1.4 Simple XOR

etwork security. Mandatory reading for aspiring system managers. Antonia J. Jones:18 December 2001 2 W. Stallings. Cryptography and Network Security: Principles and Practice. Prentice Hall. 1998. ISBN 0-13-869017-0. Fills in many aspects of the present course and goes on to discuss mail and internet security. C. P. Pfleeger. Security in Computing. Prentice Hall. 1997. ISBN 0-13-185794-0. Good general introduction. The classic 1,200 page definitive story of cryptography up to the late 1950's is: D. Kahn. The Codebreakers. Scribner, New York. 1996. A recent very interesting account including the history of RSA and PGP and a non-technical discussion of quantum cryptography is: S. Singh. The Code Book. Fourth Estate, London. 1999. Fiction: Neal Stephenson. Cryptonomicon. William Heinemann, London. 1999. Antonia J. Jones:18 December 2001 3 CONTENTS I G

One of the longstanding problems in using encryption to encode messages is that the recipient of the message needs to know the key in order to decrypt the message. Clearly we somehow have to get the key to the participants so they can use it. We can’t send the key to them without encrypting *it*, or someone might “eavesdrop ” and get it. But this puts us in an infinite loop: the

The following two computational problems are studied: Duplicate grouping: Assume that n items are given, each of which is labeled by an integer key from the set 0,..., U � 1 4. Store the items in an array of size n such that items with the same key occupy a contiguous segment of the array. Closest pair: Assume that a multiset of n points in the d-dimensional Euclidean space is given, where d � 1 is a fixed integer. Each point is represented as a d-tuple of integers in the range 0,..., U � 14 Ž or of arbitrary real numbers.. Find a closest pair, i.e., a pair of points whose distance is minimal over all such pairs.