An Image Encryption Scheme Based on Modified Logistic Map

Abstract

In order to improve the security of chaotic encryption algorithm, a modified chaotic map, which is based on the Logistic map, is proposed in this paper. Compared with original logistic map，the proposed map makes it always be chaotic, and expands the iteration range from original (0, 1) to (0, 4λ) (λ>0.25). We designed an encryption scheme based on the proposed map for implementing image encryption. Some simulation results show that the modified Logistic map possesses bigger key space, faster sequence generation rate and faster encryption speed compared with the original logistic map.

Novel image encryption by combining dynamic DNA sequence encryption and the improved 2D logistic sine map

“…However, the above chaotic systems still have some shortcomings, such as small key space, insufficient complexity, and low security, which cause the decryption process, can be easily achieved. Many studies have been completed to modify the existing 1D chaotic system [6][7][8][9][10][11]. However, a 1D chaotic system is not enough for image encryption because it is easy to be attacked.…”

Modification of the Logistic Map Using Fuzzy Numbers with Application to Pseudorandom Number Generation and Image Encryption

“…The logistic map [ 6 ] is one of the most well-known one-dimensional discrete time chaotic systems and one of the most heavily modified chaotic systems; see, for example, References [ 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ]. The map has only one parameter and a simple structure, which makes it suitable for many applications.…”

“…The resulting map presents more complex chaos related phenomena compared to the classic map as mentioned above, as well as achieves a higher value for its Lyapunov exponent. Furthermore, to showcase the applicability of the map to chaos related applications, the problems of pseudo random bit generation [ 4 , 5 , 10 , 11 , 13 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 ] and image encryption [ 4 , 7 , 9 , 14 , 15 , 33 , 35 , 39 , 44 , 45 , 46 , 47 , 48 ] are considered. It is seen that the bit sequence generated from the modified map using a simple rule passes all 15 tests of the National Institute of Standards and Technology (NIST) statistical test suite [ 49 ].…”

The generalization of mathematically simple and robust chaotic maps with absolute value nonlinearity

“…2 1 n n x a x where a is a control parameter. The well-known variant of (1) that has been employed in a variety of applications [2][3][4] quantity that characterizes the rate of separation of infinitesimally close trajectories and is expressed as [5] In addition such preliminary investigations using bifurcation diagram and LE spectrum, chaotic systems exhibit two types of chaotic attractors, i.e. a fragile chaos in which the attractors disappear with perturbations of a parameter or coexist with other attractors, and a robust chaos, defined by the x asign absence of periodic windows and coexisting attractors in some neighborhood of the parameter space [6].…”