CAJ | 학술논문

介绍了Fibonacci数列的模数列周期性定理,并推广至Fibonacci_Q变换矩阵的模周期.通过探讨Fibonacci-Q矩阵的周期与猫映射的周期的关系,揭示了猫映射的模周期与Fibonacci数列的模周期的内在联系;定义了矩阵变换的最佳周期概念,给出了猫映射的最佳周期性定理.通过图像置乱的仿真实验,验证了相关理论的正确性,从而为图像置乱提供了数学理论依据.
개소료Fibonacci수렬적모수렬주기성정리,병추엄지Fibonacci_Q변환구진적모주기.통과탐토Fibonacci-Q구진적주기여묘영사적주기적관계,게시료묘영사적모주기여Fibonacci수렬적모주기적내재련계;정의료구진변환적최가주기개념,급출료묘영사적최가주기성정리.통과도상치란적방진실험,험증료상관이론적정학성,종이위도상치란제공료수학이론의거.
The periodicity theorems of modular series of Fibonacci series were firstly presented, and then the periodicity property of Fibonacci _Q transform matrix was generalized. The relationship between the period of the Fibonacei _Q matrix and that of cat map was discussed, and the inherent relationship between the period of cat map and that of series generated from Fibonaeei series was disclosed. The best transform period was secondly defined, and the best periodicity theorem for cat map was given. Finally, the relevant theory was verified correct by several simulation experiments of cat map in image scrambling,which provided mathematical foundation for image scrambling.