IET Information Security

Research Article

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

Table 14

Fourteen-round DL distinguisher for SIMECK32 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 is , and , respectively.


Differential part

0	00100000000000000111010000000000
1	00010100000000000010000000000000
2	00001000000000000001010000000000
3	00000100000000000000100000000000
4	00000000000000000000010000000000
5	000001000000000000000000000000000

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	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

7	−0.25	−1.0	−1.0	0.9999	0.0	0.50	−1.0	−1.0
	−1.0	−1.0	−0.9999	−0.50	−1.0	−1.0	−1.0	0.0
	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

8	0.0	−1.0	0.9999	0.0	−0.2450	0.0	−0.75	−1.0
	−1.0	−0.9999	−0.2450	−0.4688	−1.0	−1.0	0.0	−0.0625
	−0.25	−1.0	−1.0	0.9999	0.0	0.50	−1.0	−1.0
	−1.0	−1.0	−0.9999	−0.50	−1.0	−1.0	−1.0	0.0

9	−0.0625	0.8750	0.0	0.1250	0.0	0.1172	−0.6426	−1.0
	−0.9999	−0.1250	−0.1556	−0.1836	−1.0	0.0	−0.0156	0.0
	0.0	−1.0	0.9999	0.0	−0.2450	0.0	−0.75	−1.0
	−1.0	−0.9999	−0.2450	−0.4688	−1.0	−1.0	0.0	−0.0625

10	0.0	0.0	−0.0625	0.0	0.0082	0.0	−0.3645	−1.0
	−0.0625	−0.0445	−0.0133	−0.1474	0.0	−0.0039	0.0	−0.0010
	−0.0625	0.8750	0.0	0.1250	0.0	0.1172	−0.6426	−1.0
	−0.9999	−0.1250	−0.1556	−0.1836	−1.0	0.0	−0.0156	0.0

Linear part

	00000001000000000000001000000000
11	00000010000000000000000000000000
12	00000000000000000000001000000000
13	00000010000000000000000100000000
14	00000001000000000000001010001000

Note: The experimental correlation of the first 10 () rounds is under sample sizes and 100 random keys, and 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 .