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Periodic Properties of Chebyshev Polynomial Sequences Over the Residue Ring $\mathbb{Z}/2^{k}\mathbb{Z}$

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Abstract:

This brief analyzes in detail the relation of the period, the initial value, and the degree of Chebyshev polynomials over the residue ring Z/2kZ. In particular, it is dem...Show More

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Abstract:

This brief analyzes in detail the relation of the period, the initial value, and the degree of Chebyshev polynomials over the residue ring Z/2^kZ. In particular, it is demonstrated that a recently proposed public-key cryptosystem based on Chebyshev polynomials over Z/2^kZ is not secure.

Published in: IEEE Transactions on Circuits and Systems II: Express Briefs ( Volume: 63, Issue: 8, August 2016)

Page(s): 778 - 782

Date of Publication: 18 February 2016

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DOI: 10.1109/TCSII.2016.2531058

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Periodic Properties of Chebyshev Polynomial Sequences Over the Residue Ring $\mathbb{Z}/2^{k}\mathbb{Z}$

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Periodic Properties of Chebyshev Polynomial Sequences Over the Residue Ring \mathbb{Z}/2^{k}\mathbb{Z}\mathbb{Z}/2^{k}\mathbb{Z}

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Periodic Properties of Chebyshev Polynomial Sequences Over the Residue Ring $\mathbb{Z}/2^{k}\mathbb{Z}$