CIF: Small: RUI: Highly Nonlinear and Uncorrelated Structures for Communications and Sensing

This project concerns the creation and analysis of structures such as Boolean functions with high nonlinearity and sequences with low correlation. These structures are used in many areas of information theory, such as information security, communications, coding, and sensing. Boolean functions and finite field permutations that are highly ordered from one point of view, but which appear random from another point of view, provide cryptographic primitives with both efficient implementation and high resilience to cryptanalytic attacks. A function's resistance against two of the most significant types of attack, linear cryptanalysis and differential cryptanalysis, is determined by its Walsh spectrum and its differential spectrum, which are some of the principal objects of study in this project. Many of the sequences used to modulate signals in communications and remote sensing are related to highly nonlinear functions over finite fields. Efficient use of channel resources requires sets of sequences that are as uncorrelated as possible: they should not resemble shifted (time-delayed) versions of each other, nor even of themselves. Random sequences are unwieldy to implement and have occasional repetitions, so they are deficient both in usability and performance. This project concerns itself with the design of pseudorandom sequences that are easier to use and provide much lower correlation.