Improving Pseudo-random Number Generators in a Floating-point Implementation

Chaotic systems are prospective for secure data transfer and processing. Over the past decades, many chaos-based encryption schemes have been proposed. It was shown that such cryptosystems are faster than traditional approaches. In this study, we consider a technique for improving pseudo-random sequence generators based on a binary representation of chaotic sequences calculated using a floating-point data type. We show that we can extract more than 40 bits from the binary representation of each real number and use them as the output of the generator in stream ciphers. Moreover, we show that the features of floating-point calculations lead to pseudo-random properties of the least significant bits of the mantissa of numbers obtained by solving the simple systems of linear and nonlinear differential equations without chaotic behavior as well. The obtained results can be used to reconsider and improve chaos-based cryptographic algorithms.