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In this paper, we propose a fast algorithm to solve the general case of cascade exponentiation of the form pi=I Mibi. On the basis of Lempel-Ziv-Welch compression method, a modified encoding scheme is used to compute the corresponding bits of exponents and encode them to a basket. By the use of the modified compression scheme, an algorithm is designed and applied to solve the problem of cascade exponentiation with general form. Several experiments are carried out and the performances are improved comparing with Chang et al.`s scheme.
