Design of Cryptographically Strong Generator By Transforming Linearly Generated Sequences

Random numbers have been used extensively in many simulation applications like Monte Carlo Integration or computer modeling. But recently security applications have increased the need for strong (secure) random number generation like automatic password generation, encryption algorithms, on-line gambling etc. Thus random number generation has become a challengingand an interesting task. Most classical random number generators, generate sequences that are either linear or predictable hence not suitable for cryptographic and security applications. Others generate sequences that even though they are secure they are not cryptographicallystrong and above all are slow in execution. Also recent advances in random number generation like the construction of Multiple Recursive Generator(MRG) with large orders, Fast Multiple Recursive Gener-ator (FMRG) and DX(system of multiple recursive generators proposed by Deng and Xu [2003]) generators does not generate a strong random number sequences. Though MRGs have extremely long period of length with good empirical performance, its recurrence equation can be solved given a small set of its generated sequence, this implies that MRGs and FMRGs are not strong cryptographic generators. We propose an algorithm that will transform linear sequences generated by both classical LCG, MRGs, FMRGs and DX generators and make them cryptographically strong generators by hiding the entire sequence generated by the generators, thus it will be difficult for cryptanalyst to predict or infer the generator sequence if even the partial sequence or the parameters or knowledge of the algorithm used in the transformation of the generators are known.