Physical Sciences and Mathematics Commons^™

Boolean Functions With Important Cryptographic Properties., Subhamoy Maitra Dr.

Doctoral Theses

In this thesis we concentrate on properties of cryptographically significant Boolean functions.The techniques are mainly combinstorial and provide new resulta on enumeration and construction of such functions. Initially we concentrate on a partieular subset of Boolean functions called the symmetric Boolean functions. A closed form expression for the Walsh transform of an arbitrary symmetric Boolean function is presented. We completely characterize the symmetric functions with maximum nonlinearity and show that the maximum nonlinearity of n-variable symmetrie function can be 2n-1-2[n-1l2], Moreover, new classes of symmetric balanced and symmetric correlation immune functions are considered.We provide a randomised heuristic to construct balanced …