A Low Complexity and Long Period Digital Random Sequence Generator Based on Residue Number System and Permutation Polynomial

Abstract

Long period digital random sequence plays an important role in reliable communications and high security scenarios. This paper improved the method of generating long period digital random sequences based on the Residue Number System (RNS) and the Chinese Remainder Theorem (CRT), and a sequence mapping method after CRT extension. This paper proves that the period of sequence after mapping will not degenerate if the modulus used in the mapping stage is coprime with the period of the original sequence. By using the parallelism of RNS, the proposed method can generate sequences at high speed with fewer hardware resources. The NIST test results show that the pass rate of each test item is above 98.40%, which meets the NIST test confidence requirements, confirming the randomness of the generated sequences. An image encryption test is given as one of the example applications of the generated sequences. On the theoretical basis, by jointly optimizing the sequence mapping and iteration procedure, a hardware implementation architecture is also presented in this paper. The implementation is based on Xilinx XC7Z020CLG484-3 FPGA and compared with the implementations of classical chaotic maps. The results show that the proposed architecture has longer sequence period with less hardware resource consumption and higher generation speed and is more general. Meanwhile, the proposed architecture has fast phase switching ability, which is about 10 clock periods. This is one of the key attributes when the sequence is used in communication systems.