Krawtchouk polynomials and their applications in cryptography and coding theory

Basic properties of the Krawtchouk polynomials are reviewed, some new results which are of interest for the theory and applications are obtained. We study analytic, number-theoretic properties and asymptotic behaviour of the Krawtchouk polynomials under different relations between their parameters along with the probabilistic properties of polynomials with random parameters. Applications of the Krawtchouk polynomials to the cryptographic properties of Boolean functions and coding theory are discussed.