Open AccessNonsingularity of Feedback Shift Registers of Degree at Most Three over a Finite Field
Author(s) -
Junying Liu,
Yupeng Jiang,
Qunxiong Zheng,
Dongdai Lin
Publication year - 2021
Publication title -
chinese journal of electronics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.267
H-Index - 25
eISSN - 2075-5597
pISSN - 1022-4653
DOI - 10.1049/cje.2021.01.009
Subject(s) - shift register , finite field , linear feedback shift register , algebraic number , coding (social sciences) , degree (music) , register (sociolinguistics) , pseudorandom number generator , computer science , field (mathematics) , arithmetic , cryptography , pseudorandom function family , stream cipher , mathematics , discrete mathematics , algorithm , pure mathematics , telecommunications , mathematical analysis , physics , acoustics , chip , statistics , linguistics , philosophy
As a kind of generators of pseudorandom sequences, the Feedback shift register (FSR) is widely used in channel coding, cryptography and digital communication. A necessary and sufficient condition for the nonsingularity of a feedback shift register of degree at most three over a finite field is established. Using the above result, we can easily determine the nonsingularity of a feedback shift register from the algebraic normal form of the corresponding feedback function.