Research Elliptic Curve Cryptographic Algorithm Based On Chebyshev Polynomial

There is a structural similarity between chotic system and cryptography,applyingchostic system to the field of cryptography gradually attracted people’s attention.a lotof researches focused on symmetric-key cryptosystems, but less applied to public-keycryptosystem. L.Kocarev proposed the public-key cryptography algorithm based onChebyshev polynomial, this algorithm has attracted people’s intrest, However, it hassome problems, affecting the practical application of chaos in the Public-keyCryptographicAlgorithm.We analyzed the problems of the Public-key Cryptographic Algorithm which wasproposed by L.Kocarev, the algorithm has low efficiency and poor practicability,on thisbasis, we propose the Elliptic Curve Cryptosystem algorithm based on Chebyshevpolynomial, it makes use of the semi-groop property of the chebyshev and theproperties of the Elliptic Curve,we extend the multiplicative group to the elliptic curegroup,so we improve the efficiency of the algorithm,to the new algorithm,we analyzedthe feasibility,safety,efficiency and practicality of the algorithm,Experimental resultsand performance analyses showed that the efficiency of the algorithm has improved,theprospect of the application is broad,the research is meaningful and innovative for thepublic-key cryptosystem based on chostic system.In addition, we propose a new algorithm which is the the Elliptic CurveCryptosystem algorithm based on Chebyshev polynomial, seudo random numbers areproduced by Chebyshev polynomial,we make use of the seudo random numbersconstructing algorithm,we analyzed the performance of the algorithm throughTheory.