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

Table 2

23-round differential propagation of New Structure III.

Rounds	0	Α	0	0	Conditions
1	0	0	α	0
2	0	0	0	α
3	α	0	0	0
4	0	α1	α1	0	α1 = ΔF(α)
5	0	0	α1	α1
6	α1	0	0	α1
7	?	?	α2	0	α2 = ΔF^2(α)
8	0	?	?	α2
9	α2	0	?	?
10	?	?	α3	?	α3 = ΔF^3(α)
11	?	?	?	α3
12	α3	?	?	?
13	?	α4	?	?	α4 = ΔF^4(α)
13	?	β1⊕β2	?	?
14	?	β1	β2	?
15	?	β1	0	β2
16	β2	β1	0	0	β2 = ΔF^−2(β)
17	0	β1	0	0
18	0	0	β1	0
19	0	0	0	β1
20	β1	0	0	0	β1 = ΔF^−1(β)
21	0	β	β	0
22	0	0	β	β
23	β	0	0	β