Abstract. In this paper we use coding theory to give simple explanations of some recent results on universal hashing. We first apply our approach to give a precise and elegant analysis of the Wegman-Carter construction for authentication codes. Using Reed-Solomon codes and the well known concept of concatenated codes we can then give some new constructions, which require much less key size than previously known constructions. The relation to coding theory allows the use of codes from algebraic curves for the construction of hash functions. Particularly, we show how codes derived from Artin-Schreier curves, Hermitian curves and Suzuki curves yield good classes of universal hash functions.
In this paper we show an explicit relation between authentication codes and codes correcting independent errors. This relation gives rise to several upper bounds on A-codes. We also show how to construct A-codes starting from error correcting codes. The latter is used to show that if Ps exceeds PI by an arbitrarily small positive amount, then the number of source states grows exponentially with the number of keys but if PS = PI it will grow only linearly. tion theory these codes are called appended authenticator schemes or Cartesian A-codes. People working in coding theory would use the term systematic codes. Furthermore, in this paper we will only deal with unconditionally secure A-codes.
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