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Cryptography, in particular public-key cryptography, has emerged in the last 20 years as an important discipline that is not only the subject of an enormous amount of research, but provides the foundation for information security in many applications. Standards are emerging to meet the demands for cryptographic protection in most areas of data communications. | This is a Chapter from the Handbook of Applied Cryptography by A. Menezes p. van Oorschot and s. Vanstone CRC Press 1996. For further information see www.cacr.math.uwaterloo.ca hac CRC Press has granted the following specific permissions for the electronic version of this book Permission is granted to retrieve print and store a single copy of this chapter for personal use. This permission does not extend to binding multiple chapters of the book photocopying or prodncing copies for other than personal use of the person creating the copy or making electronic copies available for retrieval by others without prior permission in writing from CRC Press. Except where over-ridden by the specific permission above the standard copyright notice from CRC Press applies to this electronic version Neither this book nor any part may be reproduced or transmitted in any form or by any means electronic or mechanical including photocopying microfilming and recording or by any information storage or retrieval system without prior permission in writing from the publisher. The consent of CRC Press does not extend to copying for general distribution for promotion for creating new works or for resale. Specific permission must be obtained in writing from CRC Press for such copying. 1997 by CRC Press Inc. Index Symbols 5 cardinality of a set S 49 G set member 49 c subset 49 c proper subset 49 D set intersection 49 u set union 49 set difference 49 X Cartesian product 49 0 empty set 50 O-notation big-O 58 ÍÌ-notation big-omega 59 -notation big-theta 59 o-notation little-o 59 f by definition 213 Lq a c subexponential notation 60 p polytime reduction 61 asymptotic equivalence 134 7T mathematical constant pi 49 e base of natural logarithms 49 sum 50 n product 50 factorial 50 J floor 49 r 1 ceiling 49 Ộ Euler phi function 65 286 p n Mobius function 154 lg base 2 logarithm 50 In natural logarithm 50 a 6 interval of integers 49 I divides relation 63 79 congruence relation 67 79 much less than 529 .