A Generic Model of the Pseudo-Random Generator Based on Permutations Suitable for Security Solutions in Computationally-Constrained Environments

Symmetric cryptography methods have an important role in security solutions design in data protection. In that context, symmetric cryptography algorithms and pseudo-random generators connected with them have a strong influence on designed security solutions. In the computationally constrained environment, security efficiency is also important. In this paper, we proposed the design of a new efficient pseudo-random generator parameterized by two pseudo-random sequences. By the probabilistic, information-theoretic, and number theory methods we analyze characteristics of the generator. The analysis produced several results. We derived sufficient conditions, regarding parameterizing sequences, so that the output sequence has a uniform distribution. Sufficient conditions under which there is no correlation between parameterizing sequences and output sequences are also derived. Moreover, it is shown that mutual information between the output sequence and parameterizing sequences tends to zero when the generated output sequence length tends to infinity. Regarding periodicity, it is shown that, with appropriately selected parameterizing sequences, the period of the generated sequence is significantly longer than the periods of the parameterizing sequences. All these characteristics are desirable regarding security applications. The efficiency of the proposed construction can be achieved by selecting parameterizing sequences from the set of efficient pseudo-random number generators, for example, multiple linear feedback shift registers.