BooLSPLG: A Library with Parallel Algorithms for Boolean Functions and S-Boxes for GPU

Abstract

In this paper, we present a library with sequential and parallel functions for computing some of the most important cryptographic characteristics of Boolean and vectorial Boolean functions. The library implements algorithms to calculate the nonlinearity, algebraic degree, autocorrelation, differential uniformity and related tables of vectorial Boolean functions. For the sake of completeness, we provide the mathematical basis of these algorithms. Furthermore, we compare the performance of the parallel functions from the developed software with the corresponding sequential functions and with analogous functions from the well-known SageMath and SET packages. Functions from BooLSPLG can be used to develop efficient algorithms for constructing Boolean and vectorial Boolean functions with good cryptographic properties. The parallel part of the library is implemented using a CUDA parallel programming model for recent NVIDIA GPU architectures. BooLSPLG is an open-source software library written in CUDA C/C++ with explicit documentation, test examples, and detailed input and output descriptions of all functions, both sequential and parallel, and it is available online.

Practical Improvement in the Implementation of Two Avalanche Tests to Measure Statistical Independence in Stream Ciphers

“…The increase in speed that was obtained was calculated by comparing the time between the sequential and parallel implementations of the SAC and BIC algorithms [46], independently of each other, and is given by…”

“…In this sense, when the parallelized algorithms of both tests are run on a four-core processor, an acceleration that is around two-three times faster is obtained for the SAC and BIC, respectively. Using a computer with a higher number of cores or GPUs, for example employing CUDA [46], both algorithms could derive a significantly improved performance.…”