Neural Synchronization based Secret Key Exchange over Public Channels: A survey Sandip Chakraborty Jiban Dalal Bikramjit Sarkar Debaprasad Mukherjee Dept. of Computer Science and Engineering and Dept. of Information Technology Dr. B. C. Roy Engineering College (West Bengal University of Technology), India [email protected] [email protected] [email protected] [email protected] Abstract— Exchange of secret keys over public channels based key could be created over a public channel accessible to any on neural synchronization using a variety of learning rules offer unauthorized party [2]. Since then, many public key an appealing alternative to number theory based cryptography cryptosystems have been presented which are based on algorithms. Though several forms of attacks are possible on this number theory, and they demand large computational power neural protocol e.g. geometric, genetic and majority attacks, our [3]. Moreover the processes involved in generating public key survey finds that deterministic algorithms that synchronize with are very complex and time consuming. To overcome these the end-point networks have high time complexity, while disadvantages, several other concepts and techniques have probabilistic and population-based algorithms have demonstrated ability to decode the key during its exchange over been explored. Among them, it has been found that the the public channels. Our survey also discusses queries, heuristics, concept of neural networks can be used to generate common erroneous information, group key exchange, synaptic depths, etc, secret key, and this can offer one of several possible solutions that have been proposed to increase the time complexity of to this critical issue of key exchange. algorithmic interception or decoding of the key during exchange. The paper is organized as follows. We introduce the The Tree Parity Machine and its variants, neural networks with concepts of synchronization and chaos in artificial neural tree topologies incorporating parity checking of state bits, appear networks in Section II. In Section III we discuss the basic to be one of the most secure and stable models of the end-point model of neural synchronization based key exchange and in networks. Our survey also mentions some noteworthy studies on Section IV we survey the other basic models. In Section V we neural networks applied to other necessary aspects of cryptography. We conclude that discovery of neural discuss the different types of attacks, in Section VI the parity architectures with very high synchronization speed, and machines, in Section VII Queries, Synaptic Depth and designing the encoding and entropy of the information exchanged Erroneous Information, in Section VIII we survey the most during mutual learning, and design of extremely sensitive chaotic important studies in recent times. Finally in Section IX some maps for transformation of synchronized states of the networks additional forms of cryptography and their corresponding to chaotic encryption keys, are the primary issues in this field. noteworthy studies have been mentioned. Section X summarizes and concludes the survey. IndexTerms—Cryptography, Key exchange, Neural networks, Synchronization. II. NEURAL NETWORKS, SYNCHRONIZATION AND CHAOS I. INTRODUCTION It is widely known that artificial neural networks are Cryptography is the practice of constructing and analyzing computational models inspired by animal brains that are protocols for secure exchange of information i.e. capable of machine learning and pattern recognition. Neural communication, overcoming the presence or influence of networks can learn from a training data set and then can adversaries or third parties, e.g. preventing leakage of predict or classify data. They are usually presented as systems information to unauthorized parties. It deals with various of interconnected neurons that can compute outputs from aspects in information security e.g. data confidentiality, data inputs by propagating information through the network. integrity, and authentication. Cryptographic algorithms are Neural networks are used as a form of soft computing designed around computational hardness assumptions e.g. technique to solve computationally difficult problems e.g. using number-theoretic concepts, making such algorithms hard speech and face recognition, gene prediction etc. [4]. These to break in practice by any unauthorized party. These networks constitute a form of dynamic systems which show a algorithms/schemes are termed as computationally secure variety of complex behaviour including the phenomenon of since it is infeasible to break them by known practical means, chaos and synchronization [5]. Chaotic systems are nonlinear although they are breakable, in theory. Theoretical advances dynamical systems that are highly sensitive to initial e.g. in integer factorization algorithms, and faster computing conditions. technology require these schemes to be continually improved [1]. In 1970s, Diffie & Hellmann found that a common secret Fig. 1. Schematic of a public channel using neural synchronization based key exchange In these systems, minute differences in initial conditions generate highly diverging outputs, making long-term III. FUNDAMENTAL MODEL prediction very difficult in general. This happens even though In 2002, Kanter et. al. published a series of related papers these systems are deterministic, meaning this kind of where they have shown the beautiful connection between behaviour exist even when their future dynamics is fully neural networks and cryptography [7, 8, 9]. They determined by their initial conditions, with no random demonstrated that synchronization of neural networks can lead elements involved. One popular model of chaotic systems is to a method of exchange of secret messages or keys. They chaotic maps [6]. Chaotic maps are mathematical evolution demonstrated that when two artificial neural networks are functions which show chaotic behaviour, and may be trained by suitable learning rules e.g. Hebbian rules, on their parameterized by a discrete time or continuous time mutual outputs, then these networks can develop equivalent parameter. Chaotic systems sometimes show the property of states of their internal synaptic weights, i.e., the networks synchronization. Synchronization is the coordination of events synchronize to a state with identical time dependent weights. to operate a system in unison, or, the attainment of equivalent These synchronized weights are then used to construct a key states in systems while interacting with each other. Most exchange protocol. They found that it was impossible to systems esp. the stochastic ones may be only approximately decrypt the secret message even for an opponent who knew synchronized. Phase synchronization, one of the widely used the protocol and all details of any transmission of the data. concepts of synchronization, is the process by which two or They also proved that this was primarily because the tracking more cyclic signals tend to oscillate with a repeating sequence of the weights of neural networks during synchronization was of relative phase angles [5]. One form of synchronization a NP- hard problem. But, on the other hand, the complexity of which is already known in encryption systems is the validation the generation of the secure channel is linear with the size of that the receiving ciphers are decoding the right bits at the the network. These results opened up new avenues in modern right time. cryptography, and showed how synchronization by mutual Thus, it seemed that using synchronization and chaotic learning in neural networks can be applied to secret key characteristics of dynamical systems may provide a promising exchanges over public channels. This and similar results later direction to the design of new and efficient cryptosystems. gave rise to the field of Neural Cryptography. Thereafter, Following this promise, in recent years, artificial neural researchers have tried several different methods for networks have been applied and experimented with, in several cryptography using neural networks in various forms. (Fig.1.) forms of cryptographic systems/techniques. Fig. 2. Schemata and models of Tree Parity Machine (TPM) and Permutation Parity Machine (PPM) Here, in this paper, we survey and discuss some of the most prominent problems addressed and some of their IV. OTHER BASIC MODELS solutions in the domain of neural cryptography. In 2002, Kinzel and Kanter further analyzed their previous Neural cryptography deals with the problem of key model (discussed above) using multilayer neural networks exchange between two neural networks using the mutual with discrete weight [10]. They found further validation of learning concept. Two neural networks that are trained on their previous results i.e. the in this case with discrete weights their mutual output synchronize to an identical time dependant too, the networks synchronized with identical final internal weight vector. The two networks exchange their outputs (in weights. The authors also further validated the primary bits) and the key between the two communicating parties is assumption, that synchronization by mutual learning between eventually represented in the final learned weights, when the neural networks can be applied to generate secret public two networks are said to be synchronized. This novel channel keys, through theoretical justification. In the same phenomenon has been used for creation of secure year, Rozenet.al. studied the mutual learning process