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Guide to Elliptic Curve Cryptography Springer New York Berlin Heidelberg Hong Kong London Milan Paris Tokyo Darrel Hankerson Alfred Menezes Scott Vanstone Guide to Elliptic Curve Cryptography With 3 8 Illustration s Springer Darrel Hankcrsnn Alfred Meneze s Department o f Mathematic s Departmet of Combinatorie s and Auburn Universit y Optimization Auhuni , Al . .36849-5107. USA Universit y o f Waterloo 1 Waterloo. Ontario , N2L 3G 1 Canada hankedr auburn , cdu ajmeneze@uwaterloo.ca Scott Vanslon e Depart men l of Combinatoric s and Oplimi/.alion Universit y o f Waterloo Waterloo, Ontario . N2L 3Gl Canada xavansUK 1 LI Waterloo.ea library of Congres s Calaloging-in-Publicatio n Data Hankerson . Darre l R . Guide t o ellipti c curv e cryptography / Darrel Hankerson , Alfre d J . Menezes , Scott Vanstone. p. cm. Include s bibliographical reference s and index . ISBN 0-387-95273-X ( a l k . paper ) 1. Computer securiiy . 2 . PuMi c key cryptography . I . Vunsionc , Scott A , 11. Mene/.es . A . J . (Alfre d J , ) , 1965- III . Title , QA76.9.A25H37 2003 005.8(2-dc22 2003059137 ISBN 0-387-95273-X Printed un acid-fre e paper . (c) 2004 Springer-Verla g New York, Inc .