Elliptic Curves, Modular Forms and Cryptography: Proceedings of the Advanced Instructional Workshop on Algebraic Number Theory

Front Matter ....Pages i-viii
Front Matter ....Pages 1-1
 An overview  (D. S. Nagaraj)....Pages 3-4
 A Quick Introduction to Algebraic Geometry and Elliptic Curves  (D. S. Nagaraj, B. Sury)....Pages 5-31
 Elliptic Curves over Finite Fields  (B. Sury)....Pages 33-47
 The Nagell-Lutz Theorem  (Rajat Tandon)....Pages 49-61
 Weak Mordell-Weil theorem  (C. S. Rajan)....Pages 63-72
 The Mordell-Weil Theorem  (D. S. Nagaraj, B. Sury)....Pages 73-84
 Complex Multiplication  (Eknath Ghate)....Pages 85-108
 The Main Theorem of Complex Multiplication  (Dipendra Prasad)....Pages 109-118
 Approximations of Algebraic Numbers by Rationals: A Theorem of Thue  (T. N. Shorey)....Pages 119-137
 Siegel’s Theorem: Finiteness of Integral Points  (S. D. Adhikari, D. S. Ramana)....Pages 139-149
 p-adic Theta Functions and Tate Curves  (Alexander F. Brown)....Pages 151-165
 ℓ-adic Representation Attached to an Elliptic Curve over a Number Field  (D. S. Nagaraj)....Pages 167-191
 Arithmetic on Curves  (Chandan Singh Dalawat)....Pages 193-200
Front Matter ....Pages 201-201
 Introduction  (B. Ramakrishnan)....Pages 203-204
 Elliptic Functions  (Parvati Shastri)....Pages 205-221
 An Introduction to Modular Forms and Hecke Operators  (M. Manickam, B. Ramakrishnan)....Pages 223-245
 L-Functions of modular forms  (C. S. Yogananda)....Pages 247-254
 On the Eichler-Shimura Congruence Relation  (T. N. Venkataramana)....Pages 255-265
Front Matter ....Pages 267-267
 Cryptography  (Ashwani K. Bhandari)....Pages 269-274
 Classical Cryptosystems  (R. Thangadurai)....Pages 275-286
 The Public Key Cryptography  (Ashwani K. Bhandari)....Pages 287-301
 Primality and Factoring  (Amora Nongkynrih)....Pages 303-323
 Elliptic Curves and Cryptography  (R. Balasubramanian)....Pages 325-345