A Hyperbolic Arnold's Cat Map-Based System for Multimedia Data Encryption

A Hyperbolic Arnold's Cat Map-Based System for Multimedia Data Encryption

Amine Rahmani
DOI: 10.4018/IJMDEM.2021040104
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Abstract

Cryptography is one of the most used techniques to secure data since antiquity. It has been largely improved by introducing several mathematical concepts. This paper proposes a new asymmetric cryptography approach using combined Arnold's cat map with hyperbolic function and Chebyshev chaotic map for audio and image encryption. The proposed scheme uses Chebyshev map for public and secrete keys generation and the same equation with Arnold's cat map for encryption and decryption. Hyperbolic functions are also introduced replacing regular integer values in Arnold's map. The results show a good and promising efficiency as well as the theoretical discussion. Several future possible improvements are presented in the conclusion.
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State-Of-The-Art

Sound encryption is a promising domain regarding to the increasing uses of audio in several fields including social networks, multimedia messages, and encrypted radio and TV channels. Many works had been done in this field. In (Srividya, 2016), the authors present a literature review of some used techniques in audio encryption. They started their paper by discussing and evaluating the application of conventional encryption schemes such as RC4, DES and other algorithms on audio files then they presented five other recent techniques used in the field. In (Lima,2015), the authors presented a new symmetric encryption scheme using cosine number transformation equation defined over a finite field. Their scheme is a block encryption scheme composed of seven steps using a secrete key for both encryption and decryption. In (Volos, 2017), an electronic chaotic circuit with hyperbolic sine function is proposed for sound encryption. This approach, belonging to the jerk system family, is built mathematically on a 3-D chaotic system that has five terms in which one of them is nonlinear. Their system is based on a several chaotic phenomena such as such as coexisting attractors and antimonotonicity. The main encryption process is the use of XOR function with a random number generator. Yet, as well as the previous presented paper, the approach is a secrete key encryption scheme. (Abdelfatah,2014) contains an approach of private key sound encryption scheme. The approach is mainly a random key and data depending shuffling procedure. In (Kordov, 2019), the authors presented also a symmetric encryption scheme for audio files. The authors presented a new random number generator for chaotic permutations and substitutions encryption procedures. The encryption/decryption steps are applied on bit-level code of audio file. (Liu, 2016) and his colleagues presented an encryption scheme based on confusion and diffusion of stream audio data. They introduced a new approach based on chaotic system with changeable multi-scroll in order to generate one-time key streams that are used for their Pay TV scrambling by audio encryption. In (Wang, 2010), the authors presented a new scheme for audio encryption using selective encryption based on modified discrete cosine transform (MDCT). The scheme uses also resource allocation for index-based encryption. The main objective that this paper treated is to ensure a high-level protection of audio files and energy efficiency as they apply their scheme on wireless multimedia sensor networks.

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