Annotation: Effective method of the discrete Fourier transform acceleration with the use of cloud computing is theoretically substantiated and developed. The reigning feature of the suggested method is homomorphic encryption of the input signals, which provides efficient protection during the remote calculation. It has been shown theoretically and experimentally that the proposed method allows one to 1-2 orders of magnitude to speed up the processing of signals while maintaining their

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... ality. The proposed method can be applied for effective signal stream processing in clouds.