| CPC G06F 21/602 (2013.01) [H04L 9/001 (2013.01)] | 20 Claims |
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1. A method for image encryption based on two-dimensional lag complex Logistic map, the method being performed at a sending terminal, the method comprising the steps of:
(a) reading a M×N dimensional grayscale image X to be encrypted, expressing the value of each pixel point in X by eight binary numbers, that is, dividing the value into eight bit planes; and taking the upper four-bit plane as H, and the lower four-bit plane as L, wherein each bit plane is a binary matrix of M×N;
(b) taking the value range of parameter b of the two-dimensional lag complex Logistic mapping system as [1.69,2), taking parameter a as a real number that can be positive or negative, taking the values of a and b in the range, giving any initial value to the system, and iterating the system N=N0+2×M×N times, where N0∈N*, and abandoning the previous N0 iteration tracks to avoid instantaneous effect, so as to obtain four chaotic sequences x, x1, x2, x3 with length 2×M×N, where
 sorting the previous M×N numbers of the four chaotic sequences in an ascending order to obtain the position sequences T1, T2, T3, T4; then sorting the later M×N numbers of the four chaotic sequences in an ascending order to obtain the position sequences T−1, T−2, T−3, T−4;
(c) scrambling the lower four-bit plane L by using the position sequences T1, T2, T3, T4 to obtain a new lower four-bit plane Lp; scrambling the upper four-bit plane H by using the position sequences T−1, T−2, T−3, T−4 to obtain a new upper four-bit plane HH;
(d) performing modulo operation on the chaotic sequence x1 according to the formula f1=└|x1*1015 mod 256]┘ to obtain a matrix f1 containing M×N decimal numbers; dividing f1 into eight bit planes by converting decimal numbers to binary numbers, taking the lower four-bit plane as f−1, and then sorting the sequence in f−1 in an ascending order to obtain the position sequence Tf1;
(e) superposing and performing modulo operation on a plurality of bit planes according to the formula clow=(f−1+Lp+HH) mod 2 to obtain a new binary matrix clow; scrambling clow using Tf1 to obtain the final encrypted lower four-bit binary image Clow;
(f) keeping the parameters of the system unchanged, re-taking the initial value, iterating the system N=N0+2×M×N times, and abandoning the previous N0 iteration tracks to avoid instantaneous effect, so as to obtain four chaotic sequences which is denoted as x′, x′1, x′2, x′3 with length 2×M×N, where
 sorting the previous M×N numbers of the chaotic sequences in an ascending order to obtain the position sequences T′1, T′2, T′3, T′4; then sorting the later M×N numbers of the chaotic sequences in an ascending order to obtain the position sequences T′−1, T′−2, T′−3, T′<4;
(g) scrambling the upper four-bit plane H by using the position sequence T′1, T′2, T′3, T′4 to obtain a new upper four-bit plane Hp; scrambling Clow by using the position sequence T′−1, T′−2, T′−3, T′−4 to obtain Clow;
(h) performing modulo operation on the chaotic sequence x2 according to the formula f2=└|x2|*1015 mod256┘ to obtain a matrix f2 containing M×N decimal numbers; dividing f2 into eight bit planes by converting decimal numbers to binary numbers, taking the lower four-bit plane as f−2, and then sorting the sequence in f−2 in an ascending order to obtain the position sequence Tf2;
(i) superposing and performing modulo operation on a plurality of bit planes according to the formula chigh=(f−2+Hp+Clow) mod 2 to obtain a new binary matrix chigh; scrambling chigh using Tf2 to obtain the final encrypted upper four-bit binary image Chigh;
(j) integrating Clow and Chigh to obtain a final binary image P1=[Clow; Chigh], and then restoring the pixel value of each pixel point to obtain the finally encrypted grayscale image E;
wherein the two-dimensional lag complex Logistic mapping system described in step (b) specifically comprises: starting with one-dimensional Logistic map, expanding its variables from real number domain to complex number domain, and adding an unknown parameter for amplitude modulation, thereby constructing a two-dimensional lag complex chaotic system with two unknown parameters, and its expression is as follows:
 where wn=xn+jyn is a complex variable, zn represents a constant sequence, and a and b are both system parameters in which a is a real number and b is a positive real number; and
(k) transmitting the finally encrypted grayscale image E to a receiving terminal through a wireless network.
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