IET Information Security

Research Article

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

Table 5

Fourteen-round DL distinguisher for SIMON32 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	00000000000010000000000000100010
1	00000000000000100000000000001000
2	00000000000000000000000000000010
3	00000000000000100000000000000000
4	00000000000010000000000000000010
5	00000000001000100000000000001000

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	−1.0	0.0	−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	1.0	−1.0	−1.0	−1.0	1.0	−1.0

7	0.0	−0.25	−1.0	−1.0	0.0	−0.25	1.0	0.0
	−0.5	−1.0	0.5	0.0	−0.5	−1.0	0.5	−1.0
	−1.0	−1.0	0.0	−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

8	−0.4687	−1.0	0.0	−0.0625	0.4687		0.0	−0.75
	−0.25	0.0	−0.25	−0.75	0.25	0.0	0.0	−0.0625
	0.0	−0.25	−1.0	−1.0	0.0	−0.25	1.0	0.0
	−0.5	−1.0	0.5	0.0	−0.5	−1.0	0.5	−1.0

9	0.0	−0.0039	0.1556		0.0	−0.0468	0.1093	0.0
	−0.0458	−0.4687	−0.0546	0.0		−0.0156	0.0622	−0.6425
	−0.4687	−1.0	0.0	−0.0625	0.4687		0.0	−0.75
	−0.25	0.0	−0.25	−0.75	0.25	0.0	0.0	−0.0625

10	0.0191		0.0	−0.0007	−0.0134	0.0	0.0	−0.1509
	−0.0050	0.0	0.0	−0.0029	−0.0039	0.0	0.0	0.00006
	0.0	−0.0039	0.1556		0.0	−0.0468	0.1093	0.0
	−0.0458	−0.4687	−0.05468	0.0		−0.0156	0.0622	−0.6425

Linear part

	00000000000000000000000000000001
11	00000000000000010100000000000000
12	01000000000000000001000000000001
13	00010000000000010000010000000000
14	00000100000000000001000100000001

Note: The experimental correlation of the first 10 () 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 .