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刘振亚 等: SM2 数字签名算法的两方门限计算方案框架 2211

表 A2 基于加法密钥拆分的两随机数框架的实例化 (续)

−1
w 1 w 2 k = (d 1 +d 2 ) −1 (d 1 w 1 +d 2 w 2 ) s = (1+d) (k +r)−r 序号
−2 −1 ( −1 −1 ) −1 −1 31
d k 2 (d 1 +d 2 ) d 1 +d k 1 +d k 2 d 1 +d k 1 +d k 2 +(d 1 +d 2 −1)r
2 1 2 1 2
( )
−1 −1 −1 −1 32
1+d k 2 (d 1 +d 2 ) d 1 +d k 1 +d 2 +k 2 +(d 1 +d 2 −1)r
2 d 1 +d k 1 +d 2 +k 2 1
1
( )
−2 −1 −1 −1 −1 −1 33
1+d k 2 (d 1 +d 2 ) d 1 +d k 1 +d 2 +d k 2 d 1 +d k 1 +d 2 +d k 2 +(d 1 +d 2 −1)r
2 1 2 1 2
−1
−1
d −1 +k 2 (d 1 +d 2 ) −1 ( d 1 +d k 1 +1+d 2 k 2 ) d 1 +d k 1 +1+d 2 k 2 +(d 1 +d 2 −1)r 34
2 1 1
( ) 35
d −2 +k 2 (d 1 +d 2 ) −1 d 1 +d −1 +d −1 d 1 +d −1 +d −1 +d 2 k 2 +(d 1 +d 2 −1)r
2 1 2 +d 2 k 2 1 2
k 2 (d 1 +d 2 ) −1 (1+d 1 k 1 +d 2 k 2 ) 1+d 1 k 1 +d 2 k 2 +(d 1 +d 2 −1)r 36
−1 (d 1 +d 2 ) −1 (1+d 1 k 1 +k 2 ) 1+d 1 k 1 +k 2 +(d 1 +d 2 −1)r 37
d k 2
2
−2 −1 ( −1 ) −1 38
d k 2 (d 1 +d 2 ) 1+d 1 k 1 +d k 2 1+d 1 k 1 +d k 2 +(d 1 +d 2 −1)r
2 2 2
−1
d −1 +k 1 1+d k 2 (d 1 +d 2 ) −1 (1+d 1 k 1 +d 2 +k 2 ) 1+d 1 k 1 +d 2 +k 2 +(d 1 +d 2 −1)r 39
2
1
( )
−2 −1 −1 −1 40
1+d k 2 (d 1 +d 2 ) 1+d 1 k 1 +d 2 +d k 2 +(d 1 +d 2 −1)r
2
2 1+d 1 k 1 +d 2 +d k 2 2
d −1 +k 2 (d 1 +d 2 ) −1 (1+d 1 k 1 +1+d 2 k 2 ) 1+d 1 k 1 +1+d 2 k 2 +(d 1 +d 2 −1)r 41
2
( )
d −2 +k 2 (d 1 +d 2 ) −1 1+d 1 k 1 +d −1 1+d 1 k 1 +d −1 +d 2 k 2 +(d 1 +d 2 −1)r 42
2 2 +d 2 k 2 2
k 2 (d 1 +d 2 ) −1 ( d −1 ) d −1 +d 1 k 1 +d 2 k 2 +(d 1 +d 2 −1)r
1 +d 1 k 1 +d 2 k 2 1 43
( )
−1 −1 −1 −1 44
d k 2 (d 1 +d 2 ) d d +d 1 k 1 +k 2 +(d 1 +d 2 −1)r
2 1 +d 1 k 1 +k 2 1
−2 −1 ( −1 −1 ) −1 −1 45
d k 2 (d 1 +d 2 ) d +d 1 k 1 +d k 2 d +d 1 k 1 +d k 2 +(d 1 +d 2 −1)r
2 1 2 1 2
( )
−1
d −2 +k 1 1+d k 2 (d 1 +d 2 ) −1 d −1 d −1 +d 1 k 1 +d 2 +k 2 +(d 1 +d 2 −1)r 46
1 2 1 +d 1 k 1 +d 2 +k 2 1
( )
−2 −1 −1 −1 −1 −1 47
1+d k 2 (d 1 +d 2 ) d d +d 1 k 1 +d 2 +d k 2 +(d 1 +d 2 −1)r
2 1 +d 1 k 1 +d 2 +d k 2 1 2
2
d −1 +k 2 (d 1 +d 2 ) −1 ( d −1 +d 1 k 1 +1+d 2 k 2 ) d −1 +d 1 k 1 +1+d 2 k 2 +(d 1 +d 2 −1)r 48
2 1 1
( ) 49
d −2 +k 2 (d 1 +d 2 ) −1 d −1 +d 1 k 1 +d −1 d −1 +d 1 k 1 +d −1 +d 2 k 2 +(d 1 +d 2 −1)r
2 1 2 +d 2 k 2 1 2

刘振亚(1998－), 男, 硕士, 主要研究领域为密码 林璟锵(1978－), 男, 博士, 教授, 博士生导师, 主
工程. 要研究领域为密码工程.