Characterizations of the Differential Uniformity of Vectorial Functions by the Walsh Transform

2018 ◽  
Vol 64 (9) ◽  
pp. 6443-6453 ◽  
Author(s):  
Claude Carlet
Keyword(s):  
Walsh Transform ◽  
Differential Uniformity ◽  
Vectorial Functions

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

2018 ◽  
Vol 18 (5) ◽  
pp. 21-43
Author(s):  
Dusan Bikov ◽  
Iliya Bouyukliev
Keyword(s):  
Boolean Functions ◽  
Parallel Execution ◽  
Experimental Results ◽  
Walsh Transform ◽  
Sequential Algorithm ◽  
Differential Uniformity ◽  
Walsh Spectrum

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.

Calculation of Multiplication, Using Walsh Transform

2010 ◽  
Vol 42 (4) ◽  
pp. 37-65
Author(s):  
Andrey N. Tereshchenko ◽  
Svetlana S. Melnikova ◽  
Lev A. Hnativ ◽  
Valeriy K. Zadiraka ◽  
Natalya V. Koshkina
Keyword(s):  
Walsh Transform

An automatic seismic signal detection algorithm based on the Walsh transform

1981 ◽  
Vol 71 (4) ◽  
pp. 1351-1360
Author(s):  
Tom Goforth ◽  
Eugene Herrin
Keyword(s):  
Signal Detection ◽  
Real Time ◽  
Seismic Signal ◽  
Detection Algorithm ◽  
Machine Language ◽  
Walsh Transform ◽  
Time Signal ◽  
Data Systems ◽  
Detection Capability ◽  
Short Period

abstract An automatic seismic signal detection algorithm based on the Walsh transform has been developed for short-period data sampled at 20 samples/sec. Since the amplitude of Walsh function is either +1 or −1, the Walsh transform can be accomplished in a computer with a series of shifts and fixed-point additions. The savings in computation time makes it possible to compute the Walsh transform and to perform prewhitening and band-pass filtering in the Walsh domain with a microcomputer for use in real-time signal detection. The algorithm was initially programmed in FORTRAN on a Raytheon Data Systems 500 minicomputer. Tests utilizing seismic data recorded in Dallas, Albuquerque, and Norway indicate that the algorithm has a detection capability comparable to a human analyst. Programming of the detection algorithm in machine language on a Z80 microprocessor-based computer has been accomplished; run time on the microcomputer is approximately 110 real time. The detection capability of the Z80 version of the algorithm is not degraded relative to the FORTRAN version.

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