Study Of Cryptosystem Based On The Elliptic Curve

With the progress of science and technology and the continuous development ofsociety and economy, the application of computer and Internet has pervaded everycorner of the world, and people seriously rely on the network. From national defenseforces, financial institutions to daily necessities in people’s lives, is likely to beinextricably relationship with the Internet. How to ensure the information securitytransmission on the Internet is one of the important subject of academia.Due to the openness of the network, data transferred over a network isnecessarily to be encrypted. The method is divided into two main types of encryptionalgorithms, symmetric encryption algorithm and asymmetric encryption algorithm.The former has high operation speed, high security, easy hardware implementation,and is suitable for large amounts of data to be fast encrypted. The latter one whichoperation efficiency is not so good as the former one, can effectively solve theproblem of key distribution, and has much advantages in situation where the cipherinformation is transferred among large numbers of people.In this article we first introduced the contents of several encryption algorithmsand the research situation at home and abroad. The second chapter focuses on learningrelated knowledge of elliptic curve cryptography. Afinite field is introduced as well asthe related concepts of elliptic curve, and the elliptic curve group. We establishedpublic key cryptography on this group of elliptic curve, and introduced several typicalalgorithms.Then we made a further introduction to the point multiplication operation in theelliptic curve encryption algorithm, which is the most expensive when operates in theelliptic curve cryptosystem and the key point to improve the operation efficiency ofelliptic curve cryptosystems. This paper introduces several fast points multiplicationalgorithm and introduces a kind of improved algorithm. At last a hybrid cryptosystembased on AES and ECC is introduced combining the advantages of symmetricencryption system and that of asymmetric encryption system. This hybridcryptosystem can guarantee the high speed in the process of data encryption anddecryption and also have very good solve of the key distribution and managementproblem.