Improved Impossible Differentials and Zero-Correlation Linear Hulls of New Structure III

Table 3

23-round linear propagation of New Structure III.

Rounds	0	0	α	0	Conditions
1	0	0	0	α
2	α	0	0	0
3	0	α1	0	0	α1 = ΛF(α)
4	0	α1	α1	0
5	0	α1	α1	α1
6	α1	α1	α1	α1
7	?	α1⊕α2	?	?	α2 = ΛF^2(α)
8	?	?	α1⊕α2	?
9	?	?	?	α1⊕α2
10	α1⊕α2	?	?	?
10	β4	?	?	?	β4 = ΛF^−4(β)
11	?	0	β3	?
12	?	?	0	β3
13	β3	?	?	0	β3 = ΛF^−3(β)
14	0	0	β2	?
15	?	0	0	β2
16	β2	?	0	0	β2 = ΛF^−2(β)
17	0	0	β1	0
18	0	0	0	β1
19	β1	0	0	0	β1 = ΛF^−1(β)
20	0	β	0	0
21	0	β	β	0
22	0	β	β	β
23	β	β	β	β