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The purpose of this paper is to focus on the local echo-canceling problem of full-duplex scrambled speech communications over a two-wire telephone network when the scrambling transformation is located between the handset and body of a telephone. Such a design makes possible very efficient protection against electromagnetic compromising emanation, which in turn substantially enhances the overall security of a protected communication. We propose a new adaptive FIR filter algorithm for local echo cancellation in such applications. The proposed algorithm differs from the conventional one by the construction of input signals in an optimal way using the D-optimal experiment design. In this way, at each step, we generate a new sample of the D-optimal pilot sequence for the filter parameter estimation. Consequently, the adaptation of the local echo canceler is defined as an initialization process in the first phase of each protected telephone call. The advantage in using the proposed adaptive FIR echo canceler is demonstrated through simulation results.