Constructing Elliptic Curves of Prescribed Order

Over the past 20 years, elliptic curves have becomean integral part of manycryptographic protocols. As a consequence, methodsfor constructing ellipticcurves suitable for cryptography have been studiedintensively. This book givesa new and very efficient method to construct anelliptic curve of prescribedorder. It includes a basic introduction to ellipticcurves, written forbeginning graduate students in mathematics. Thepresented constructionnaturally leads into a discussion of the relationshipbetween elliptic curvesand algebraic number theory. This more advancedtopic, known as complexmultiplication theory, was first pioneered byKronecker in the 19th century andit has recently regained popularity. The second partof this book containsvarious new p-adic algorithms in this area and itgives a description of p-adicclass invariants.