Properties of Chebyshev Polynomials Modulo p^k

Chebyshev polynomials are employed in various applications, such as cryptography and pseudorandom numbers. The sequences generated by iterating Chebyshev polynomials over finite sets should have a finite period. Therefore, determining the period is considerably important in such applications, where...

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Bibliographic Details
Published inIEEE transactions on circuits and systems. II, Express briefs Vol. 65; no. 3; pp. 386 - 390
Main Author Yoshioka, Daisaburo
Format Journal Article
LanguageEnglish
Published IEEE 01.03.2018
Subjects
Chaotic communication
Chebyshev approximation
Chebyshev polynomial
Circuits and systems
cryptography
Indexes
period
permutation
Public key cryptography
sequence
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Summary:Chebyshev polynomials are employed in various applications, such as cryptography and pseudorandom numbers. The sequences generated by iterating Chebyshev polynomials over finite sets should have a finite period. Therefore, determining the period is considerably important in such applications, where the period is often required to be sufficiently large. In this brief, the sequence period of Chebyshev polynomials modulo a prime power is obtained analytically. The results of this brief provide a design strategy for applications requiring a specific period.
ISSN:1549-7747
1558-3791
DOI:10.1109/TCSII.2017.2739190