Malaysian Journal of Mathematical Sciences, August 2013, Vol. 7(S)
Special Issue: The 3rd International Conference on Cryptology & Computer Security 2012 (CRYPTOLOGY2012)
Calculation Enhancement of Chebyshev Polynomial over $\mathbb{Z}_p$
Mohammed Benasser Algehawi, Azman Samsudin and Shahram Jahani
Corresponding Email: [email protected]
Received date: -
Accepted date: -
Abstract:
It has been recommended that the safe size of the keyspace for any cryptosystem based on Chebyshev polynomial extended over the finite field $\mathbb{Z}_p$ must be chosen such that $p \geq 2^{256}$. For such size of $p$, the normal Chebyshev polynomial calculation speed will be slow and impractical. Thus, there is a need to improve the Chebyshev polynomial calculation before the polynomial can be used in mainstream cryptosystems. In this paper, two types of Chebyshev polynomial calculation models are being considered, the Matrix Algorithm and the Characteristic Polynomial Algorithm. This paper introduces new technique to improve both of these calculation models. Preliminary results show indications that the proposed technique is a reliable alternative for implementing Chebyshev polynomial calculation.
Keywords: Public-key cryptography, Chebyshev polynomial, and Chaos cryptography
