Cryptanalysis of a Chaotic Neural Network Based Multimedia Encryption Scheme

1. Cryptanalysis of a Chaotic Neural Network Based Multimedia Encryption Scheme Chengqing Lia, Shujun Lib, Dan Zhanga and Guanrong Chenb a Zhejiang University, Hangzhou, China b City University of Hong Kong, HK, China

2. Abstract • This research points out some security problems with a recently-proposed multimedia encryption scheme based on chaotic neural networks [1-5]. • It can be broken in known/chosen-plaintext attacks, with only one known/chosen plain-image. • A mask image can be derived as the equivalent key. • The secret key itself can be broken with a small complexity. • The security against brute-force attack was over-estimated. PCM 2004, Tokyo, Japan

3. References • Yen, J.C., Guo, J.I.: A chaotic neural network for signal encryption/decryption and its VLSI architecture. In: Proc. 10th VLSI Design/CAD Symposium. (1999) 319–322 • Su, S., Lin, A., Yen, J.C.: Design and realization of a new chaotic neural encryption/decryption network. In: Proc. APCCAS. (2000) 335–338 • Yen, J.C., Guo, J.I.: The design and realization of a chaotic neural signal security system. Pattern Recognition and Image Analysis 12 (2002) 70–79 • Lian, S., Chen, G., Cheung, A., Wang, Z.: A chaotic-neural-network-based encryption algorithm for JPEG2000 encoded images. In: Proc. ISNN 2004-II. LNCS 3174 (2004) 627–632 • Lian, S., Sun J., Li Z., Wang, Z.: A Fast MPEG4 Video Encryption Scheme Based on Chaotic Neural Network. In: Proc. ICONIP 2004. LNCS 3316 (2004) 720-725 PCM 2004, Tokyo, Japan

4. The CNN-Based Cipher (1) • Given the chaotic logistic map f(x)=μx(1-x), the secret key is μ and the initial condition x(0). • Generate a secret pseudo-random bit sequence (PRBS) by iterating the logistic map from x(0): {bi}, i=0,… • Use the PRBS to control the 64 weights {wji= ±1} and the 8 biases {θi = ±1/2} (i, j=0~7) of a neural network and encrypt the plaintext as follows: Here, di(n) and d’i (n) denote the i-th bits of the n-th plain-byte and the n-th cipher-byte, respectively. PCM 2004, Tokyo, Japan

5. The CNN-Based Cipher (2) • The CNN-based cipher can be simplified to the following form: • So, the CNN-based cipher is actually a simple stream cipher based on a chaotic PRBS. • This cipher was initially proposed in [1-3] for image and video encryption, and then employed in [4,5] for encrypting JPEG2000 images and MPEG-4 videos. PCM 2004, Tokyo, Japan

6. Brute-Force Attack • The original claims in [1-3]: • the attack complexity is O(28M), when there are M plain bytes for encryption. • Our results in this work: • the attack complexity is only O(22L M), when there are M plain bytes for encryption and the finite precision of the system is L; • in [1-3], L=8, which is too small to provide a sufficiently high security level. PCM 2004, Tokyo, Japan

7. Known/Chosen-Plaintext Attack The requirement: one known/chosen plain signal f and the corresponding cipher signal f’. • Get a mask signal from f and f’: fm= f f’, which can be used to (partially) decrypt other cipher signals encrypted with the same secret key. • The short cycle of the chaotic PRBS makes it possible to completely recover other cipher signals. • Break the sub-key μ and a chaotic state x(i) from fm. Then, all bytes in any cipher signals can be recovered. PCM 2004, Tokyo, Japan

8. Known/Chosen-Plaintext Attack – Experiments (1) PCM 2004, Tokyo, Japan

9. Known/Chosen-Plaintext Attack - Experiments (2) PCM 2004, Tokyo, Japan

10. Known/Chosen-Plaintext Attack - Experiments (3) PCM 2004, Tokyo, Japan