Security Analysis and Improvement of the Pseudo-random Number Generator Based on Piecewise Logistic Map

In this paper, a security analysis of the pseudo-random number generator based on piecewise logistic map is made, which reveals the existence of a serious problem. Although the assumed safety of this pseudo-random number generator (PRNG) is estimated at 2¹³⁶, it is possible to carry out successful brute-force attack whose complexity is about 2¹⁰³. Furthermore, the attack on the analyzed PRNG based on a known sequence of output bits is presented which can reduce the complexity of the brute-attack to about 2⁹⁵. The examples of both attacks are provided in this paper. For the above mentioned reasons, the analyzed PRNG cannot be considered safe for the use in cryptographic systems. An improved version of the analyzed PRNG is proposed, which can eliminate the perceived shortcomings.