摘要：

在图像加密应用中，为抵抗攻击需要构造更多的混沌序列。针对该问题，研究二次函数在单位区域内的混沌问题，分析论证标准单位二次函数是Li-Yorke混沌的，在特殊情况下是Devaney混沌的。讨论当单位区域内二次函数的最大值小于1时的混沌状况，绘制能够产生混沌的控制点近似区域，计算单位区域内二次函数的周期点以及Lyapunov指数，并将交叉迭代构造的序列用于图像加密。实验结果表明，使用二次曲线构造的混沌序列用于图像加密可获得较好的效果。

关键词: 图像加密, 混沌, 二次函数, 有理贝塞尔曲线, 平面单位区域, 交叉迭代

Abstract:

In the research of image encryption application, in order to resist the attacks, it needs to construct more chaotic sequence. Aiming at this problem, this paper studies the quadratic problem of quadratic function in unit area. The study finds that, a large number of the quadratic mapping is Li-Yorke chaos under certain conditions, some special cases is Devaney chaotic. It discusses chaos condition when unit area of the quadratic function value is less than 1, draws approximate area of control point which can generate chaos, computes cycle point of quadratic function in unit area and Lyapunov exponent, and generates a chaotic sequence which is available for image encryption. Experimental results show that constructing chaotic sequence by the quadratic curve for image encryption has a good result.

Key words: image encryption, chaos, quadratic function, rational Bézier curve, planar unit area, cross-iteration

中图分类号: 

• TP309.7