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

Table 6

Fifteen-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	100000000000000000000000001000100000000000000010
1	001000100000000000000000100000000000000000000000
2	000010000000000000000000001000100000000000000000
3	000000100000000000000000000010000000000000000000
4	000000000000000000000000000000100000000000000000
5	000000100000000000000000000000000000000000000000
6	000010000000000000000000000000100000000000000000
7	001000100000000000000000000010000000000000000000
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	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	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	−1.0
9	−0.5	−1.0	1.0	0.0	−0.5	−1.0	1.0	−1.0
	−1.0	−1.0	−0.50	−1.0	−1.0	−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	−1.0	−1.0	−1.0	−1.0	−1.0	−1.0
	−1.0	−1.0	0.0	−1.0	−1.0	−1.0	0.0	−1.0
10	−1.0	0.0	−0.1875	−0.75	1.0	0.0	−0.75	−1.0
	−0.2499	−0.4687	−1.0	−0.9999	−0.25	−0.4687	0.0	−0.0625
	−0.4687	−1.0	0.0	−0.0625	0.4687	0.0	0.0	−0.75
	−0.5	−1.0	1.0	0.0	−0.5	−1.0	1.0	−1.0
	−1.0	−1.0	−0.50	−1.0	−1.0	−1.0	−0.5	−1.0
	0.0	−0.25	−1.0	−1.0	0.0	−0.25	1.0	0.0
11	−0.0292	−0.3270	−0.8750	0.0	−0.1171	−0.6425	0.1249	−0.1556
	−0.5393	−0.9999	−0.0625	−0.1556	0.0	−0.0156	−0.0622	−0.6425
	0.0	−0.0039	0.1478	0.0	0.0	−0.0468	0.7656
	−1.0	0.0	−0.1875	−0.75	1.0	0.0	−0.75	−1.0
	−0.2499	−0.4687	−1.0	−0.9999	−0.25	−0.4687	0.0	−0.0625
	−0.4687	−1.0	0.0	−0.0625	0.4687	0.0	0.0	−0.75
Linear part
	001000000000000000000000100000000000000000000000
12	100000000000000000000000000000000000000000000000
13	000000000000000000000000100000000000000000000000
14	100000000000000000000000001000000000000000000000
15	001000000000000000000000100010000000000000000000

Note: The experimental correlation of the first 11 () 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 .