Contemporary image coding schemes provide compression by exploiting spatial and psycho-visual redundancies. Encryption of an uncompressed image removes intelligibility from the original image, thereby incurring compression penalties. This results in a trade-off between the competing requirements of encryption and compression.

A variety of encryption algorithms can be employed to remove intelligibility from an uncompressed archived image. This local encryption is generally performed to preserve data security without assuming compression at another time. However, post-encryption transmission of such locally-stored images stipulates compression to improve bandwidth utilization.

The performance of image compression standards for encrypted images has been largely unexplored. The only work to date, by Johnson et al.,^{1} shows that through the use of coding with side information principles, the compression of encrypted data can theoretically be accomplished without loss of coding efficiency or perfect secrecy in certain scenarios. For example, if the original source is Gaussian, the same efficiency can be achieved for lossy compression of an encrypted source, as when encryption is effected after compression. In Johnson, the decompression and decryption operations were performed jointly at the receiver. However, most commercial image compression standards accomplish compression/decompression without any supposition about encryption/decryption at later stages.

First we evaluate an existing compression standard without making any modifications to it. We employed JPEG 2000^{2} as our compression strategy for exploring the encryption-compression trade-off. For security, we used the pre/post-filter based encryption scheme proposed by Kuo et al.^{3} This kind of filtering effects encryption by scrambling the phase spectrum of the image. An example of an image encrypted using pre/post-filtering is shown in Figure 1.

**Figure 1.** (a) Original and (b) pre/post-filtered\break (encrypted) images.

Most image-compression encoders, including JPEG 2000, rely on perceptual details for compression, namely frequency weighting, color weighting, and visual progressive weighting. On the other hand, the pre-filtering process removes perceptual details from an image. Consequently, the encrypted images yield compression inefficiencies. The compression inefficiency for JPEG 2000 is illustrated in Figure 2. For any given compression rate, an unencrypted image always renders a higher peak signal-to-noise ratio (PSNR) than its encrypted counterpart.

**Figure 2.** PSNR of original and pre/post-filtered images.

Next we evaluated a partial-phase encryption scheme in a bid to improve compression efficiency: here, only a fraction of the phase spectrum is subjected to encryption. Figure 3. illustrates that the pre/post-filter approach renders effective encryption even when a very small fraction of the total phase is subjected to encryption: 25% encryption in Figure 3(a). While partial encryption does not reduce complexity considerably in the present fast-Fourier-transform (FFT)-based phase encryption scheme, in other encryption schemes (such as DES and AES), encryption complexity is generally a linear function of the data length. In such encryption schemes, partial encryption—typically effected in the frequency domain—renders the added advantage of complexity reduction.

**Figure 3.** Images with partial phase encryption; only (a) 25% and (b) 75% of the phase spectrum of Fig. 1(a) is encrypted.

The important question here is whether a partially-encrypted image improves compression efficiency compared to a fully encrypted image. Figure 4 illustrates, in terms of PSNR, the compression efficiencies of images with varying levels of partial encryption. Note that the performance for all encryption levels at low compression rates (0.5—4.5bpp) is satisfactory. Regardless of the encryption level, compared to no encryption, compression performance deteriorates rapidly for compression rates greater than 4.5bpp.

**Figure 4.** PSNR of images with different levels of partial encryption.

We conclude that encryption can be employed at low compression rates without significantly compromising compression efficiency. Such low bit-rate compression has applications in bandwidth-constrained wireless environments. Decreasing the level of encryption—using partial encryption, for example—does not yield much improvement in compression efficiency. Hence, if complexity permits, full encryption should be employed to maximize security of the transmitted images. In complexity-constrained environments, partial encryption can provide reasonable security.

The authors would like to thank Professors Hayder Radha and John R. Deller, Jr. for their guidance, and gratefully acknowledge the generous financial support extended by the MSU CyberSecurity Initiative for this project.