Neural synchronization based secret key exchange over public channels: A survey <s> IX. ADDITIONAL FORMS OF NEURAL CRYPTOGRAPHY <s> Abstract A model of a single neuron with chaotic dynamics is proposed by considering the following properties of biological neurons: (1) graded responses, (2) relative refractoriness and (3) spatio-temporal summation of inputs. The model includes some conventional models of a neuron as its special cases; namely, chaotic dynamics is introduced as a natural extension of the former models. Chaotic solutions of both the single chaotic neuron and the chaotic neural network composed of such neurons are numerically demonstrated. <s> BIB001 </s> Neural synchronization based secret key exchange over public channels: A survey <s> IX. ADDITIONAL FORMS OF NEURAL CRYPTOGRAPHY <s> Visual cryptography finds many applications in the cryptographic field such as key management, message concealment, authorization, authentication, identification, and entertainment. The authors propose a novel approach for visual cryptography using neural networks (NNs). To perform encrypting, the input to the NN is a set of gray level images, and the output is a set of binary images (shares) that fulfils the desirable access scheme. This approach is considerably different from the traditional one, and can be applied to cope with very complex access schemes. <s> BIB002 </s> Neural synchronization based secret key exchange over public channels: A survey <s> IX. ADDITIONAL FORMS OF NEURAL CRYPTOGRAPHY <s> Abstract The authors in their papers (Liao and Mao, Stochast. Anal. Appl. 14 (2) (1996a) 165–185; Neural, Parallel Sci. Comput. 4 (2) (1996b) 205–244) initiated the study of stability and instability of stochastic neural networks and this paper is the continuation of their research in this area. The main aim of this paper is to discuss almost sure exponential stability for a stochastic delay neural network d x(t)=[−Bx(t)+Ag(x τ (t))] d t+σ(x(t),g(x τ (t),t) d w(t) . The techniques used in this paper are different from those in their earlier papers. Especially, the nonnegative semimartingale convergence theorem will play an important role in this paper. Several examples are also given for illustration. <s> BIB003 </s> Neural synchronization based secret key exchange over public channels: A survey <s> IX. ADDITIONAL FORMS OF NEURAL CRYPTOGRAPHY <s> In this Letter, a novel approach of encryption based on chaotic Hopfield neural networks with time varying delay is proposed. We use the chaotic neural network to generate binary sequences which will be used for masking plaintext. The plaintext is masked by switching of chaotic neural network maps and permutation of generated binary sequences. Simulation results were given to show the feasibility and effectiveness in the proposed scheme of this Letter. As a result, chaotic cryptography becomes more practical in the secure transmission of large multi-media files over public data communication network. <s> BIB004 </s> Neural synchronization based secret key exchange over public channels: A survey <s> IX. ADDITIONAL FORMS OF NEURAL CRYPTOGRAPHY <s> In this paper, the adaptive synchronization and lag synchronization are considered for uncertain dynamical system with time delay based on parameter identification and a novel control method is then further given using the Lyapunov functional method. With this new and effective method, parameter identification and lag synchronization can be achieved simultaneously. Simulation results are given to justify the theoretical analysis in this paper. <s> BIB005 </s> Neural synchronization based secret key exchange over public channels: A survey <s> IX. ADDITIONAL FORMS OF NEURAL CRYPTOGRAPHY <s> Using Chaotic characteristics of dynamic system is a promising direction to design cryptosystems that play a pivotal role in a very important engineering application of cognitive informatics, i.e., information assurance and security. However, encryption algorithms based on the lowdimensional chaotic maps face a potential risk of the keystream being reconstructed via return map technique or neural network method. In this paper, we propose a new digital image encryption algorithm that employs a hyper-chaotic cellular neural network. To substantiate its security characteristics, we conduct the following security analyses of the proposed algorithm: key space analysis, sensitivity analysis, information entropy analysis and correlation coefficients analysis of adjacent pixels. The results demonstrate that the proposed encryption algorithm has desirable security properties and can be deployed as a cornerstone in a sound security cryptosystem. The comparison of the proposed algorithm with five other chaos-based image encryption algorithms indicates that our algorithm has a better security performance. <s> BIB006 </s> Neural synchronization based secret key exchange over public channels: A survey <s> IX. ADDITIONAL FORMS OF NEURAL CRYPTOGRAPHY <s> Recently, various hash functions based on chaos or neural networks were proposed. Nevertheless, none of them works efficiently in parallel computing environment. In this paper, an algorithm for parallel keyed hash function construction based on chaotic neural network is proposed. The mechanism of changeable-parameter and self-synchronization establishes a close relation between the hash value bit and message, and the algorithm structure ensures the uniform sensitivity of the hash value to the message blocks at different positions. The proposed algorithm can satisfy the performance requirements of hash function. These properties make it a promising choice for hashing on parallel computing platform. <s> BIB007 </s> Neural synchronization based secret key exchange over public channels: A survey <s> IX. ADDITIONAL FORMS OF NEURAL CRYPTOGRAPHY <s> Abstract In this paper, the parallel structure of hash function is analyzed. Then, a parallel hash function based on coupled map lattices is proposed. The message is partitioned into blocks with fixed length. The message block is firstly processed by the hash round function. The final hash value is the mixed result of all the outputs of the hash round functions. The hash round functions are mainly implemented by the coupled map lattices and can work in a parallel mode, which guarantees good security and high efficiency. Theoretic analyses and numerical simulations both show that the proposed hash algorithm possesses good statistical properties, strong collision resistance and high efficiency. These properties make it a good candidate for hash on parallel computing platform. <s> BIB008
In addition to the core issues of neural cryptography that we have discussed in this paper, neural networks have put to good use for other important issues in general cryptography e.g. generation of cipher text, image encryption, generation of image keys, generation of pseudo random numbers, construction of well-formed has functions for transformation of messages, etc. For algorithms for such purposes, neural models incorporating delay, chaos & hyper-chaos, state machines, switching, dimension reduction, Hopfield, Hebbian and random walk dynamics, and other similar properties. Out of these, chaotic and delay based neural models have high visibility in research literature BIB001 BIB003 . Previous to the form of neural synchronization based cryptography, a form of cryptography, called visual neural cryptography became popular (and still is), when Yue and Chiang in 2000 proposed a neural network based approach for the encryption of images BIB002 . The neural networks used here took gray level images as input and processed them to produce binary images in the output. Since then, it has been found that these neural net based models for image encryption has been able to address issues with various access schemes, and complex images. In a widely acknowledge work in 2009, Penget. al. proposed a digital image encryption algorithm using novel model based on hyper-chaotic cellular neural networks BIB006 . The authors performed key space analysis, sensitivity analysis, information entropy analysis and correlation coefficients analysis of adjacent pixels for the algorithm, and found its results quite satisfactory. In another parallel development, some researchers in neural cryptography have proposed novel models using neural networks for generating cipher text. Among them, one of the most influential models is that of Hopfield neural networks with embedded chaotic behaviour. In 2006, Yu and Cao proposed such a model with time varying delay BIB004 . The chaotic neural network was primarily used for generation of binary strings or sequences. These binary sequences were used for masking plain text. The method they proposed for masking the text was to switch off the neural network maps, and subsequent permutation of the generated binary sequences. Several papers have validated this idea in recent times and have proposed this model as a significant methodology for secure transmission of large complex multidimensional data BIB005 . For a different kind of issue in cryptography, recently, in 2009, Xiao et. al. proposed a novel scheme to overcome issues of hash functions in parallel computing models BIB007 . They proposed an algorithm for the construction of parallel keyed hash functions. They used the chaotic neural network model to study such hash functions. They developed two mechanisms, one was of changeable-parameter and the other was of self synchronization. These two mechanisms established a well formed relation between the hash value bits and the message. The authors claimed that the algorithm structure ensured the uniform sensitivity of the hash value to the message blocks at different positions. Although this claim has been disputed later on by several researchers, but their basic model has found validation in some other popular schemes BIB008 .