附录A(资料性附录) 关于椭圆曲线的背景知识 ················································ 11
A.1 素域F
p
················································································ 11
A.1.1 素域F
p
的定义 ·································································· 11
A.1.2 F
p
上椭圆曲线的定义···························································· 11
A.1.3 F
p
上椭圆曲线的阶 ······························································ 13
A.2 二元扩域F
2
m
··········································································· 13
A.2.1 二元扩域F
2
m
的定义 ····························································· 13
A.2.2 F
2
m
上椭圆曲线的定义 ··························································· 19
A.2.3 F
2
m
上椭圆曲线的阶 ····························································· 22
A.3 椭圆曲线多倍点运算 ·································································· 22
A.3.1 概述 ··········································································· 22
A.3.2 椭圆曲线多倍点运算的实现 ····················································· 22
A.3.3 椭圆曲线多倍点运算复杂度估计 ················································ 23
A.4 求解椭圆曲线离散对数问题的方法 ····················································· 24
A.4.1 椭圆曲线离散对数求解方法 ····················································· 24
A.4.2 安全椭圆曲线满足的条件 ······················································· 25
A.5 椭圆曲线上点的压缩 ·································································· 26
A.5.1 概述 ··········································································· 26
A.5.2 F
p
上椭圆曲线点的压缩与解压缩方法 ············································ 26
A.5.3 F
2
m
上椭圆曲线点的压缩与解压缩方法 ··········································· 26
附录B(资料性附录) 数论算法 ································································ 27
B.1 有限域和模运算 ······································································· 27
B.1.1 有限域中的指数运算···························································· 27
B.1.2 有限域中的逆运算 ······························································ 27
B.1.3 Lucas序列的生成 ······························································· 27
B.1.4 模素数平方根的求解···························································· 28
B.1.5 迹函数和半迹函数 ······························································ 28
B.1.6 F
2
m
上二次方程的求解 ··························································· 28
B.1.7 整数模素数阶的检查···························································· 29
B.1.8 整数模素数阶的计算···························································· 29
B.1.9 模素数的阶为给定值的整数的构造 ·············································· 30
B.1.10 概率素性检测 ································································· 30
B.1.11 近似素性检测 ································································· 30
B.2 有限域上的多项式 ····································································· 31
B.2.1 最大公因式····································································· 31
B.2.2 F
2
上不可约多项式在F
2
m
中根的求解 ·············································· 31
B.2.3 基的转换 ······································································· 31
B.2.4 F
2
上多项式不可约性的检测 ····················································· 33
B.3 椭圆曲线算法 ········································································· 33
B.3.1 椭圆曲线阶的计算 ······························································ 33
B.3.2 椭圆曲线上点的寻找···························································· 33
附录C(资料性附录) 曲线示例 ································································ 35
C.1 一般要求 ·············································································· 35
C.2 F
p
上椭圆曲线 ········································································· 35
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