K. Gopalakrishnan

Protocols for watermark verification

In current digital watermarking schemes used to deter piracy of multimedia content, the owner typically reveals the watermark in the process of establishing piracy. Once revealed, a watermark can be removed. We eliminate this limitation by using cryptographic protocols to demonstrate the presence of a watermark without revealing it.

Three characterizations of non-binary correlation-immune and resilient functions

A functionf(X1,X2, ...,Xn) is said to betth-order correlation-immune if the random variableZ=f(X1,X2,...,Xn) is independent of every set oft random variables chosen from the independent equiprobable random variablesX1,X2,...,Xn. Additionally, if all possible outputs are equally likely, thenf is called at-resilient function. In this paper, we provide three different characterizations oft th-order correlation immune functions and resilient functions where the random variable is overGF (q). The first is in terms of the structure of a certain associated matrix. The second characterization involves Fourier transforms. The third characterization establishes the equivalence of resilient functions and large sets of orthogonal arrays.

Bounds for Resilient Functions and Orthogonal Arrays

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 Delsartes linear programming method. Then we derive bounds on resilient functions and discuss when these bounds can be met.

A note on a conjecture concerning symmetric resilient functions

Abstract In 1985, Chor et al. conjectured that the only 1-resilient symmetric functions are the exclusive-or of all n variables and its negation. In this note the existence of symmetric resilient functions is shown to be equivalent to the existence of a solution to a simultaneous subset sum problem. Then, using arithmetic properties of certain binomial coefficients, an infinite class of counterexamples to the conjecture is obtained.

Orthogonal Arrays, Resilient Functions, Error-Correcting Codes, and Linear Programming Bounds

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 Delsartes linear programming method. Specifically, we prove that the minimum number of rows in a binary orthogonal array of length

Consecutive retrieval property-revisited

n

A simple analysis of the error probability of two-point based sampling

and strength

Solving discrete logarithms from partial knowledge of the key

t

Applications of Orthogonal Arrays to Computer Science

is at least

A Note on the Duality of Linear Programming Bounds for Orthogonal Arrays and Codes

2^{n} - (n 2^{n-1}/t+1)