IET Information Security / 2024 / Article / Tab 9 / Research Article
MILP/MIQCP-Based Fully Automatic Method of Searching for Differential-Linear Distinguishers for SIMON-Like Ciphers Table 9 Twenty-round DL distinguisher for SIMON64 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 0000000000100000000000000000000000000000100010001000000000000000 7 0000000000001000100000000000000000000000000000100000000000000000 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 −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 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 −1.0 1.0 −1.0 −1.0 −1.0 1.0 −1.0 −1.0 −1.0 −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 −0.0 −0.25 −1.0 −1.0 −0.0 −0.25 1.0 −0.0 −0.5 −1.0 1.0 −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 −0.5 −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 −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 10 −0.0 −0.0625 −0.4688 −1.0 −0.0 −0.0625 0.4688 −0.0 −0.0 −0.75 −1.0 −0.0 −0.25 −0.75 1.0 −0.0 −1.0 −1.0 −1.0 −1.0 −0.75 −1.0 −1.0 −1.0 −0.75 −1.0 −0.25 −0.4688 −1.0 −1.0 −0.25 −0.4688 −0.5 −1.0 −0.0 −0.25 −1.0 −1.0 −0.0 −0.25 1.0 −0.0 −0.5 −1.0 1.0 −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 −0.5 −1.0 −1.0 −1.0 11 −0.0623 −0.6426 −0.0 −0.0039 0.1556 −0.0 −0.0 −0.0469 0.875 −0.0 −0.0625 −0.4688 −0.7656 −0.0 −0.25 −1.0 0.875 −1.0 −0.4688 −0.6426 −1.0 −1.0 −0.4688 −0.6426 −0.125 −0.1556 −0.5393 −1.0 −0.0625 −0.1556 −0.0 −0.0156 −0.0 −0.0625 −0.4688 −1.0 −0.0 −0.0625 0.4688 −0.0 −0.0 −0.75 −1.0 −0.0 −0.25 −0.75 1.0 −0.0 −1.0 −1.0 −1.0 −1.0 −0.75 −1.0 −1.0 −1.0 −0.75 −1.0 −0.25 −0.4688 −1.0 −1.0 −0.25 −0.4688 12 −0.0 −0.00006 0.0195 −0.0 −0.0 −0.0007 −0.1342 −0.0 −0.0 −0.1868 −0.4129 −0.0 −0.0313 −0.4688 −0.6426 −0.0 −0.2637 −0.2727 −0.6321 −1.0 −0.1868 −0.2727 −0.0513 −0.0445 −0.1241 −0.6321 −0.0078 −0.0195 −0.0 −0.0039 −0.0040 −0.0837 −0.0623 −0.6426 −0.0 −0.0039 0.1556 −0.0 −0.0 −0.0469 0.875 −0.0 −0.0625 −0.4688 −0.7656 −0.0 −0.25 −1.0 0.875 −1.0 −0.4688 −0.6426 −1.0 −1.0 −0.4688 −0.6426 −0.125 −0.1556 −0.5393 −1.0 −0.0625 −0.1556 −0.0 −0.0156 13 0.0003 −0.0 −0.0 0.0054 −0.0 −0.0 −0.0022 0.1355 −0.0 −0.0008 −0.1133 −0.2144 −0.0 −0.0173 −0.09 0.1978 −0.6659 −0.0441 −0.0530 −0.0163 −0.0117 −0.0153 −0.1237 −0.0004 −0.0008 −0.0 −0.0010 −0.00006 −0.0033 −0.0 −0.0 −0.00006 0.0195 −0.0 −0.0 −0.0007 −0.1342 −0.0 −0.0 −0.1868 −0.4129 −0.0 −0.0313 −0.4688 −0.6426 −0.0 −0.2637 −0.2727 −0.6321 −1.0 −0.1868 −0.2727 −0.0513 −0.0445 −0.1241 −0.6321 −0.0078 −0.0195 −0.0 −0.0039 −0.0040 −0.0837 14 −0.0 −0.00002 −0.0 −0.0 0.0046 −0.0 −0.0 −0.0088 −0.0257 −0.0 −0.00014 −0.0109 0.0352 −0.0 −0.0048 −0.0038 −0.0027 −0.0030 −0.0007 −0.0086 −0.0 −0.0002 −0.00001 −0.0 −0.0 0.0003 −0.0 −0.0 0.0054 −0.0 −0.0 −0.0022 0.1355 −0.0 −0.00080 −0.1133 −0.2144 −0.0 −0.0173 −0.0900 0.1978 −0.6659 −0.0441 −0.0530 −0.0163 −0.0117 −0.0153 −0.1237 −0.0004 −0.0008 −0.0 −0.0010 −0.00006 −0.0033 −0.0 Linear part 0000000000000000000000000000000000000000000000000100000000000000 15 0000000000000000010000000000000000000000000000000001000000000000 16 0000000000000000000100000000000000000000000000000100010000000000 17 0000000000000000010001000000000000000000000000000000000100000000 18 0000000000000000000000010000000000000000000000000100010001000000 19 0000000000000000010001000100000000000000000000000001000000010000 20 0000000000000000000100000001000000000000000000000100000001000100
Note : The experimental correlation of the first 14 (
rounds is
under
sample sizes and 100 random keys, the experimental correlation of the 6 rounds at the bottom is
under
sample sizes and 100 random keys. According to piling-up lemma, the experimental correlation is
