MA4550 Combinatorial and Cryptographic Properties of Boolean Functions

The course will discuss the Fourier analysis of Boolean functions and the relevant combinatorics with an eye toward cryptography and coding theory. Particular topics will include avalanche features of Boolean functions, correlation immunity and resiliency, bentness, trade-offs among cryptographic criteria and real-life applications in the designs of stream and block ciphers.

Prerequisite

MA3025 or a similar combinatorial/discrete mathematics course (and recommended, but not required, an introductory course in probability)

Lecture Hours

4

Lab Hours

0

Course Learning Outcomes

• Students should learn the concept of a Boolean function and how to represent it in different ways.
• Students should be able to use Boolean functions as combiners in the context of linear feedback registers.
• Students should be able to use the Walsh-Hadamard transform and its connection to nonlinearity, Hamming weights.
• Students should be able to check the local and global avalanche, immunity features of a Boolean function.
• Students should be able to check the bent property of a Boolean function and define some classes of such functions.
• Students should be able to describe some attacks on ciphers depending upon the lack of certain properties of the used Boolean function.
• Students should be able to describe the usage of Boolean functions in the context of block and stream ciphers, like DES, AES, etc.