Strongly universal hashing and identification codes via channels

Universal Hashing and Geometric Codes

We describe a new application of algebraic coding theory to universal hashing and authentication without secrecy. This permits to make use of the hitherto sharpest weapon of coding theory, the construction of codes from algebraic curves. We show in particular how codes derived from Artin-Schreier curves, Hermitian curves and Suzuki curves yield classes of universal hash functions which are subs...

Bucket Hashing with a Small Key Size

In this paper we consider very fast evaluation of strongly universal hash functions, or equivalently, authentication codes. We show how it is possible to modify some known families of hash functions into a form such that the evaluation is similar to \bucket hashing", a technique for very fast hashing introduced by Rogaway. Rogaway's bucket hash family has a huge key size, which for common param...

Universal Hashing and Authentication Codes

Universal Hashing and Multiple Authentication

In this paper, we study unconditionally secure codes that provide authentication without secrecy. Our point of view is the univcrsal hashing approach pioneered by Wegman and Carter in 1981. We first compare several recent universal-hashing based constructions for mthenticatmion codes. Then we gencralize the theory of universal hashing in order t,o accommodate the situation where we would like t...

On the Connections Between Universal Hashing, Combinatorial Designs and Error-Correcting Codes

In this primarily expository paper, we discuss the connections between two popular and useful tools in theoretical computer science, namely, universal hashing and pairwise independent random variables ; and classical combinatorial stuctures such as error-correcting codes, balanced incomplete block designs, diierence matrices and orthogonal arrays.