【摘要】 利用Fibonacci数列本身的自相似性和Logistic映射在混沌状态下对初值的敏感性,以Logistic映射作为混沌模型,采用Fibonacci数列与混沌映射混合的方法产生混沌的伪随机数列.在取Fibonacci数列初始循环10万次,Logistic非线性差分方程系数3.8,进行1 000次迭代的条件下仿真.结果表明,这种方法提高了输出的混沌序列的随机特性,改进了有限精度的局限性,使混沌序列退化为周期序列的问题,使数列具有很好的随机性,使输出的伪随机数列的周期加大.利用该方法对数据进行加密,具有较高的稳定性和安全性.更多还原

【Abstract】 Making use of Fibonacci sequences’s self-similarity and the sensitivity of logistic mapping to the initial value under chaotic condition, the Fibonacci sequence and chaotic mapping are mixed together to generate a chaotic pseudo-random sequence with logistic mapping as chaotic model. A simulation was carried out the way the Fibonacci sequence was initially cycled 10000 times taking the coefficient of nonlinear logistic difference equation as 3.8 and then the sequence was reiterated 1000 times. The result showed that the approach proposed can improve the randomness of chaotic sequence output and the limitation of precision so as to degrade the chaotic sequences into periodic sequences, thus enabling the sequences to have good randomness and the period of pseudo-random sequences output to lengthen. It has been proved that encrypting data in such a way can get higher stability and security.更多还原