Calculation Enhancement of Chebyshev Polynomial over Zp

It has been recommended that the safe size of the key space for any cryptosystem based on chebyshev polynomial extended over the finite field zp must be chosen such that p≥2256. for such size of p,the normalchebyshev 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.