Application Research Of Ellipse Curve Encryption Algorithm Based On Asymmetric Key System

As some potentially unsafe factors exist in computer networks, data communications and storage system, cryptography technology not only is an effective method that can protect confidentiality and integrity of information system, but also is core problem that can deal with data security and application security of information network. Looking for the higher safety algorithms and protocols to support the consumption authentications, digital signature and electronic commence system is main task of the cryptograph coding technology. Ellipse Curve Cryptosystem that has special features has been paid a high attention in the security and cryptography fields, cryptosystem have broad prospects on the safety and effectiveness. At present, Ellipse Curve Cryptosystem has become main stream of the public key cryptosystem research, and has become a hotspot in the process of the public key cryptosystem research and development.Information security service depends on the security system, at same time security system mainly depends on the cryptography, so cryptography is a core problem of the information security. Cryptography algorithm is mathematic functions of the encryption and decryptions and is core of the cryptography. Cryptography algorithms play an important role in the information security. Cryptography algorithms can be divided into two categories: symmetric key algorithm (also called private key algorithm) and public key algorithm(also called asymmetric key algorithm), the encryption speed of private key algorithm is quick, but its distributions and managements are complex, it has higher cost and can't finish the digital signature. In public key cryptography algorithm Kp is not equal to Ks , Kp is public ,so it is briefly called public key, otherwise Kp have to been secret, it simply called private key. Kp can been gained easily from Ks , vice versa is not easily. The one way feature of public key cryptography algorithm is realized on the basis of trapdoor one way functions, its advantages, such as simple allocations and management on the key and easily finishing the digital signature, can be suitable of the requirements of electronic commerce and electronic government, and can realize safe objects such as identification, data integrity and repudiation, etc.At present, RSA and ECC are the more influential cryptograph algorithms among presented public key algorithms. RSA is a kind of block encryption algorithms, its working theory is simple, and easy to use, its safety is based on the mode of large integer prime factorization, the encryption key length that RSA makes use of often is 512 bits, its encryption have to been longer, as RSA-512 had been decrypted. With large integer factorization methods improvement and implement and higher speed computers and parallel computing development, encryption key of RSA will become more and more long, the systems that use RSA become more and more slow, so applications of RSA have more burdens. In order to have 128 bits safety level in the symmetric encryption key , NIST suggested to make use of the encryption key of 3072 bits, but Ellipse encryption algorithms can reach this safe level, so it make possible to apply the Ellipse encryption algorithms widely.safety of public key system often depends on the difficulty of solving the mathematic problems, Ellipse encryption algorithm is based on the discrete log problems, Ellipse curve theory is a crossing point of some mathematics branches such as linear algebra and number theory, it is an Ellipse curve encryption system based on Abel group of relational points on Ellipse curve. Ellipse curve encryption system not only can be used in the field of information encryptions but also used in the digital signature as best method of new public key cryptograph, Ellipse curve encryption systems that have widely application prospects in the fields of computer networks security and information security have the following advantages:1. In case of suitable security level, short encryption key can be use. Generally, in Ellipse curve encryption system of q fields, when the length of q is 160 bits, its security level is equal to the length of 1024 bits in RSA, short passwords means the requirement of small brand and storage, this is important factor in some applications(for example: IC card and wireless networks)2. There a plenty of Ellipse curves in the same limited fields in the Ellipse curve encryption system resources, this can increase extra guarantee in security field and bring convenience for realization of software and hardware.3. There are mild exponential algorithms in analyzing the RSA and DSA systems, but there are no in Ellipse curve encryptions, the declassification difficulty is exponential and is more difficult than the question of integer factorization and discrete log of mode p(p is prime),can avoid attacking.In the paper the basic theory knowledge and current study situations of Ellipse curve encryption had been discussed, the problem of curve finite domain defining, safe ellipse curve selecting algorithm, basic point selecting algorithm and the design and realization of quick Ellipse curve encryption algorithm ,etc are discussed deeply. The construction methods and algorithms of Ellipse curve encryption system had been given, the advantages and disadvantages of Ellipse curve encryption system had been compared with other typical public key encryption system, making safe Ellipse curve and selecting the basic point of Ellipse curve encryption system is key problem. Scalar multiplication is very import section that has effect on the finishing speed of Ellipse curve encryption algorithm. By designing and improving the quick algorithm of Ellipse curve encryption, the speed of Ellipse curve encryption can be improved, the discrete log problem had been discussed at same time, lastly the applications of Ellipse encryption algorithm on the fields of electronic commerce, digital signature and WPKI had been studied.Ellipse curve encryption study now is at the beginning phase, some problems still need to be solved (for example, the improving study of Ellipse encryption algorithm coding methods, Ellipse encryption algorithm parallel computing and hardware and software realization, etc.), on the one hand, deeply studying can provide the foundation and guarantee of the application and security of Ellipse encryption algorithm, on the other hand show richer mathematic background to encryption theory.