Research And Application Of Chaotic Sequence With High Speed And Long Period

Chaotic sequence has many excellent characteristics,for example,aperiodicity,initial value sensitivity,and mean ergodicity.Therefore,chaotic sequence has been widely used in the field of secure communication and digital image encryption.The traditional chaotic sequence generation method is limited by the storage word length of the computer.Thus,the period degradation problem is inevitable.On the other hand,an excessively large computational bit width leads to an increase in the iterative boundary in hardware implementation,making it difficult to obtain a sequence of high-speed outputs,thereby reducing encryption efficiency.In this paper,a chaotic sequence generation method based on Residue Number System and permutation polynomials is adopted.This method uses the Residue Number System to replace the multiply-add operation of large bit width with multiple parallel operations of small bit width,which reduces the computational complexity and increase the rate of sequence generation.In this paper,the chaotic sequence generated by this method is used in image encryption and spread spectrum communication.The main work of this paper is as follows:(1)The chaotic sequence mapping method is investigated.Besides,the performance of chaotic sequence based on the Residue Number System and permutation polynomial is analyzed.Meanwhile,comparing this chaotic sequence with the traditional chaotic sequences,such as Tent,Logistic and Chebyshev.(2)Proposing a new plaintext-related image encryption scheme based on chaotic sequence.This method not only enhances the robustness of resisting plaintext attacks but also improving the performance of defending noise and data loss attacks.(3)The digital image encryption algorithm based on chaotic sequence proposed in this paper has been tested and compared with the latest literatures.The analyzing contents include: key space,key sensitivity,correlation,anti-differential attack capability,histogram chi-square test,anti-noise and data loss attacks capability and information entropy.Simulation results show that our encryption algorithm outperforms 2D-LASM(two-dimensional Logistic-adjusted-Sine Map,2D-LASM),MIE-BX(Medical Image Encryption: Bitwise XOR,MIE-BX)and 2D-LICM(two-dimensional Logistic IMIC Cascade Map,2D-LICM)in resisting nosie and data-loss attack.The ability of resisting noise attack of our algorithm is more than 40% higher than 2D-LASM and MIE-BX.For the aility to resist data-loss attack,our algorithm is more than 33% higher than 2D-LASM and MIE-BX.However,Cao's 2D-LICM cannot defend the noise and dataloss attacks at all.In addtition,the performance of resisting differential attack of our algorithm is similar with 2D-LASM,MIE-BX and 2D-LICM.(4)The BER performance of chaotic sequences in spread spectrum communication systems is analyzed from different aspects,and compared with traditional sequences,such as m,Gold,Logistic,Tent and Chebyshev.