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与现有其他混沌系统不同, 本文探索了一种具有简单结构的$n$维离散超混沌系统. 首先, 根据利用正弦函数和幂函数以及简单运算构建 n维离散超混沌系统; 然后, 理论分析该系统可以设置正的Lyapunov指数; 接下来, 以六维混沌系统为例, 对其进行了相图、分岔图、Lyapunov指数、复杂性等特征进行了动力学分析, 结果说明该系统具有良好的混沌特性; 最后, 将新的混沌系统结合前后项异或运算和真随机数构建一次一密音频加密新方法. 通过实验仿真, 所提出的算法与现有音频加密算法进行比较, 该算法具有更高安全性, 能够抵御各种常见攻击.Discrete chaotic system, as a pseudo-random signal source, plays a very important role in realizing secure communication. However, many low-dimensional chaotic systems are prone to chaos degradation. Therefore, many scholars have studied the construction of high-dimensional chaotic systems. However, many existing algorithms for constructing high-dimensional chaotic systems have relatively high time complexity and relatively complex structures. To solve this problem, this paper explores an n-dimensional discrete hyperchaotic system with a simple structure. Firstly, the n-dimensional discrete hyperchaotic system is constructed by using sine function and power function and simple operations. Then, it is theoretically analyzed based on Jacobian matrix method that the system can have the positive Lyapunov exponents. Next, the algorithm time complexity, sample entropy, correlation dimension and other indexes are compared with those of the existing methods. The experimental results show that our system has a simple structure, high complexity and good algorithm time complexity. Therewith, a six-dimensional chaotic system is chosen as an example, and the phase diagram, bifurcation diagram, Lyapunov expnonents, complexity and other characteristics of the system are analyzed. The results show that the proposed system has good chaotic characteristics. Moreover, to show the application of the proposed system, we apply it to audio encryption. According to this system, we combine it with the XOR operation and true random numbers to explore a novel method of one-cipher audio encryption. Through experimental simulation, compared with some existing audio encryption algorithms, this algorithm can satisfy various statistical tests and resist various common attacks. It is also validated that the proposed system can be effectively applied to the field of audio encryption.
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离散混沌系统 元素加法个数 矩阵乘法复杂度 算法时间复杂度 Wang et al., 2018[22] $n(n - 1)$ $O({n^3})$ $O({n^3})$ Hua et al., 2021[15] $\dfrac{{n(n - 1)}}{2}$ $O({n^3})$ $O({n^3})$ Fan et al., 2022[17] $\dfrac{{n(n - 1)}}{2}$ $O({n^3})$ $O({n^3})$ Liu et al., 2023[18] $\dfrac{{n(n - 1)}}{2}$ $O({n^3})$ $O({n^3})$ 本文方法 $3 n - 4$(${b_i} \ne 0$)
$2 n - 3$(${b_i}{=}0$)无 $O(n)$ 
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维度 KE SE CD 3 0.4312 2.0120 2.1857 4 0.4212 2.0446 2.8712 5 0.4320 2.0973 2.2378 6 0.4226 2.9321 2.7423 下载:
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增益为1015 $ {x_1} $ $ {x_2} $ $ {x_3} $ $ {x_4} $ $ {x_5} $ $ {x_6} $ SmallCrush(15) 0 0 0 0 2 0 Crush(144) 6 4 7 6 78 4 下载:
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音频 明文 $ A_{n}, A_{n+1} $ $ A_{n}, A_{n+2} $ $ A_{n}, A_{n+s} $ 1-67152-A-17.wav 0.8980 0.6885 0.5066 1-121951-A-8.wav 0.9695 0.8840 0.7583 5-261464-A-23.wav 0.9559 0.8041 0.6811 平均 0.9411 0.7922 0.6487 下载:
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音频 密文 $ A_{n}, A_{n+1} $ $ A_{n}, A_{n+2} $ $ A_{n}, A_{n+s} $ 1-67152-A-17.wav –0.0029 –0.0036 0.0011 1-121951-A-8.wav –0.0017 0.0017 –0.0013 5-261464-A-23.wav 0.0020 0.0019 0.0027 绝对值平均 0.0022 0.0024 0.0017 下载:
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音频 明文 密文 1-67152-A-17.wav 1.0577 7.9993 1-121951-A-8.wav 1.9480 7.9993 5-261464-A-23.wav 1.3021 7.9993 平均 1.4359 7.9993 下载:
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音频 大小 加密时间/s 速度/(s·KB–1) 1-67152-A-17.wav 430 0.2809 0.00065 1-121951-A-8.wav 430 0.2097 0.00048 5-261464-A-23.wav 430 0.2167 0.00050 平均 430 0.2357 0.00054 下载:
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