One of the widely-used ways in chaos-based cryptography to generate pseudo-random sequences is to use the least significant bits or digits of finite-precision numbers defined by the chaotic orbits. In this study, we show that the results obtained using such an approach are very prone to rounding errors and discretization effects. Thus, it appears that the generated sequences are close to random even when parameters correspond to non-chaotic oscillations. In this study, we confirm that the actual source of pseudo-random properties of bits in a binary representation of numbers can not be chaos, but computer simulation. We propose a technique for determining the maximum number of bits that can be used as the output of a pseudo-random sequence generator including chaos-based algorithms. The considered approach involves evaluating the difference of the binary representation of two points obtained by different numerical methods of the same order of accuracy. Experimental results show that such estimation can significantly increase the performance of the existing chaos-based generators. The obtained results can be used to reconsider and improve chaos-based cryptographic algorithms.

在基于混沌的密码术中生成伪随机序列的一种广泛使用的方法是使用由混沌轨道定义的有限精度数字的最低有效位或数字。在这项研究中，我们表明使用这种方法获得的结果非常容易出现舍入误差和离散化效果。因此，即使参数对应于非混沌振荡，似乎产生的序列也接近随机。在这项研究中，我们确认数字的二进制表示形式中位的伪随机属性的实际来源不能是混乱的，而是计算机模拟的。我们提出一种确定最大位数的技术，该技术可以用作包括基于混沌的算法的伪随机序列生成器的输出。所考虑的方法涉及评估通过相同精度的不同数值方法获得的两个点的二进制表示形式的差异。实验结果表明，这种估计可以显着提高现有基于混沌的发电机的性能。获得的结果可用于重新考虑和改进基于混沌的密码算法。