Elliptic Curve Cryptography Using Chaotic Neural Network Ayush Sethi 1 , Ayush Mittal 2 , Ritu Tiwari 3 , Deepa Singh 4 1234 Robotics & Intelligent System Design Lab,Indian Institute of Information Technology & Management,Gwalior,India 1 ayushsethi22031992@gmail.com, 2 ayush2709@gmail.com, 3 tiwariritu2@gmail.com, 4 deepa@iiitm.ac.in Abstract—Cryptography is the science of hiding important information while transmiting over an insecure channel mak-ing it impossible for any adversary to read.Cryptography is very important for transmission and sharing of confidential information preventing any missuse of it.Neural Networks is a mathematical model which simulates the structure and functionality of biological neural network.A chaotic neural network is a network which adds randomness to a signal which is extremely hard to predict.Adding a Chaotic Neural Network to a Cryptographic system enhances the security of the system making it difficult to decode by the adversaries.In this research paper we have collaborated a Chaotic Neural Network with an Elliptic Curve Cryptographic System which is then compared with the conventional models such as RSA,Blowfish and RC2 models and is found to be better than various models based on certainparameters. Index Terms—Chaotic Neural Networks,Elliptic Curve Arith- metic, Cryptography,Information Security,Logistic Maps. Elliptic Curve Arithmetic which is difficult to break than the Integer Factorization Problem[20]. Also the key size for Elliptic Curve Cryptography is typically less due to the extremely hard Elliptic Curve Arithmetic. In this paper we are using a combination of Elliptic Curve Cryptography along with a Chaotic Neural Network to provide a more secure and faster algorithm. 1.1. Concept of Artificial NeuralNetwork 1. Introduction Figure 1. Artificial neural network[1] The main aim of a cryptographic framework is the exchange of information of among the expected parties with no exposure of data to any adversaries who may get un- authoritative access to it[1].In 1977, Diffie-Hellmann discov- ered that a secret can be computed over any insecure channel which can be transfered safely over the channel. After that period many open key cryptography algorithms came into existence which are dependent on many different theories and need a lot of computation power. Also the time required and computation needed to transfer information was quite high before and thus to limit this disadvantage along with increasing the security of the framework, Neural Networks wereused. Chaotic Neural Network is a class of Neural Network whose output is a random value dependent upon various parameters[32].The transmission of secret key can be made possible by the sychronization of common learning. The Chaos generated by a Chaotic Neural Network makes it difficult for any adversary to decode the secret message[8] sent by a party as the relationship among various plaintext and ciphertext paris is quite vague[31].Thus making attacks like ciphertext-only and known plaintext attacks impossible. Elliptic Curve Cryptography is a class of Cryptography where instead of using discrete logarithm, we are using Artificial Neural Networks are mathematical models which are used to imitate a biological neural network. ANN’s are used to approximate or estimate functions which require a lot of inputs. These mathematical models are used where the human brain is considered to be more efficient in computing a typical function as comparedto a machine e.g identifying various images,or identifying different handwritings [4]etc. Neural Network is a network of nodes known as neurons which are connected by directed links, where every link (X,Y) that connects the node X and Y has a weight w, also there is an activation function f which depending upon a threshold value maps the input state into an output state[24]. Neural Networks can be differentiated into two types: Feedforward Networks and Recurrent Networks. A Feedforward Neural Network is acyclic and thus it doesnot have any other state rather than the weights themselves. On the opposite side, a Recurrent Network is a cyclic network where the output is fed back into the network along with weights. Becuase of this feedback, Recurrent Networks need small amount of memory to store thatdata. International Journal of Pure and Applied Mathematics Volume 119 No. 10 2018, 1195-1201 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu Special Issue ijpam.eu 1195