椭圆曲线密码体制基点选取算法的设计与实现

在有限素整数域Ｅｐ上定义了一条椭圆曲线及点群运算规则，并由此构造出一种椭圆曲线密友体制。结合椭圆曲线域参数属性，讨论了平方剩余的定义、性质，完整地设计出选取基点Ｇ的Ｘ坐标的算法，根据Ｆｐ上素数Ｐ的不同性质，提出２种基点Ｇ的Ｙ坐标的计算方法，并给出了其数学证明。在ＰＣ机上用汇编语言实现的结果表明，该基点选取算法适于微机实现且实际可行，从而全面解决了椭工线密码体制中基占选取及如何把数据编码为椭圆曲线上

Point Choosing Algorithm of Elliptic Curve Cryptography

An elliptic curve is defined over a finite field GF( p ) for a given set of operation rules. An elliptic curve cryptosystem (ECC) is thus built. Defined are the characters of quadratic remainder while the arithmetic is provided for choosing X coordinate of base point G . According to the different properties of the prime p , two methods of calculating Y coordinate of base point G are proven mathematically. The algorithm has been realized on PC by assembly language. Hence the problem of how to choose a base point and how to code data into a point over an elliptic curve is resolved completely.