IET Information Security / 2024 / Article / Tab 18 / Research Article
MILP/MIQCP-Based Fully Automatic Method of Searching for Differential-Linear Distinguishers for SIMON-Like Ciphers Table 18 Twenty-three-round DL distinguisher for SIMECK64 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 (optimal differential trail) 0 0000000000000000001000000000000000000000000000000101010000000000 7 0000000000000000000101000000000000000000000000000000100000000000 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 −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 −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 −0.0 −1.0 1.0 −0.0 −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 −1.0 −1.0 −1.0 −1.0 −1.0 9 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −0.5 −1.0 −0.5 −1.0 −0.0 −0.25 −0.0 −0.25 1.0 −0.0 0.5 −0.0 0.5 −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 −0.0 −1.0 −0.0 −1.0 1.0 −0.0 −1.0 −0.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 10 −1.0 −1.0 −1.0 −1.0 −0.75 −1.0 −0.75 −1.0 −0.25 −0.4688 −0.25 −0.4688 −0.0 −0.0625 −0.0 −0.0625 −0.0 −0.0 −0.25 −0.0 0.25 −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 −0.5 −1.0 −0.5 −1.0 −0.0 −0.25 −0.0 −0.25 1.0 −0.0 0.5 −0.0 0.5 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 11 −1.0 −0.875 −1.0 −0.4688 −0.6426 −0.4688 −0.6426 −0.125 −0.1556 −0.0459 −0.1556 −0.0 −0.0156 −0.0 −0.0039 −0.0 −0.0 0.125 −0.0 −0.0625 −0.0 0.25 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −0.875 −1.0 −1.0 −1.0 −1.0 −0.75 −1.0 −0.75 −1.0 −0.25 −0.4688 −0.25 −0.4688 −0.0 −0.0625 −0.0 −0.0625 −0.0 −0.0 −0.25 −0.0 0.25 −0.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 12 −0.6426 −0.77 −0.2637 −0.2727 −0.1510 −0.2727 −0.0385 −0.0445 −0.0033 −0.0192 −0.0 −0.0018 −0.0 −0.00006 −0.0 −0.0 −0.0 −0.0 −0.0078 −0.0 −0.0313 −0.0 −1.0 −1.0 −1.0 −1.0 −0.9375 −1.0 −0.9375 −1.0 −0.6426 −0.77 −1.0 −0.875 −1.0 −0.4688 −0.6426 −0.4688 −0.6426 −0.125 −0.1556 −0.0459 −0.1556 −0.0 −0.0156 −0.0 −0.0039 −0.0 −0.0 0.125 −0.0 −0.0625 −0.0 0.25 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −0.875 13 −0.4024 −0.1060 −0.09 −0.0226 −0.0514 −0.0057 −0.0074 −0.0001 −0.00075 −0.0 −0.00007 −0.0 −0.0 −0.0 −0.0 −0.0 0.0005 −0.0 −0.00098 −0.0 0.1211 −1.0 −0.9688 −1.0 −0.77 −0.8573 −0.77 −0.8573 −0.4060 −0.4024 −0.2864 −0.6426 −0.77 −0.2637 −0.2727 −0.1510 −0.2727 −0.0385 −0.0445 −0.0033 −0.0192 −0.0 −0.0018 −0.0 −0.00006 −0.0 −0.0 −0.0 −0.0 −0.0078 −0.0 −0.0313 −0.0 −1.0 −1.0 −1.0 −1.0 −0.9375 −1.0 −0.9375 −1.0 −0.6426 −0.77 14 −0.0240 −0.0193 −0.0016 −0.0036 −0.0002 −0.0005 −0.000001 −0.000008 −0.0 −0.0 −0.0 −0.0 −0.0 −0.0 −0.0 −0.0 −0.000003 −0.0 0.0017 −0.0 −0.8573 −0.9142 −0.5413 −0.5320 −0.4311 −0.5320 −0.1955 −0.1542 −0.0660 −0.1048 −0.4024 −0.1060 −0.09 −0.0226 −0.0514 −0.0057 −0.0074 −0.0001 −0.0007 −0.0 −0.00007 −0.0 −0.0 −0.0 −0.0 −0.0 0.0005 −0.0 −0.00098 −0.0 0.1211 −1.0 −0.96875 −1.0 −0.77 −0.8573 −0.77 −0.8573 −0.4060 −0.4024 −0.2864 Linear part 0000000000000000000000010000000000000000000000000000000000000000 15 0000000000000000000000000000000000000000000000000000000100000000 16 0000000000000000000000010000000000000000000000000000000010000000 17 0000000000000000000000001000000000000000000000000000000101000000 18 0000000000000000000000010100000000000000000000000000000000100000 19 0000000000000000000000000010000000000000000000000000000101010000 20 0000000000000000000000010101000000000000000000000000000010000000 21 0000000000000000000000001000000000000000000000000000000100010000 22 0000000000000000000000010001000000000000000000000000000000000000 23 0000000000000000000000000000000000000000000000000000000100010000
Note : The experimental correlation of the first 14 (
rounds is
under
sample sizes and 100 random keys, and the experimental correlation of the 9 rounds at the bottom is
under
sample sizes and 100 random keys. According to piling-up lemma, the experimental correlation is
