First, the reviews dated below (July 25, 2002, July 29, 2000 [Lee Carlson] and January 31, 2000) are refering to Blake, Seroussi and Smart's first book: Elliptic Curves in Cryptography: London Mathematical Society Lecture Note Series 265, not the new book Advances in Elliptic Curve Cryptography, London Mathematical Society Lecture Note Series 317.Contents of Advances in Elliptic Curve Cryptography, London Mathematical Society Lecture Note Series 317 (ISBN-10: 052160415X).Chapter I: covers Elliptic Curve Based Protocols in the IEEE 1363 standard, ECDSA (EC Digital Signature Algorithm), ECDH (EC Diffie-Hellman) /ECMQV (EC MQV protocol of Law, Menezes, QU, Solinas and Vanstone) and ECIES (EC Integrated Encryption Scheme).Chapter II: on the provable security of ECDSA.Chapter III: proofs of security for ECIES,Chapter IV: side-channel analysis.Chapter V: defenses against side-analysis.Chapter VI: advances in point counting. (This is an advanced chapter covering Takakazu Satoh's fast p-adic algorithm. Note, a very brief introduction to p-adic fields and extensions is given at the start of this chapter.)Chapter VII: hyperelliptic curves and HCDLP.Chapter VIII: Weil descent attacks.Chapter IX: pairings.Chapter X: cryptography from pairings. (Highlight: covers Boneh and Franklin's identity based encryption (IBE) using Weil pairings.)This book, published in April, 2005, brings the reader up to date with much of the latest research on Elliptic Curve Cryptography.The algorithms are in the same format as in Elliptic Curves in Cryptography. Also, like in their first book, this book also does not always give proofs.Highly recommended for advanced graduate students, applied mathematicians and computer scientists in the field of public key cryptography. The mathematics is more advanced than in their first book on Elliptic Curve Cryptography.