Designing Bent Boolean Functions With Parallelized Linear Genetic Programming

Bent Boolean functions, nonlinearity, parallelization, linear programming.

Bent Boolean functions are cryptographic primitives essential for the safety of cryptographic algorithms, providing a degree of non-linearity to otherwise linear systems. The maximum possible non-linearity of a Boolean function is limited by the number of its inputs, and as technology advances, functions with higher number of inputs are required in order to guarantee a level of security demanded in many modern applications. Genetic programming has been successfully used to discover new larger bent Boolean functions in the past. This paper proposes the use of linear genetic programming for this purpose. It shows that this approach is suitable for designing of bent Boolean functions larger than those designed using other approaches, and explores the influence of multiple evolutionary parameters on the evolution runtime. Parallelized implementation of the proposed approach is used to search for new, larger bent functions, and the results are compared with other related work. The results show that linear genetic programming copes better with growing number of function inputs than genetic programming, and is able to create significantly larger bent functions in comparable time.

Bent Boolean functions are cryptographic primitives essential to safety of cryptographic algorithms, providing a degree nonlinearity to otherwise linear systems. Maximum possible nonlinearity of a Boolean function is limited by the number of it's inputs, and as technology advances, functions with higher number of inputs are required to guarantee a level of security, demanded in many modern applications. Two of the possible ways to design bent Boolean functions, are genetic programming and Cartesian genetic programming, both of which have been successfully used to discover new larger bent Boolean functions in the past. This paper proposes a new approach using linear genetic programming. It shows that this new approach is suitable for design of bent Boolean functions, and explores the influence of multiple evolutionary parameters on evolution run time. Parallelized implementation of the proposed approach is used to search for new, larger bent functions, and it's results are compared to those obtained in other related works. The results show that linear genetic programming copes better with growing number of function inputs than Cartesian genetic programming, and is able to create significantly larger bent functions in comparable time.