make this volume complete to some extent. We hope that the graduate students who want to pursue their research career in number theory will benefit from this volume." (jacket)