Summary
International Symposium on Nonlinear Theory and Its Applications
2022
Session Number:C3L-E
Session:
Number:C3L-E-01
Investigations of Degree Period of Commutative Polynomials Defined by Fourth-Order Recurrence Relations with Two Variables Over $Z_{2^k}$
Takuma Nishizaka , Daisaburo Yoshioka,
pp.499-502
Publication Date:12/12/2022
Online ISSN:2188-5079
Summary:
In recent years, a public-key cryptosystem based on Chebyshev polynomials over Z2k has been presented. Unfortunately, however, the cryptosystem is broken using knowledge of the periodic properties of Chebyshev polynomials. Although commutative polynomials with two variables can be candidates for the cryptosystem instead of Chebyshev polynomials, the periodic properties of the polynomials should be discussed carefully. In this study, we investigated the degree period of commutative polynomials with two variables over residue ring Z2k.