Open AccessA Pseudorandom Sequence Generated over a Finite Field Using The Möbius Function
Author(s) -
Václav Zvoníček
Publication year - 2021
Publication title -
journal of the asb society
Language(s) - English
Resource type - Journals
ISSN - 2695-1010
DOI - 10.51337/jasb20211227005
Subject(s) - pseudorandomness , pseudorandom number generator , sequence (biology) , autocorrelation , finite field , pseudorandom generator theorem , pseudorandom function family , generator (circuit theory) , pseudorandom generator , field (mathematics) , pseudorandom binary sequence , mathematics , function (biology) , pseudorandom noise , discrete mathematics , complementary sequences , linear congruential generator , combinatorics , algorithm , computer science , arithmetic , pure mathematics , physics , spread spectrum , statistics , quantum mechanics , telecommunications , channel (broadcasting) , binary number , biology , genetics , power (physics) , evolutionary biology
The aim of this paper is to generate and examine a pseudorandom sequence over a finite field using the Möbius function. In the main part of the paper, after generating a number of sequences using the Möbius function, we examine the sequences’ pseudorandomness using autocorrelation and prove that the second half of any sequence in $\mathbb{F}_{3^n}$ is the same as the first, but for the sign of the terms. I reach the conclusion, that it is preferable to generate sequences in fields of the form $\mathbb{F}_{3^n}$, thereby obtaining a sequence of the numbers $-1$,$0$,$1$, each of which appear in the same amounts. There is a variety of applications of the discussed pseudorandom generator and other generators such as cryptography or randomized algorithms.