Parallel Fast Walsh Transform Algorithm and Its Implementation with CUDA on GPUs

Abstract

Some of the most important cryptographic characteristics of the Boolean and vector Boolean functions (nonlinearity, autocorrelation, differential uniformity) are connected with the Walsh spectrum. In this paper, we present several algorithms for computing the Walsh spectrum implemented in CUDA for parallel execution on GPU. They are based on the most popular sequential algorithm. The algorithms differ in the complexity of implementations, resources used, optimization strategies and techniques. In the end, we give some experimental results.

Improved Algoritms in Parallel Evaluation of Large Cryptographic S-Box

“…They also concluded that implementation was not suitable for large S-Boxes in terms of time and memory and suggested use of parallelization for solving this problem. Bikov et al (2018) parallelized the walsh spectrum of boolean functions by using fast walsh al. in alternative ways, running them on GPU, and finally, comparing the results [15].…”

“…Bikov et al (2018) parallelized the walsh spectrum of boolean functions by using fast walsh al. in alternative ways, running them on GPU, and finally, comparing the results [15]. Various parallelization of fast walsh al.…”

Bijective S-boxes of different sizes obtained from quasi-cyclic codes

“…For the programs we have used GPU computing model with CUDA. This allows us to interact directly with the GPUs and run programs on them, thus effectively utilizing the advantages of parallelization (many details about the parallel algorithms and programs are given in [2]). For this research, we have used a graphic card NVIDIA GeForce Titan X Pascal which we have as a donation from NVIDIA Corporation.…”

Characteristic vector and weight distribution of a linear code

“…The algorithms that use listings of codewords, are faster for small lengths because they use bitwise representation of the codewords and bitwise operations. For larger lengths, the algorithms close to discrete Fourier transforms, can be represented by a butterfly diagram and are therefore suitable for parallelization [4].…”