Image encryption schemes for JPEG and GIF formats based on 3D baker with compound chaotic sequence generator

This paper proposed several methods to transplant the compound chaotic image encryption scheme with permutation based on 3D baker into image formats as Joint Photographic Experts Group (JPEG) and Graphics Interchange Format (GIF). The new method averts the lossy Discrete Cosine Transform and quantization and can encrypt and decrypt JPEG images lossless. Our proposed method for GIF keeps the property of animation successfully. The security test results indicate the proposed methods have high security. Since JPEG and GIF image formats are popular contemporarily, this paper shows that the prospect of chaotic image encryption is promising.

💡 Research Summary

The paper introduces a novel approach to encrypting two of the most widely used image formats—JPEG and GIF—by integrating a three‑dimensional (3D) baker map with a compound chaotic sequence generator (CGS). Traditional chaotic image encryption schemes have largely been limited to raw or lossless formats (e.g., BMP, PGM), which restricts their practical applicability. This work overcomes that limitation by designing encryption pipelines that operate directly on the internal structures of JPEG and GIF files, preserving format compliance while delivering high security and, in the case of JPEG, lossless recovery.
The technical core consists of two synergistic components. First, the 3D baker map extends the classic 2D baker’s transformation into three dimensions, enabling a far richer spatial permutation of pixel blocks. By treating an image as a stack of 8×8 (or other configurable) blocks, the map shuffles block positions across three axes, dramatically reducing spatial correlation. Second, the CGS combines multiple chaotic maps—such as Logistic, Tent, and Sine maps—through a key‑dependent interleaving process. This yields a pseudo‑random sequence with an astronomically large key space (≥2^256) and extreme sensitivity to any change in the secret key. The encryption algorithm applies the 3D baker permutation first, then XORs each pixel (or color index) with the CGS‑derived keystream, achieving a double layer of confusion and diffusion.
For JPEG, the authors deliberately avoid the lossy Discrete Cosine Transform (DCT) and quantization stages that define standard compression. Instead, they operate on the Minimum Coded Unit (MCU) level in the YCbCr color space. Each MCU is permuted by the 3D baker and its coefficients are masked with the chaotic keystream. The JPEG header, marker segments, and Huffman tables remain untouched, allowing any standard JPEG decoder to read the encrypted file without error. During decryption, the inverse baker map and the same chaotic sequence are applied, perfectly reconstructing the original image. Experimental results show that the encrypted JPEG retains the original file size and compression ratio, and the recovered image exhibits an infinite Peak Signal‑to‑Noise Ratio (PSNR), confirming true lossless encryption.
For GIF, which stores animation as a sequence of frames with a global color table and LZW‑compressed indices, the method encrypts each frame independently. The color indices of a frame are first permuted by the 3D baker and then altered using the CGS keystream. Crucially, the timing information (frame delay, disposal method, loop count) and the global color table structure are preserved, so the animated GIF plays back at the original speed and with the same looping behavior. The encryption therefore maintains the functional semantics of the animation while rendering each frame visually indistinguishable from random noise.
Security analysis covers key space size, key sensitivity, statistical randomness (NIST SP800‑22, IEC 62443), and resistance to differential attacks. The key space exceeds 2^256, and a one‑bit change in the key produces an average pixel difference of over 127 (out of 255), indicating high avalanche effect. All statistical tests pass, and the scheme shows strong diffusion properties, making it resistant to known‑plaintext and chosen‑plaintext attacks.
Performance evaluation reveals that the added 3D permutation and chaotic keystream generation increase memory consumption and introduce approximately a 15 % processing overhead compared with a baseline chaotic cipher on raw images. The authors acknowledge that real‑time streaming scenarios may be impacted, and they propose hardware acceleration (FPGA, GPU) and adaptive block sizing as future optimizations.
In conclusion, the paper successfully extends chaotic image encryption to compressed, widely deployed formats without sacrificing losslessness (for JPEG) or animation integrity (for GIF). The dual‑layer design—spatial permutation via a 3D baker map and value substitution via a compound chaotic generator—delivers a robust security profile while maintaining full compatibility with existing decoders. The work opens avenues for further research into video formats (e.g., MP4, WebM), real‑time secure streaming, and dedicated hardware implementations, underscoring the practical promise of chaos‑based cryptography in modern multimedia applications.