Abstract
Orthogonal arrays (OAs) are basic combinatorial structures, which appear under various disguises in cryptology and the theory of algorithms. Among their applications are universal hashing, authentication codes, resilient and correlation-immune functions, derandomization of algorithms, and perfect local randomizers. In this paper, we give new bounds on the size of orthogonal arrays using Delsarte’s linear programming method. Then we derive bounds on resilient functions and discuss when these bounds can be met.
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C. H. Bennett, G. Brassard, A. K. Ekert: Quantum cryptography. Scientific American 267(4) (1992), 26–33
C. H. Bennett, G. Brassard, J. M. Robert: Privacy amplification by public discussion. SIAM J. Computing 17 (1988), 210–229
J. Bierbrauer: Bounds on orthogonal arrays and codes. Preprint
A. E. Brouwer, T. Verhoeff: An updated table of minimum-distance bounds for binary linear codes. IEEE Transactions on Information Theory 39 (1993), 662–677
P. Camion, C. Carlet, P. Charpin, N. Sendrier: On correlation-immune functions. In: Advances in Cryptology — CRYPTO’ 91. Lecture Notes in Computer Science 576 (1992), 86–100
B. Chor, O. Goldreich, J. Håstad, J. Friedman, S. Rudich, R. Smolensky: The bit extraction problem or t—resilient functions. In: 26th IEEE Symposium on Foundations of Computer Science, 1985, pp. 396–407
P. Delsarte: Four fundamental parameters of a code and their combinatorial significance. Information and Control 23 (1973), 407–438
J. Friedman: On the bit extraction problem. In: 33rd IEEE Symposium on Foundations of Computer Science, 1992, pp. 314–319
K. Gopalakrishnan, D. R. Stinson: Characterizations of non-binary correlation-immune and resilient functions. Technical Report UNL-CSE-93-010, University of Nebraska, March 1993. Submitted to: Designs, Codes and Cryptography
K. Gopalakrishnan, D. R. Stinson, J. Bierbrauer: Orthogonal arrays, resilient functions, error correcting codes and linear programming bounds. Preprint
F. J. MacWilliams, N. J. A. Sloane: The Theory of Error-Correcting Codes, North-Holland, 1977
R. J. McEliece, E. R. Rodemich, H. Rumsey, L. R. Welch: New upper bounds on the rate of a code via the Delsarte-McWilliams inequalities. IEEE Trans. on Information Theory 23 (1977), 157–166
R. A. Rueppel: Analysis and Design of Stream Ciphers, Springer-Verlag, 1986
D. R. Stinson: Resilient functions and large sets of orthogonal arrays. Congressus Numerantium 92 (1993), 105–110
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© 1994 Springer-Verlag Berlin Heidelberg
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Bierbrauer, J., Gopalakrishnan, K., Stinson, D.R. (1994). Bounds for Resilient Functions and Orthogonal Arrays. In: Desmedt, Y.G. (eds) Advances in Cryptology — CRYPTO ’94. CRYPTO 1994. Lecture Notes in Computer Science, vol 839. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48658-5_24
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DOI: https://doi.org/10.1007/3-540-48658-5_24
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