Abstract
The best known constructions for arrays with low bias are those from [1] and the exponential sum method based on the Weil-Carlitz-Uchiyama bound. They all yield essentially the same parameters. We present new efficient coding-theoretic constructions, which allow far-reaching 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
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Bierbrauer, J., Schellwat, H. (2000). Almost Independent and Weakly Biased Arrays: Efficient Constructions and Cryptologic Applications. In: Bellare, M. (eds) Advances in Cryptology — CRYPTO 2000. CRYPTO 2000. Lecture Notes in Computer Science, vol 1880. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44598-6_33
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DOI: https://doi.org/10.1007/3-540-44598-6_33
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