Properties of Chebyshev Polynomials Modulo $p^k$
Daisaburo Yoshioka · IEEE Transactions on Circuits & Systems II Express Briefs · 2017
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.