Review: Advances in Elliptic Curve Cryptography
Abstract
Book Reviews Review of Advances in Elliptic Curve Cryptography, by I. F. Blake, G. Seroussi and N. P. Smart, eds, London Mathematical Society Lecture Note Series 317, Cambridge University Press, 2005, ISBN 0-521-60415-X, pp.xvi+281, pbk. This volume updates the editorsâ earlier volume on Elliptic Curve Cryptography (ECC) which appeared as LMS LNS 265 in 1999. It is divided into four parts entitled respectively Protocols, Implementation Techniques, Mathematical Foundations, and Pairing Based Techniques. Altogether the book contains ten chapters by diï¬erent authors (including one of the editors) along with a bibliography of some 359 articles and 59 source volumes, plus comprehensive author and subject indexes. The technical developments that have taken place in ECC since 1999 are impressive in terms of both their quantity and quality: provable security of practical encryption and signature schemes has made major advances; side channel analysis and Weil descent have become powerful tools for breaking certain ECC schemes; pairing schemes have been developed to construct protocols which cannot be implemented in any other way; and eï¬cient methods for determining the group order of ECs over ï¬elds of small characteristic by means of point counting are now available. Thus, in Chapter IV (by Elisabeth Oswald)