A trade-off between collision probability and key size in universal hashing using polynomials

Let F be a finite field and suppose that a single element of F is used as an authenticator (or tag). Further, suppose that any message consists of at most L elements of IF. For this setting, usual polynomial based universal hashing achieves a collision bound of (L-1)/|F| using a single element of F as the key. The well-known multi-linear hashing achieves a collision bound of F using L elements of IF as the key. In this work, we present a new universal hash function which achieves a collision bound of m[logmL]/|H|,m≥2, using 1+[logmL] elements of F as the key. This provides a new trade-off between key size and collision probability for universal hash functions. © 2010 Springer Science+Business Media, LLC.