No abstract

We consider the problem of bounding the maximum possible number f k,d (n) of ksimplices that are spanned by a set of n points in R d and are similar to a given simplex. We first show that f 2,3 (n) = O(n 13/6 ), and then tackle the general case, and show

The protection of time sharing systems from unauthorized users is often achieved by the use of passwords. By using one-way ciphers to code the passwords, the risks involved with storing the passwords in the computer can be avoided. We discuss the selection of a suitable one-way cipher and suggest that for this purpose polynomials over a prime modulus are superior to one-way ciphers derived from Shannon codes.

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In his 1983 paper, Neal Wagner' defines a perfect fingerprint to be an identifying fingerprint added to an object in such a way t h a t any alteration to it that makes the fingerprint unrecognizable will also make the object unusable. A perfect fingerprinting scheme for binary data would seem difficult t o devise, since it would be possible t o discover the fingerprints by comparing different fingerprinted copies of the same piece of data. In this paper we discuss a fingerprinting scheme which, although i t does not surmount this problem entirely, at least specifies the number of copies an opponent must obtain in order to erase the fingerprints. The fingerprints involved will be rather lengthy, so we will restrict ourselves to what we will call long forgiving messages. A forgiving message is one which is still readily understandable and not jarring when up t o 0.1% of i t has been altered. Examples are voice and television. People can speak comfortably amid the noise of a cafeteria and can enjoy watching a television show with several pixels per frame altered. The idea in each case is that the support of the noise (the set outside which the additive noise must vanish) must have small