IET Information Security

Research Article

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

Table 15

Seventeen-round DL distinguisher for SIMECK48 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	000000000000100000000000000000000001010000000000
1	000000000000010000000000000000000000100000000000
2	000000000000000000000000000000000000010000000000
3	000000000000010000000000000000000000000000000000
4	000000000000100000000000000000000000010000000000
5	000000000001010000000000000000000000100000000000
6	000000000010000000000000000000000001010000000000

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

7	−1.0	−1.0	−1.0	−1.0	−1.0	0.0	−1.0	−1.0
	−1.0	1.0	0.0	1.0	−1.0	1.0	−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	−0.5	−1.0	−1.0	−1.0	0.0	−0.25		−1.0
	0.0	0.0	−0.5		1.0	0.0	−0.9999	−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	0.0	−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

9	−0.4688	−0.50	−1.0	0.0	−0.0625	0.0	−0.25	0.0
	0.0	0.25	0.0	−0.50		0.50	−0.9999	−1.0
	−1.0	−1.0	−1.0	−0.75	−1.0	−1.0	−1.0	−0.25
	−0.5	−1.0	−1.0	−1.0	0.0	−0.25		−1.0
	0.0	0.0	−0.5		1.0	0.0	−0.9999	−1.0
	−1.0	−1.0	−1.0	−1.0	−1.0	−1.0	−1.0	−1.0

10	−0.0918	−0.4688	0.0	−0.0156	0.0	−0.0156	0.0
	0.0	0.0	−0.1250		−0.25		−0.8750	−1.0
	−1.0	−1.0	−0.4688	−0.6426	−0.75	−1.0	−0.1250	−0.1556
	−0.4688	−0.50	−1.0	0.0	−0.0625	0.0	−0.25	0.0
	0.0	0.25	0.0	−0.50		0.50	−0.9999	−1.0
	−1.0	−1.0	−1.0	−0.750	−1.0	−1.0	−1.0	−0.25

11	−0.0609		−0.0039		−0.00024	0.0	0.0	0.0
		0.0146	0.0	−0.0625	0.0	0.1606	−0.77	−0.8750
	−1.0	−0.2637	−0.2727	−0.2522	−0.6426	−0.0625	−0.0445	−0.0066
	−0.0918	−0.4688	0.0	−0.0156	0.0	−0.0156	0.0
	0.0	0.0	−0.1250		−0.25		−0.8750	−1.0
	−1.0	−1.0	−0.4688	−0.6426	−0.75	−1.0	−0.1250	−0.1556

12	0.0	−0.0005	0.0		0.0	0.0	0.0	0.0
	0.0	0.0	−0.0037	0.0	0.0127		−0.4242	−0.77
	−0.1401	−0.09	−0.0379	−0.1371	−0.0193	−0.0119	−0.0002	−0.0024
	−0.0609		−0.0039		−0.0002	0.0	0.0	0.0
		0.0146	0.0	−0.0625	0.0	0.1606	−0.77	−0.8750
	−1.0	−0.2637	−0.2727	−0.2522	−0.6426	−0.0625	−0.0445	−0.0066

Linear part

	000000000000000100000000000000000000000000000000
13	000000000000000000000000000000000000000100000000
14	000000000000000100000000000000000000000010000000
15	000000000000000010000000000000000000000101000000
16	000000000000000101000000000000000000000000100000
17	000000000000000000100000000000000000000101010000

Note: The experimental correlation of the first 12 () rounds is under sample sizes and 100 random keys, and the experimental correlation of the 5 rounds at the bottom is under sample sizes and 100 random keys. According to piling-up lemma, the experimental correlation is .