An 8-bit integer true periodic orbit PRNG based on delayed Arnold’s cat map

A two-dimensional chaotic model and its application in image encryption

“…Delayed digital chaotic systems avoid the whole chaotic system from falling into a loop by introducing the current state and the previous state to influence the next state in the expectation that when there is x p = x q , which makes x p+1 ≠ x q+1 due to x p−1 = x q−1 . Many researches have shown that this method is effective [7,16,17]. However, if it appears that x p−1 = x q−1 and x p = x q , then the whole chaotic system will inevitably fall into a loop.…”

“…))⌉ -´´+ > , i.e., when the cycle length is greater than or equal to 8, the method can satisfy the above requirements. According to the [7,16,17], the cycle length of chaotic map is generally greater than 8 when the precision is greater than 6.…”

“…According to the first four keys generated as the initial value, iterate the equation (9) L × W × 3 times, take a 1 = 1.9, a 3 = 0.1, precision is 16, to get two sequences X, Y, where X is used to generate the diffusion matrix D, Y is sorted to get the index Y index , and the last four keys are also used as the initial value, iterate the equation (9) L × W times to get two sequences X1, Y1, X1 has two purposes , one is used to determine the kind of DNA operation and the other is used to determine the DNA encoding rules, and Y1 is used to generate the decoding rules. The elements of matrix D are obtained from equation (17), DNA operation kinds are obtained from equation (18), DNA encoding rules are obtained from equation (19), and DNA decoding rules are obtained from equation (20). Table 2.…”