MILP/MIQCP-Based Fully Automatic Method of Searching for Differential-Linear Distinguishers for SIMON-Like Ciphers
Table 4
Thirteen-round DL distinguisher for SIMON32 with the theoretical correlation and experimental correlation , where the theoretical probability of the differential part, the theoretical correlation of the DL part, and the theoretical correlation of the linear part are , and , respectively.
Differential part
0
00001000000000000010001000001000
1
00000010000000000000100000000000
2
00000000000000000000001000000000
3
00000010000000000000000000000000
4
00001000000000000000001000000000
5
00100010000000000000100000000000
DL part
−1.0
−1.0
1.0
−1.0
−1.0
−1.0
1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
6
1.0
0.0
−1.0
−1.0
−1.0
0.0
−1.0
−1.0
−1.0
−1.0
0.0
−1.0
−1.0
−1.0
0.0
−1.0
−1.0
−1.0
1.0
−1.0
−1.0
−1.0
1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
−1.0
7
−0.5
−1.0
0.5
0.0
−0.5
−1.0
0.5
−1.0
0.0
−0.25
−1.0
−1.0
0.0
−0.25
1.0
0.0
1.0
0.0
−1.0
−1.0
−1.0
0.0
−1.0
−1.0
−1.0
−1.0
0.0
−1.0
−1.0
−1.0
0.0
−1.0
8
−0.25
0.0
−0.2499
−0.75
0.25
0.0
0.0
−0.0625
−0.4687
−1.0
0.0
−0.0625
0.4687
0.0
0.0
−0.75
−0.5
−1.0
0.5
0.0
−0.5
−1.0
0.5
−1.0
0.0
−0.25
−1.0
−1.0
0.0
−0.25
1.0
0.0
9
−0.0459
−0.4687
−0.0546
0.0
0.0
−0.1556
0.0622
−0.6425
0.0
−0.0039
0.1556
0.0
0.0
−0.0468
0.1093
0.0
−0.25
0.0
−0.2499
−0.75
0.25
0.0
0.0
−0.0625
−0.4687
−1.0
0.0
−0.0625
0.4687
0.0
0.0
−0.75
10
−0.0050
0.0
0.0
−0.0029
−0.0039
0.0
0.0
−0.00006
0.0191
0.0
0.0
0.0007
−0.0134
0.0
0.0
−0.1509
−0.0458
−0.4687
−0.0546
0.0
0.0
−0.0156
0.0622
−0.6425
0.0
−0.0039
0.1556
0.0
0.0
−0.0468
0.1093
0.0
Linear part
00000000000000000000000100000000
11
00000001000000000000000001000001
12
00000000010000010000000000010000
13
00000000000100000000000001000101
Note: The experimental correlation is under sample sizes and 100 random keys.
