Algorithms for Modular Elliptic Curves

Elliptic curves are of central importance in computational number theory with numerous applications in such areas as cryptography primality testing and factorization. This book presents a thorough treatment of many algorithms concerning the arithmetic of elliptic curves complete with computer implementation. In the first part the author describes in detail the construction of modular elliptic curves giving an explicit algorithm for their computation. Then a collection of algorithms for the arithmetic of elliptic curves is presented, some of these have not appeared in book form before. Finally an extensive set of tables is provided giving the results of the author's implentations of the algorithms. Researchers and graduate students of number theory will find this book useful particularly those interested in computation. That aspect will make it appeal also to computer scientists and coding theorists.