Constructing elliptic curves of prescribed order

Over the past 20 years, elliptic curves have become
an integral part of many
cryptographic protocols. As a consequence, methods
for constructing elliptic
curves suitable for cryptography have been studied
intensively. This book gives
a new and very efficient method to construct an
elliptic curve of prescribed
order. It includes a basic introduction to elliptic
curves, written for
beginning graduate students in mathematics. The
presented construction
naturally leads into a discussion of the relationship
between elliptic curves
and algebraic number theory. This more advanced
topic, known as complex
multiplication theory, was first pioneered by
Kronecker in the 19th century and
it has recently regained popularity. The second part
of this book contains
various new p-adic algorithms in this area and it
gives a description of p-adic
class invariants.

Autorentext
Reinier Bröker received his PhD in Mathematics from the University of Leiden in 2006. He is currently working for Microsoft Research.

Klappentext
Over the past 20 years, elliptic curves have become an integral part of many cryptographic protocols. As a consequence, methods for constructing elliptic curves suitable for cryptography have been studied intensively. This book gives a new and very efficient method to construct an elliptic curve of prescribed order. It includes a basic introduction to elliptic curves, written for beginning graduate students in mathematics. The presented construction naturally leads into a discussion of the relationship between elliptic curves and algebraic number theory. This more advanced topic, known as complex multiplication theory, was first pioneered by Kronecker in the 19th century and it has recently regained popularity. The second part of this book contains various new p-adic algorithms in this area and it gives a description of p-adic class invariants.