One-Time Pad as a nonlinear dynamical system |
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| Authors: | Nithin Nagaraj |
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| Affiliation: | 1. Department of Electronics and Electrical Communications, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt;2. Department of Computer Science and Engineering, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, Egypt;3. Intelligent Systems Research Centre, Faculty of Computing, London Metropolitan University, London, UK;4. Department of Electrical Engineering, Faculty of Engineering, Menoufia University, Shebin El-kom 32511, Egypt;5. Department of Information Technology, College of Computers and Information Technology, Taif University, Al-Hawiya, 21974, Kingdom of Saudi Arabia;1. Dept. of Electrical Engineering, The University of Suwon, San 2-2, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, South Korea;2. Department of Electrical & Computer Engineering, University of Alberta, Edmonton T6R 2V4 AB, Canada;3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland;4. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia;1. Shanghai Key Lab of Modern Optical System, Department of Control Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China;2. Department of Mathematics, Yangzhou University, Yangzhou 225002, China.;3. Communication Systems and Networks (CSN) Research Group, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia;4. Informatization Office, University of Shanghai for Science and Technology, Shanghai 200093, China;1. Department of Optics, School of Information Science and Engineering, and Shandong Provincial Key Laboratory of Laser Technology and Application, Shandong University, Jinan 250100, China;2. College of Optoelectronics Engineering, Shenzhen University, Shenzhen 518060, China;3. College of Materials Science and Opto-Electronic Techology, University of Chinese Academy of Sciences, Beijing 100049, China;4. College of Electronic Science and Technology, Shenzhen University, Shenzhen 518060, China;1. College of Optoelectronic Engineering, Key Laboratory of Optoelectronics Devices and Systems, Education Ministry of China, Shenzhen University, Shenzhen 518060, China;2. School of Information Science and Engineering, Shandong University, Jinan 250100, China |
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| Abstract: | The One-Time Pad (OTP) is the only known unbreakable cipher, proved mathematically by Shannon in 1949. In spite of several practical drawbacks of using the OTP, it continues to be used in quantum cryptography, DNA cryptography and even in classical cryptography when the highest form of security is desired (other popular algorithms like RSA, ECC, AES are not even proven to be computationally secure). In this work, we prove that the OTP encryption and decryption is equivalent to finding the initial condition on a pair of binary maps (Bernoulli shift). The binary map belongs to a family of 1D nonlinear chaotic and ergodic dynamical systems known as Generalized Luröth Series (GLS). Having established these interesting connections, we construct other perfect secrecy systems on the GLS that are equivalent to the One-Time Pad, generalizing for larger alphabets. We further show that OTP encryption is related to Randomized Arithmetic Coding – a scheme for joint compression and encryption. |
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