Research On Key Agreement Protocol Based On Chebyshev Map Chaotic Public Key Cryptography

Today’s society has increasing requirements and dependence of informationsecurity. Secure cryptography system plays a central role in that,and cryptographicprotocols is the a part of it. The key agreement protocol is the most important, the mostwidely used cryptographic protocols. The role of the key agreement protocol prominentin more and more interactive communications in the open network environment.Theycan establish secret shared keys and provide safe channel for both or partiescommunication.Especially the application of public key cryptography, complete withkey agreement protocol as the fundamental basis. The mathematical theory and therapid development of the computer networks is to promote the continuous expansion ofits range of applications. Chaotic cryptography is the product of the combination ofchaos theory and cryptography. The chaotic system which have natural cryptographicproperties is the new direction of development of cryptography, one after another, therehave been key agreement protocol based on chaotic systems.Now,chaotic cryptographyresearch is mostly concentrated in the area of symmetric cryptography, public keycryptography in chaos still in its early stages, especially key agreement protocol basedon the chaotic public key algorithm. Chebyshev chaotic public key cryptography is ause of the the Chebyshev polynomial semigroups nature to construct a chaotic publickey cryptography algorithm. Since the algorithms have been proposed, the experiencefrom the real number field to finite field extensions. And agreement protocol, alsoexperienced a number of continuous improvement to compensate for the deficiencies ofthe algorithm itself and respond to a variety of attacks.Safety assessment and demonstration of chaotic cryptography needs a bettersystem. Because the digitization process in the practical application of Chaotic systemwill reduce its chaotic characteristics, such as the latest research shows that Chebyshevchaotic map defined on the finite field will have short-cycle phenomenon caused byimproper selection of parameters, this phenomenon threat to the public inkey algorithmfor security, so key agreement protocol that based on it also should note these problems.So this paper study of the phenomenon of the cycle distribution of the Chebyshevmap on the finite field or ring in depth, and then pursuant the phenomenon to analysissome recently proposed relatively mature key agreement protocol use of the Chebyshevmap public key cryptography. Found that the security issues when they face this phenomenon, and put forward a method of attack to these two protocols on this basis. Inresponse to this attack, one of the protocols to be modified and the following analysisprove the security of this protocol has been enhanced. Then the softwareimplementation show the algorithm acceleration and procedures simulation. Finally,outlook the future direction of development.