We propose a new method for image encryption and decryption in which the image is broken up into bit planes. Each bit plane undergoes a jigsaw transform. The transformed bit planes are combined together and then encrypted using random phase masks and fractional Fourier transforms. The different fractional parameters, the random phase codes, and the jigsaw transform index form the key to the encrypted data. This increases the robustness of the encryption system by several orders of magnitude. Different variations of the juxtaposition of the pieces of the image are also considered. These include the rotated version of the jigsaw pieces. The computational complexity of the bit-plane-based jigsaw algorithm is further improved using the third dimension (i.e., along different bit planes) for scrambling as well. The results of computer simulation are presented to verify the proposed idea and analyze the performance of the proposed techniques.