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The contribution of this paper are twofold. First, we present an efficient computationally secure anonymous channel which has no problem of ciphertext length expansion. The length is irrelevant to the number of MIXes (control centers). It improves the efficiency of Chaum's election scheme based on the MIX net automatically. Second, we show an election scheme which satisfies fairness. That is, if some vote is distrupted, no one obtains any information about all the other votes. Each voter sends O(nk) bits so that the probability of the fairness is 1 - 2-k, where n is the bit length of the ciphertext.