Cryptanalysis of a cryptographic scheme based on delayed chaotic neural networks Jiyun Yang a, * , Xiaofeng Liao a,b , Wenwu Yu c , Kwok-wo Wong d , Jun Wei e a Department of Computer Science and Engineering, Chongqing University, Chongqing 400044, PR China b The Key laboratory of Optoelectric Technology and Systems, Ministry of Education, PR China c Department of Mathematics, Southeast University, Nanjing 210096, PR China d Department of Computer Engineering and Information Technology, City University of Hong Kong, Hong Kong e Zhunyi Medical College, Zhunyi 563000, Guizhou, PR China Accepted 13 August 2007 Abstract Recently, Yu et al. presented a new cryptographic scheme based on delayed chaotic neural networks. In this letter, a fundamental flaw in Yu’s scheme is described. By means of chosen plaintext attack, the secret keystream used can easily be obtained. Ó 2007 Elsevier Ltd. All rights reserved. 1. Introduction Chaotic systems possess many interesting properties such as ergodicity, mixing and sensitivity to initial conditions which match with the requirements for a good cryptosystem. Recently, there are an increasing number of researchers working in this field, resulting in a variety of designs of cryptosystems based on chaotic systems [1–3,5]. Recently, Yu et al. designed a cryptosystem based on delayed chaotic neural networks [6]. This cryptosystem makes use of the chaotic trajectories of two neurons to generate basic binary sequences for encrypting plaintext according to some rules. Yu et al. claimed that it is difficult to synchronize the unknown chaotic neural networks through classical attacks since neural networks usually possess complicated parameters [6]. However, a detailed analysis on the encryp- tion algorithm shows that the cipher behaves as a stream cipher indeed [9, p. 20] although it looks like a block cipher. Moreover, every new encryption process has the same basic binary sequences. This weakness leads to the re-generation of the keystream under chosen plaintext attacks. By the fact that knowing the keystream generated by certain neural networks is equivalent to knowing the parameters of the neural networks, the cipher is broken. In this letter, we will first give a brief introduction to Yu et al.’s cryptographic scheme. Then the flaw of this scheme will be analyzed in detail. The method on how to obtain the keystream under chosen plaintext attacks will also be described. Finally, a conclusion of our findings will be drawn. 0960-0779/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2007.08.029 * Corresponding author. E-mail address: yangjy@cqu.edu.cn (J. Yang). Chaos, Solitons and Fractals 40 (2009) 821–825 www.elsevier.com/locate/chaos