Design And Implementation Of Secure Elliptic Curves

With the development and application of information technology, the problem of information security becomes more and more important. RSA cryptosystem, a public-key cryptosystem being used widely today, seems to have difficulty in meeting the users'need of higher security. So far, the Elliptic Curve Cryptosystem (ECC) provides the highest strength-per-bit of any cryptosystem known. In addition to its high security, ECC also has many other merits over other public-key cryptosystems such as less computation overheads, shorter key size, considerable bandwidth savings, and so on. All of these merits have made it the best public-key cryptosystem that is suitable for current use in future.This paper first analyses and summarizes the status quo and evolution trend of encryption, and introduces in detail the development of private-key cryptosystem and public-key cryptosystem, and provides the brief analysis of a few typical schemes. Second, the principle of ECC is discussed, including the math foundation of ECC, basic conception of elliptic curve, constructing idea of ECC, operation on the elliptic curve and so on. Meanwhile, the security and efficiency off ECC are analyzed and thus three conditions required by ECC are given. Third, two methods to generate the safe elliptic curve are introduced. The CM algorithm being ameliorated and algorithm to generate base point are presented by C++. Thus, Elliptic Curve generated by this algorithm can be safer. It can resist the attack named MOV. An algorithm of detecting prime number based on division has been given. At last, the evolution trend and research direction are discussed.