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张语晗 等: 对缩减轮 SPECK 改进的差分-线性分析 2283

SPECK48的 S 的部分元素
4
表 7
∆

b的取值 p = 2 −6 p = 2 −7 p = 2 −8 p = 2 −9
−9
4
S (2 ,3) = {[2,23,47],[13,16,37],
∆
[0,21,45],[8,11,32],[10,13,34],
−8
4
b = 3 － － S (2 ,3) = {[0,21,45]}
∆ [16,19,40],[2,5,26],[18,21,42],
[5,8,29]}
b = 4 － － － －
4
−9
−8
4
−7
4
S (2 ,5) S (2 ,5) S (2 ,5)
∆ ∆ ∆
b = 5 － = {[2,15,23,39,47], = {[0,13,21,37,45],..., = {[6,14,17,30,38],...,
[7,10,23,31,47]} [7,15,18,31,39]} [3,6,19,27,43]}
−9
4
−8
4
4
−7
S (2 ,6) S (2 ,6) S (2 ,6)
−6
4
S (2 ,6) ∆ ∆ ∆
b = 6 ∆ = {[0,10,18,34,42,45],..., = {[1,11,19,35,43,46],..., = {[6,12,22,30,33,46],...,
= {[5,15,23,26,39,47]}
[2,12,20,36,44,47]} [3,9,19,27,30,43]} [5,11,21,29,32,45]}
−7
−9
4
−8
4
4
S (2 ,7) S (2 ,7) S (2 ,7)
4
−6
S (2 ,7) ∆ ∆ ∆
b = 7 ∆ = {[2,7,13,15,31,34,39],..., = {[5,7,18,23,26,31,47],..., = {[9,14,20,22,38,41,46],...,
= {[5,7,18,23,26,31,47]}
[10,15,21,23,39,42,47]} [2,4,15,20,28,44,47]} [1,7,9,20,25,28,33]}

表 8 中列出了 S 的部分元素.
3
Λ
SPECK48的 S 的部分元素
3
表 8
Λ

b的取值 q = 2 −1 q = 2 −2 q = 2 −3
−3
3
b = 1 － － S (2 ,1) = {[5,10],[2,3]}
Λ
−3
3
b = 2 － － S (2 ,2) = {[9,10],...,[16,24]}
Λ
3
−3
−2
−1
3
3
b = 3 S (2 ,3) = {[0,21,32]} S (2 ,3) = {[0,21,32],[1,22,33]} S (2 ,3) = {[0,21,32],...,[15,16,24]}
Λ Λ Λ
3
3
−3
−2
−1
3
b = 4 S (2 ,4) = {[2,4,5,37],[2,5,36,37]} S (2 ,4) = {[5,7,8,40],...,[4,5,8,40]} S (2 ,4) = {[7,8,10,42],...,[7,10,41,42]}
Λ
Λ
Λ

基于算法 1, 我们首次搜索到了 SPECK48 的两条 12 轮差分-线性区分器, 两条 12 轮差分-线性区分器的具体
细节如下所示.
● SPECK48 的 12 轮差分-线性区分器 1:


r 0 = 4, r m = 5, r 1 = 3





 ∆ m = [0,21,45], λ m = [5]





 r 0 =4 −8

 p = Pr(∆ in −−−→ ∆ m ) = 2



 .
 r m =5 −9.73

 r = Cor(∆ m −−−→ λ m ) = 2




 r 1 =3
 −3

q = Cor(λ m −−−→ λ out ) = 2





 r DL =12
 −23.73
 Cor(∆ in −−−−→ λ out ) = 2
最终我们得到了如下 8 个 SPECK48 的 12 轮区分器:

 r DL =12 r DL =12
 D 3 : (148090,101080) −−−−→ (65400c,6c4000), D 4 : (148090,101080) −−−−→ (41400c,4c4000)






 r DL =12 r DL =12

D 5 : (148090,101080) −−−−→ (45c00c,484000), D 6 : (148090,101080) −−−−→ (61c00c,684000)


.

 r DL =12 r DL =12

 D 7 : (148090,101080) −−−−→ (61c028,684020), D 8 : (148090,101080) −−−−→ (45c028,484020)





 r DL =12 r DL =12

D 9 : (148090,101080) −−−−→ (414028,4c4020), D 10 : (148090,101080) −−−−→ (654028,6c4020)

● SPECK48 的 12 轮差分-线性区分器 2: