Chaotic Encryption Scheme Based on a Fast
Permutation and Diffusion Structure
Jean De Dieu Nkapkop1,2, Joseph Effa1, Monica Borda2,
Laurent Bitjoka3, and Alidou Mohamadou4
1Department of Physics, University
of Ngaoundéré, Cameroon
2Department of
Communications, Technical University of Cluj-Napoca, Romania
3Department of Electrical Engineering, Energetics and Automatics, University of Ngaoundéré, Cameroon
4Department of Physics, University of Maroua, Cameroon
Abstract: The image encryption
architecture presented in this paper employs a novel permutation and diffusion
strategy based on the sorting of chaotic solutions of the Linear Diophantine Equation
(LDE) which aims to reduce the computational time observed in Chong's
permutation structure. In this scheme, firstly, the sequence generated by the
combination of Piece Wise Linear Chaotic Map (PWLCM) with solutions of LDE is
used as a permutation key to shuffle the sub-image. Secondly, the shuffled
sub-image is masked by using diffusion scheme based on Chebyshev map. Finally,
in order to improve the influence of the encrypted image to the statistical
attack, the recombined image is again shuffle by using the same permutation
strategy applied in the first step. The design of the proposed algorithm is
simple and efficient, and based on three phases which provide the necessary
properties for a secure image encryption algorithm. According to NIST
randomness tests the image sequence encrypted by the proposed algorithm passes
all the statistical tests with the high P-values. Extensive cryptanalysis has
also been performed and results of our analysis indicate that the scheme is
satisfactory in term of the superior security and high speed as compared to the
existing algorithms.
Keywords: Fast and secure encryption,
chaotic sequence, linear diophantine equation, NIST test.
Received May 16, 2015;
accepted September 7, 2015