Page 308 - 《软件学报》2025年第5期

2208 软件学报 2025 年第 36 卷第 5 期

序号 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

s = (1+d) −1 (k +r)−r d 1 d 2 +d 1 d 2 k 2 +k 1 +(d 1 d 2 −1)r 2 ) +d 1 d 2 +(d 1 d 2 −1)r d 1 d 2 +d 1 d 2 k 2 +k 1 +(d 1 d 2 −1)r d 1 +d 1 d 2 k 2 +k 1 +(d 1 d 2 −1)r d 1 d 2 k 2 +d 1 +d 2 k 1 +(d 1 d 2 −1)r 1 d 1 d 2 k 2 +d 1 +d 2 k 1 +(d 1 d 2 −1)r 1 d 1 k 2 +d 1 +d 2 k 1 +(d 1 d 2 −1)r 1 d 1 d 2 +d 1 d 2 k 2 +d 1 +d 2 k 1 +(d 1 d 2 −1)r 1 d 1 d 2 +d 1 k 2 +d 1 +d 2 k 1 +(d 1 d 2 −1)r 1 d 1 d 2 +d 1 d 2 k 2 +d 1 +d 2 k 1 +(d 1 d 2

( k 2 +d −1 k 1 1 2 2 2 2 2
d 1
2 2

) ) ) ) ) )
) ) ) ) ) ) ) 1 1 1 1 ) ) ) )
(续) 2 1 1 1 )
1 2
2 +w ′ 2
表 A1 基于乘法密钥拆分的两随机数框架的实例化
k = d 1 w ′ (1+d) ( d 1 d 2 +k 1 +d 1 d 2 k 2 (1+d) ( d 1 d 2 +d 1 k 2 +k 1 (1+d) ( d 1 d 2 +d 1 d 2 k 2 +k 1 2 (1+d) ( d 1 +d 1 d 2 k 2 +k 1 (1+d) ( d 1 d 2 k 2 +d 1 +d 2 k 1 (1+d) ( d 1 d 2 k 2 +d 1 +d 2 k 1 2 (1+d) ( d 1 k 2 +d 1 +d 2 k 1 (1+d) ( d 1 d 2 +d 1 d 2 k 2 +d 1 +d 2 k 1 (1+d) ( d 1 d 2 +d 1 k 2 +d 1 +d 2 k 1 (1+d) ( d 1 d 2 +d 1 d 2 k 2 +d 1 +d 2 k 1 (1+d) ( d 1 +d 1 d 2 k 2 +d 1 +d 2 k 1 (1+d) ( d 1 d 2 k 2 +d 1 +k 1 (

2

2

)
k = w 2 +d −1 w 1 2 1+d 2 k 2 +d −1 d −1 k 1 2 1 1+d −1 ( k 2 +d −1 k 1 1 d 2 +k 2 +d −1 d −1 k 1 2 1 d −1 +k 2 +d −1 d −1 k 1 2 1 k 2 +d −1 +d 1 d −1 k 1 2 2 d 2 k 2 +d −1 +d 1 d −1 k 1 2 2 d −1 k 2 +d −1 +d 1 d −1 k 1 2 2 1+d 2 k 2 +d −1 +d 1 d −1 k 1 2 2 1+d −1 k 2 +d −1 +d 1 d −1 k 1 2 2 d 2 +k 2 +d −1 +d 1 d −1 k 1 2 2 d −1 +k 2 +d −1 +d 1 d −1 k 1 2 2 k 2 +d −1 +d −1 d −1 k 1 2 1 2 d 2 k 2 +d −1 +d −1 d −

2 2 2 2
2 2
2
2

) 2 ) ) 2 ) ) 2 )
(1+d) ( d 2 +d 2 k 2 (1+d) ( d 2 +d 2 k 2 (1+d) ( d 2 +d 2 k 2 (1+d) ( d 2 +d 2 k 2 (1+d) ( d 2 +d 2 k 2 (1+d) ( d 2 +d 2 k 2
w ′ 2 (1+d)(d 2 +k 2 ) 2 (1+d)(1+d 2 k 2 ) (1+d)d 2 k 2 (1+d)d 2 k 2 2 (1+d)k 2 (1+d)(d 2 +k 2 ) 2 (1+d)(1+d 2 k 2 ) (1+d)d 2 k 2 (1+d)d 2 k 2 2 (1+d)k 2 (1+d)(d 2 +k 2 ) 2 (1+d)(1+d 2 k 2 )

) 1
w ′ 1 (1+d) ( d 1 +d 2 k 1 (1+d)(d 1 +k 1 )

w 2 1+d 2 k 2 1+d −1 k 2 2 d 2 +k 2 d −1 +k 2 k 2 d 2 k 2 d −1 k 2 1+d 2 k 2 1+d −1 k 2 2 d 2 +k 2 d −1 +k 2 k 2 d 2 k 2 d −1 k 2 1+d 2 k 2 1+d −1 k 2 2 d 2 +k 2 d −1 +k 2
2 2 2 2 2

w 1 1+d 1 k 1 1+d −1 k 1 1