A pseudo-random sequence generation scheme based on RNS and permutation polynomials

Abstract

Long period pseudo-random sequence plays an important role in modern information processing systems. Base on residue number system (RNS) and permutation polynomials over finite fields, a pseudorandom sequence generation scheme is proposed in this paper. It extends several short period random sequences to a long period pseudo-random sequence by using RNS. The short period random sequences are generated parallel by the iterations of permutation polynomials over finite fields. Due to the small dynamic range of each iterative calculation, the bit width in hardware implementation is reduced. As a result, we can use full look-up table (LUT) architecture to achieve high-speed sequence output. The methods to find proper permutation polynomials to generate long period sequences and the optimization algorithm of Chinese remainder theorem (CRT) mapping are also proposed in this paper. The period of generated pseudorandom sequence can exceed 2 100 easily based on common used field programmable gate array (FPGA) chips. Meanwhile, this scheme has extensive freedom in choosing permutation polynomials. For example, 10905 permutation polynomials meet the long period requirement over the finite field Fq with q ≡ 1(mod 3) and q 503. The hardware implementation architecture is simple and multiplier free. Using Xilinx XC7020 FPGA chip, we implement a sequence generator with the period over 2 50 , which only costs 20 18kb-BRAMs (block RAM) and a small amount of logics. And the speed can reach 449.236 Mbps. The National Institute of Standards and Technology (NIST) test results show that the sequence has good random properties.

A New Plaintext-Related Image Encryption Scheme Based on Chaotic Sequence

“…In our method, the requirement of same polynomial for each residue channel is not necessary. The performance evaluations for the chaotic sequence in [17] showed that our generation method has similar random performance with that of Harris company. However, our method has more flexible choices in polynomial construction.…”

“…As a result, a higher sequence generation rate can be achieved, leading to higher efficiency of the image encryption system. In [17], we have presented the sequence generation method, polynomial construction method, performance evaluations and hardware implementation structure in detail. Compared with the method of Harris Corporation, the construction of iteration polynomials in [17] is more flexible.…”

“…When it is implemented in hardware, we can use 6 iteration channels with small bit width to achieve high speed sequence output. Meanwhile, they can be implemented by several LUTs, so that the sequence output rate can be further increased [17]. However, due to the large iteration bit width, the other chaotic sequence generation methods might not be able to use LUTs in hardware implementation, thus making it be difficult to increase the sequence output rate.…”

“…Hence, the space of parameter selection in sequence generation was limited. To address this problem, we proposed a chaotic sequence generation method by combining RNS and permutation polynomials in [17]. In our method, the requirement of same polynomial for each residue channel is not necessary.…”

Review of Target Geo-Location Algorithms for Aerial Remote Sensing Cameras without Control Points

“…Carrying out simulation analysis, which establishes models to assess different algorithms' performances in most situations, is crucial before the actual flight test. In this section, the total differential method and Monte Carlo method will be discussed as the error analysis methods [74][75][76][77][78][79][80][81][82][83][84][85][86][87].…”