中文摘要：

在有限的地上的 Chebyshev 多项式的计算是为公钥 cryptosystem 的统治操作。有运用时间的二个通用算法为这计算被介绍了：矩阵算法和典型多项式算法，它可行然而并非优化。在这份报纸，这二个算法在过程被修改得到更快的实行速度。修改算法的复杂性是静止的，但是要求的操作的数字被减少因此实行速度被改进。而且，如果某些条件满足，与在 Chebyshev 多项式的表示的矩阵的特征值相关的一个新算法也被介绍，它能进一步减少那计算的跑的时间。这些算法的软件实现被认识到，并且跑的时间比较被给。最后，为在有限的地上的 Chebyshev 多项式的计算的一个有效计划被介绍。

英文摘要：

The computation of Chebyshev polynomial over finite field is a dominating operation for a public key cryptosystem.Two generic algorithms with running time of have been presented for this computation：the matrix algorithm and the characteristic polynomial algorithm,which are feasible but not optimized.In this paper,these two algorithms are modified in procedure to get faster execution speed.The complexity of modified algorithms is still,but the number of required operations is reduced,so the execution speed is improved.Besides,a new algorithm relevant with eigenvalues of matrix in representation of Chebyshev polynomials is also presented,which can further reduce the running time of that computation if certain conditions are satisfied.Software implementations of these algorithms are realized,and the running time comparison is given.Finally an efficient scheme for the computation of Chebyshev polynomial over finite field is presented.