The Research And Realizing Of The Base Choice On Elliptic Curve

The network security increasingly brings man attention with the rapid development and popularization of the computer network. The ECC takes on the characteristic of short private key and high encrypting intensity and so on, becomes next generation public key cryptogram system very possibly. But building a security fast ECC is complex.At first this thesis introduced cryptography and ECC and research actuality, discussed the elliptic curve security problem, deduced the group character and mutuality theorem, probed into the base choice and the relation among the base choice and security and the calculation efficiency of the point multiply a number from theory, the choice scheme was came out basing on the group character when the exponent of the elliptic curve group is prime or nonprime .It brought forward three kind of brief and fast the candidate base algorithms combining the character of the entirely square remain, particularly analyzed and compared with these algorithms, pointed out how to make use of this three kinds of algorithm calculated the candidate base. It brought forward the base exponent calculation and validate and choice and a series of other algorithm on the base of thoroughly researching the exponent of the point on the elliptic curve, realized the base choice of the elliptic curve group that the exponent is prime. It developed an encrypting simulation system to validated the choice of base correctness and validity by the encrypting experiment result in C# environment. At the same time the exponent of the calculation algorithm of the elliptic curve group and the determinant of prime were done analysis and comparing research. At last it summed up and prospected the entire text.