Based On Elliptic Curve Proposed Primes Inspection

Prime research has a history of over 2000 years,Countless mathematicians paid a lifetime effort, has made one after another gratifying achievements.the development of information technology and cryptography to it put forward new challenges,Especially reliance on big primes public key cryptosystems,such as the RSA public-key cryptosystem and elliptic curve cryptosystem (ECC).As the most widely used and most development potential of the cryptosystems, and its security are built on the large prime, therefore, fast, efficient and safe test whether a large integer is prime for this type of cryptosystems became a vital part.In this paper, first, the research history of prime and current obtained some achievements has also briefly discussed, then several element to the common primality testing algorithm are simply analyzed, Secondly, the related theory of elliptic curve was briefly discussed,Focus on the finite field of elliptic curve theory were introduced, and then based on elliptic curve meal to analyzesprimality testing algorithms, especially for GK algorithm is studied in detail.And get an improved algorithm,which is called to be generalizing prime testing algorithm, based on elliptic curve primality test that it's conditions is more broader, the results can also be used in the well-known RSA system.An explame of Visual Basic be used to calculate the point on the elliptic curve and order.Finally, the full-text summary of the work done and make no place, and future planning to do further research.