Cryptanalysis of a random number generator based on continuous-time chaos

This study presents the algebraic cryptanalysis of a continuous-time chaotic random number generator (RNG) based on a Zhongtang chaotic system. The chaos-based RNG provides key values for logic encryption, round key formation and the substitution box (S-box) generation steps in AES (advanced encryption standard). In this study, an attack method is proposed to exploit the weaknesses of the chaos-based RNG used in this cryptographic system. By observing a chaotic state variable and knowing the structure of the target RNG, output bit sequence of the target RNG is reproduced by a clone RNG used in master-slave synchronisation scheme. The feasibility of the attack system is confirmed through simulation and numerical results. Through this attack method, the same S-box parameters and key values can be obtained which can be used for decryption of the proposed encryption algorithm. This study targets a specific continuous-time chaos-based RNG and the associated cryptographic system as a case study. However, the cryptanalysis method described in this study is applicable to any continuous-time or discrete-time chaos-based RNGs. Therefore, this study highlights the security vulnerabilities of chaos-based RNGs and emphasises that deterministic chaos phenomena itself should not be considered as the actual source of randomness.