Page 310 - 《软件学报》2025年第5期

2210 软件学报 2025 年第 36 卷第 5 期

表 A2 基于加法密钥拆分的两随机数框架的实例化

−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
k 2 (d 1 +d 2 ) −1 (d 1 k 1 +d 2 k 2 ) d 1 k 1 +d 2 k 2 +(d 1 +d 2 −1)r 1
−1 (d 1 +d 2 ) −1 (d 1 k 1 +k 2 ) d 1 k 1 +k 2 +(d 1 +d 2 −1)r 2
d k 2
2
−2 −1 −1 −1 3
d k 2 (d 1 +d 2 ) (d 1 k 1 +d k 2 ) . d 1 k 1 +d k 2 +(d 1 +d 2 −1)r
2 2 2
−1 (d 1 +d 2 ) −1 (d 1 k 1 +d 2 +k 2 ) d 1 k 1 +d 2 +k 2 +(d 1 +d 2 −1)r 4
k 1 1+d k 2
2
−2 −1 −1 −1 5
1+d k 2 (d 1 +d 2 ) (d 1 k 1 +d 2 +d k 2 ) d 1 k 1 +d 2 +d k 2 +(d 1 +d 2 −1)r
2 2 2
d −1 +k 2 (d 1 +d 2 ) −1 (d 1 k 1 +1+d 2 k 2 ) d 1 k 1 +1+d 2 k 2 +(d 1 +d 2 −1)r 6
2
( ) 7
d −2 +k 2 (d 1 +d 2 ) −1 d 1 k 1 +d −1 +d 2 k 2 d 1 k 1 +d −1 +d 2 k 2 +(d 1 +d 2 −1)r
2 2 2
k 2 (d 1 +d 2 ) −1 (k 1 +d 2 k 2 ) k 1 +d 2 k 2 +(d 1 +d 2 −1)r 8
−1 −1 k 1 +k 2 +(d 1 +d 2 −1)r 9
d k 2 (d 1 +d 2 ) (k 1 +k 2 )
2
−2 −1 −1 −1 10
d k 2 (d 1 +d 2 ) (k 1 +d k 2 ) k 1 +d k 2 +(d 1 +d 2 −1)r
2 2 2
−1 −1 (d 1 +d 2 ) −1 (k 1 +d 2 +k 2 ) k 1 +d 2 +k 2 +(d 1 +d 2 −1)r 11
2
d k 1 1+d k 2
1
−2 −1 −1 −1 12
1+d k 2 (d 1 +d 2 ) (k 1 +d 2 +d k 2 ) k 1 +d 2 +d k 2 +(d 1 +d 2 −1)r
2 2 2
d −1 +k 2 (d 1 +d 2 ) −1 (k 1 +1+d 2 k 2 ) k 1 +1+d 2 k 2 +(d 1 +d 2 −1)r 13
2
( −1 ) −1 14
−2
−1
d +k 2 (d 1 +d 2 ) k 1 +d +d 2 k 2 k 1 +d +d 2 k 2 +(d 1 +d 2 −1)r
2 2 2
( ) 15
−1
k 2 (d 1 +d 2 ) −1 −1 d k 1 +d 2 k 2 +(d 1 +d 2 −1)r
d k 1 +d 2 k 2
1 1
( )
−1 −1 −1 −1 16
d k 2 (d 1 +d 2 ) d k 1 +k 2 d k 1 +k 2 +(d 1 +d 2 −1)r
2 1 1
−2 −1 ( −1 −1 ) −1 −1 17
d k 2 (d 1 +d 2 ) d k 1 +d k 2 d k 1 +d k 2 +(d 1 +d 2 −1)r
2 1 2 1 2
( )
−2 −1 −1 −1 −1 18
d k 1 1+d k 2 (d 1 +d 2 ) d k 1 +d 2 +k 2 d k 1 +d 2 +k 2 +(d 1 +d 2 −1)r
1 2 1 1
−2 −1 ( −1 −1 ) −1 −1 19
1+d k 2 (d 1 +d 2 ) d k 1 +d 2 +d k 2 d k 1 +d 2 +d k 2 +(d 1 +d 2 −1)r
2 1 2 1 2
( )
−1
d −1 +k 2 (d 1 +d 2 ) −1 −1 d k 1 +1+d 2 k 2 +(d 1 +d 2 −1)r 20
2 d k 1 +1+d 2 k 2 1
1
( −1 −1 ) −1 −1 21
−2
−1
d +k 2 (d 1 +d 2 ) d +d +d 2 k 2 d +d +d 2 k 2 +(d 1 +d 2 −1)r
2 1 2 1 2
k 2 (d 1 +d 2 ) −1 (d 1 +k 1 +d 2 k 2 ) d 1 +k 1 +d 2 k 2 +(d 1 +d 2 −1)r 22
−1
−1 (d 1 +d 2 ) (d 1 +k 1 +k 2 ) d 1 +k 1 +k 2 +(d 1 +d 2 −1)r 23
d k 2
2
−2 −1 −1 −1 24
d k 2 (d 1 +d 2 ) (d 1 +k 1 +d k 2 ) d 1 +k 1 +d k 2 +(d 1 +d 2 −1)r
2 2 2
−1 −1 d 1 +k 1 +d 2 +k 2 +(d 1 +d 2 −1)r 25
−1 1+d k 2 (d 1 +d 2 ) (d 1 +k 1 +d 2 +k 2 )
1+d k 1 2
1
−2 −1 −1 −1 26
1+d k 2 (d 1 +d 2 ) (d 1 +k 1 +d 2 +d k 2 ) d 1 +k 1 +d 2 +d k 2 +(d 1 +d 2 −1)r
2 2 2
d −1 +k 2 (d 1 +d 2 ) −1 (d 1 +k 1 +1+d 2 k 2 ) d 1 +k 1 +1+d 2 k 2 +(d 1 +d 2 −1)r 27
2
( ) 28
d −2 +k 2 (d 1 +d 2 ) −1 d 1 +k 1 +d −1 +d 2 k 2 d 1 +k 1 +d −1 +d 2 k 2 +(d 1 +d 2 −1)r
2 2 2
( ) 29
−1
k 2 (d 1 +d 2 ) −1 −1 d 1 +d k 1 +d 2 k 2 +(d 1 +d 2 −1)r
d 1 +d k 1 +d 2 k 2 1
1
−2
1+d k 1
1 −1 −1 ( ) −1 30
−1
d k 2 (d 1 +d 2 ) d 1 +d k 1 +k 2 d 1 +d k 1 +k 2 +(d 1 +d 2 −1)r
2 1 1