IET Information Security

Research Article

MILP/MIQCP-Based Fully Automatic Method of Searching for Differential-Linear Distinguishers for SIMON-Like Ciphers

Table 7

Sixteen-round DL distinguisher for SIMON48 with 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	000001000000000000000000000100010001000000000000
1	000000010001000000000000000001000000000000000000
2	000000000100000000000000000000010001000000000000
3	000000000001000000000000000000000100000000000000
4	000000000000000000000000000000000001000000000000
5	000000000001000000000000000000000000000000000000
6	000000000100000000000000000000000001000000000000
7	000000010001000000000000000000000100000000000000

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
	−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

8	−1.0	−1.0	−1.0	0.0	−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	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	−1.0	−1.0	−1.0	−1.0	−1.0	−1.0	−1.0

9	−1.0	0.0	−0.2500	1.0	0.0	−0.5	−1.0	1.0
	0.0	−0.5	−1.0	1.0	−1.0	−1.0	−1.0	−0.5
	−1.0	−1.0	−1.0	−0.5000	−1.0	0.0	−0.25	−1.0
	−1.0	−1.0	−1.0	0.0	−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	0.0

10	−0.0625	0.4688	0.0	0.0	−0.75	−1.0	0.0	−0.1875
	−0.75	1.0	0.0	−0.7500	−1.0	−0.25	−0.4688	−1.0
	−1.0	−0.2500	−0.4688	0.0	−0.0625	−0.4688	−1.0	0.0
	−1.0	0.0	−0.2500	1.0	0.0	−0.5	−1.0	1.0
	0.0	−0.5	−1.0	1.0	−1.0	−1.0	−1.0	−0.5
	−1.0	−1.0	−1.0	−0.5000	−1.0	0.0	−0.25	−1.0

11	0.0	0.0	−0.0469	0.7656	0.0	−0.0293	−0.3270	−0.875
	0.0	−0.1172	−0.6426	0.125	−0.1556	−0.5393	−1.0	−0.0625
	−0.1556	0.0	−0.0156	−0.0623	−0.6426	0.0	−0.0039	0.1479
	−0.0625	0.4688	0.0	0.0	−0.75	−1.0	0.0	−0.1875
	−0.75	1.0	0.0	−0.75	−1.0	−0.25	−0.4688	−1.0
	−1.0	−0.2500	−0.4688	0.0	−0.0625	−0.4688	−1.0	0.0

12	−0.0007	−0.1049	0.0	0.0	−0.0729	−0.4468	0.0	−0.0058
	−0.1556	−0.0513	0.0	−0.1241	−0.6321	−0.0078	−0.0195	0.0
	−0.0039	−0.0040	−0.0837	0.0	−0.00006	0.0179	0.0	0.0
	0.0	0.0	−0.0469	0.7656	0.0	−0.0293	−0.3270	−0.875
	0.0	−0.1172	−0.6426	0.125	−0.1556	−0.5393	−1.0	−0.0625
	−0.1556	0.0	−0.0156	−0.0623	−0.6426	0.0	−0.0039	0.1479

Linear part

	000000000000100000000000000000000000000000000000
13	000000000000000000000000000000000000100000000000
14	000000000000100000000000000000000000001000000000
15	000000000000001000000000000000000000100010000000
16	000000000000100010000000000000000000000000100000

Note: The experimental correlation of the first 12 () rounds is under sample sizes and 100 random keys, the experimental correlation of the 4 rounds at the bottom is under sample sizes and 100 random keys. According to piling-up lemma, the experimental correlation is .