The Research On Chaotic Elliptic Curve Cryptography Systems And Implementation Of FPGA

Elliptic Curve Cryptography(ECC)algorithm is a public-key cryptosystem based on elliptic curve discrete logarithm problem.This system of cryptography,on the one hand,solves the problem of private-key distribution and management difficulty of symmetric cipher system,and ensures the relative security of private-key in encrypted data communication.On the other hand,ECC algorithm has the characteristics of large computational volume and solving elliptic curve discrete logarithm complex.,so that compared with other public-key cryptosystem,such as:with the Rivest,Shamir and Adleman(RSA)public-Key cryptosystem based on the problem of large integer factor,the security is higher with the same private-key length.In addition,because the public-key algorithm,based on the mathematical difficult problem,can increase the private-key length to improve the security,the operation efficiency of the whole cipher-system is reduced and the occupancy rate of storage space is increased.Therefore,ECC cipher algorithm is suitable for the password system with high running speed and limited storage space.By analyzing the practical application of chaos mapping in asymmetric cipher system and using its high sensitivity to initial value and control parameter,this paper proposes to apply one-dimensional logistic chaos mapping to ECC cipher algorithm to improve the attack resistance of the whole cipher system.By analyzing the application of logistic chaotic system in public key cryptosystem and the characteristics of ECC cipher algorithm,the paper first uses the pseudo random chaotic sequence generated by logistic chaotic map to eliminate the language characteristics of the plaintext and enhance its randomness,then the ECC on finite-fields(FF)GF(2m)The decryption algorithm is discussed in detail,the modules are designed and implemented,and the FPGA hardware simulation is given.This paper focuses on the FPGA hardware implementation of the scalar multiplication module on the binary finite domain GF(2m),through analyzing the performance of each scalar multiplication algorithm in different coordinate systems,and finally selecting the scalar multiplication operation module based on Montgomery algorithm in Lopez&Dahab(LD)projection-affine coordinate system.The project uses the software and hardware collaborative design pattern,the function and efficiency of each-module of the system are validated by Altera HSEP4CE30 V3.2 FPGA devices,and its simulation and test results are given.The test results show that the each module has good functions,the most time-consuming point-multiplication module maximum operation frequency up to 257.069MHz,the time of point-multiplication operation is 16.12?s,and 14.59%of FPGA logic resources is occupied.The whole chaotic ECC cryptosystem is in the correct function and the time of the encryption operation is about 4.413MS.