The algorithm presented in this paper performs data encryption by serially concatenating two transform stages. The outer stage uses one of the orthogonal matrices obtained from the singular value decomposition (SVD) of an arbitrary signal, such as white noise or the sum of cosines of different frequencies. The inner stage of encryption uses a fast, parallelized wavelet filter bank using the algorithm presented by Koh and Rodriguez-Marek. This algorithm is generalized for an arbitrary number of nodes and decomposition levels. Past algorithms based on the wavelet packet tree structure present a drawback for band-limited signals, because attackers can guess the approximate frequency bands of the wavelet decomposition. In this paper, the algorithm uses orthogonal matrices generated by the SVD, which spread the frequency content of the signal into the available spectrum when applied to the original vector. Furthermore, the algorithm is based on parallelized filter banks, which provide a flexible and highly adaptive structure for encryption and decryption.