We present a turbo coding scheme whose constituent codes are designed using convolutional encoders with time-varying coefficients. These encoders are finite state sequence machines that operate over the Galois field GF(q). The scheme includes an encryption polynomial whose coefficients are changed periodically by means of a user key. The trellis coding procedure thus hops from one trellis to another, following a random sequence taken over a set of subtrellises which correspond to different convolutional encoders. The proposed scheme is introduced as a turbo code with encryption properties, and is presented in two forms, the systematic and the nonsystematic schemes.