Split Orthogonal Arrays and Maximum Independent ResilientSystems of Functions
Designs, Codes and Cryptography
On Some Methods for Unconditionally Secure Key Distributionand Broadcast Encryption
Designs, Codes and Cryptography - Special issue: selected areas in cryptography I
Some New Results on Key Distribution Patterns and BroadcastEncryption
Designs, Codes and Cryptography
On Perfect and Adaptive Security in Exposure-Resilient Cryptography
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
Autocorrelation Coefficients and Correlation Immunity of Boolean Functions
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Analysis and construction of correctors
IEEE Transactions on Information Theory
| Hi-index | 0.06 |
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 explicit bounds on the size of orthogonal arrays using Delsarte's linear programming method. Specifically, we prove that the minimum number of rows in a binary orthogonal array of length $n$ and strength $t$ is at least $ 2^{n} - (n 2^{n-1}/t+1)$ and also at least $ 2^{n} - (2^{n-2}(n+1)/\lceil \frac{t+1}{2} \rceil).$ We also prove that these bounds are as powerful as the linear programming bound itself for many parametric situations. An $(n,m,t)$-resilient function is a function $f: \{0,1\}^{n} \longrightarrow \{0,1\}^{m}$ such that every possible output $m$-tuple is equally likely to occur when the values of $t$ arbitrary inputs are fixed by an opponent and the remaining $n-t$ input bits are chosen independently at random. A basic problem is to maximize $t$ given $m$ and $n$, i.e., to determine the largest value of $t$ such that an $(n,m,t)$-resilient function exists. In this paper, we obtain upper and lower bounds for the optimal values of $t$ where $1 \leq n \leq 25$ and $1 \leq m It was proved by Chor et al. in [{\em Proc. {\rm 26}th IEEE Symp. on Foundations of Computer Science}, 1985, pp. 396--407] that an $(n,2,t)$-resilient function exists if and only if $ t