On some cryptographic properties of Boolean functions and their second-order derivatives
This work addresses cryptographic security analysis for Boolean functions, but it appears incremental as it builds on existing properties and methods.
The paper investigates cryptographic properties of Boolean functions, such as weight, balancedness, and nonlinearity, with a focus on splitting and cubic functions, and introduces quantities from second-order derivatives to determine if quadratic or cubic functions are APN.
In this paper some cryptographic properties of Boolean functions, including weight, balancedness and nonlinearity, are studied, particularly focusing on splitting functions and cubic Boolean functions. Moreover, we present some quantities derived from the behaviour of second-order derivatives which allow us to determine whether a quadratic or cubic function is APN.