椭圆曲线密码体制基点选取算法的设计与实现

Point Choosing Algorithm of Elliptic Curve Cryptography

在有限素整数域Fp 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码体制 .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 。

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.