Almost Independent and Weakly Biased Arrays: Efficient Constructions and Cryptologic Applications

The best known constructions for arrays with low bias are those from [1] and the exponential sum method based on the WeilCarlitz-Uchiyama bound. They all yield essentially the same parameters. We present new efficient coding-theoretic constructions, which allow farreaching generalizations and improvements. The classical constructions can be described as making use of Reed-Solomon codes. Our recursive construction yields greatly improved parameters even when applied to Reed-Solomon codes. Use of algebraic-geometric codes leads to even better results, which are optimal in an asymptotic sense. The applications comprise universal hashing, authentication, resilient functions and pseudorandomness. Key Words Low bias, almost independent arrays, Reed-Solomon codes, Hermitian codes, Suzuki codes, Fourier transform, Weil-Carlitz-Uchiyama bound, exponential sum method, Zyablov bound, hashing, authentication, resiliency.

• Type: Conference
• Year: 2000
• Where: CRYPTO
• Authors: Jürgen Bierbrauer, Holger Schellwat
• Keywords: CRYPTO 2000, Cryptology, Exponential Sum Method, Low Bias, Reed-Solomon Codes