An Approach to Encryption Using Superior Fractal Sets
The voluminous digital data exchange between various computers has introduced large amount of security vulnerabilities. Encryption schemes have been increasingly studied to meet the demand for real-time secure transmission of data over the Internet and th
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An Approach to Encryption Using Superior Fractal Sets Charu Gupta and Manish Kumar
Abstract The voluminous digital data exchange between various computers has introduced large amount of security vulnerabilities. Encryption schemes have been increasingly studied to meet the demand for real-time secure transmission of data over the Internet and through wireless networks. In this paper, we try to study a new cryptographic key exchange protocol based on superior Mandelbrot and Superior Julia sets. In this study we analyze a cryptographic system utilizing fractal theories; this approach uses concept of public key cryptography by taking advantage of the connection of Superior Julia and Superior Mandelbrot sets. This paper exploits the main feature of public key security. Keywords Superior Mandelbrot and Julia sets
Fractal geometry Public key
49.1 Introduction Enhanced security will definitely be a great relief for paranoid people. RSA cipher is most commonly used for public-key encryption depends on the difficulty of factoring large numbers [20]. RSA uses a variable size encryption block and a variable size key [17]. This study proposes a new fractal (based on Superior Mandelbrot and Superior Julia sets) encryption key protocol which secures
C. Gupta (&) Computer Science Department, NIMS University, Jaipur, India e-mail: [email protected] M. Kumar Sri Ram Murti Smarak International Business School, Kanpur Road, Lucknow, India e-mail: [email protected]
V. V. Das (ed.), Proceedings of the Third International Conference on Trends in Information, Telecommunication and Computing, Lecture Notes in Electrical Engineering 150, DOI: 10.1007/978-1-4614-3363-7_49, Springer Science+Business Media New York 2013
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transmission of data between computers. The working of the proposed scheme depends on the strong interconnection between two Superior Julia and Superior Mandelbrot sets which generates the corresponding public and private keys. In general, a security protocol uses public-key cryptosystem to exchange the secret key between communicating nodes and then uses secret-key algorithms with the agreed secret key as the password to ensure confidentiality on the data transferred (Branovic et al. 2003) [1]. Fractal is a geometric pattern that cannot be represented by classical geometry as it is a geometric figure that repeats itself under several levels of magnification; a shape that appears irregular at all scales of length, e.g. a fern. This geometric figure, built up from a simple shape, by generating the same or similar changes on successively smaller scales; it shows self-similarity… The backbone of the fractal is iteration method i.e. feedback system. The Superior Mandelbrot Fractal sets and Superior Julia sets is the set of points on a complex plane. The Fractal image can be generated by applying Eq. 49.1 recursively [13]. xn ¼ bn f ðxn 1Þ þ ð1 bnÞxn 1; n ¼ 1; 2; ;
ð49:1Þ
where 0 B bn B 1 and {bn} is convergent to b away from 0. The difference between the Mandelb
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