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Table 6 Impossible subspace trails for SIMON. For simplicities, we denote 0000 by 0 and arbitrary four bits by ?

From: Searching for impossible subspace trails and improved impossible differential characteristics for SIMON-like block ciphers

 

Rounds

Impossible subspace trails

SIMON32

11

\((\textbf {0}|\textbf {0}|\textbf {0}|\textbf {0},0*00|\textbf {0}|\textbf {0}|000*) \nrightarrow (0*00|\textbf {0}|1000|000*,\textbf {0}|\textbf {0}|\textbf {0}|\textbf {0})\)

  

(0|0|0|0,0*00 |0|1000|000*) \(\nrightarrow \) (0*00 |0|0|000*, 0|0|0|0)

SIMON48

12

(0|0|0|0|0|0,0|0|0|0|0|000*) \(\nrightarrow \) (1000 |0|0|000* |0*00 |0***,

  

0|0|0|0|y0|000*)

  

(0|0|0|0|0|000*,1000 |0|0|000* |0*00 |0***) \(\nrightarrow \) (0|0|0|0|0|

  

000*, 0|0|0|0|0|0)

SIMON64

13

(0|0|0|0|0|0|0|0,0*00 |0|0|0|0|0|0|000*) \(\nrightarrow \) (0*00 |0|1000|

  

000* |0*00 |0*** |*00* |?,*000 |0|0|0|0|000* |0*00 |0***)

  

(*000 |0|0|0|0|000* |0*00 |0***,0*00 |0|1000|000* |0*00 |

  

0*** |*00* |?) \(\nrightarrow \) (0*00 |0|0|0|0|0|0|000*, 0|0|0|0|0|0|0|0)

SIMON96

16

(0|0|0|0|0|0|0|0|0|0|0|0,0*00 |0|0|0|0|0|0|0|0|0|0|000*)

  

\(\nrightarrow \) (*010 |0|0|0|0|000* |0*00 |0*** |*00* |?|0*** |?,0*00 |

  

0|0|0|0|0|0|000* |0*00 |0*** |*00* |?)

  

(0*00 |0|0|0|0|0|0|000* |0*00 |0*** |*00* |?,*010 |0|0|0|0|

  

000* |0*00 |0*** |*00* |?|0*** |?) \(\nrightarrow \) (0*00 |0|0|0|0|0|0|0|

  

0|0|0|000*, 0|0|0|0|0|0|0|0|0|0|0|0)

SIMON128

19

(0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0,0*00 |0|0|0|0|0|0|0|0|

  

0|0|0|0|0|0|000*) \(\nrightarrow \) (1*00 |0|0|0|0|0|0|000* |0*00 |0*** |

  

*00* |?|0*** |?|?|?,*000 |0|0|0|0|0|0|0|0|000* |0*00 |0*** |

  

*00* |?|0*** |?)

  

(0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0,0*00 |0|0|0|0|0|0|0|0|0|

  

0|0|0|0|0|000*) \(\nrightarrow \) (1*00 |0|0|0|0|0|0|000* |0*00 |0*** |

  

*00* |?|0*** |?|?|?,*010 |0|0|0|0|0|0|0|0|000* |0*00 |0*** |

  

*00* |?|0*** |?)

  

(*000 |0|0|0|0|0|0|0|0|000* |0*00 |0*** |*00* |?|0*** |?,

  

1*00 |0|0|0|0|0|0|000* |0*00 |0*** |*00* |?|0*** |?|?|?) \(\nrightarrow \)

  

(0|0|0|0|0|0|0|0|0|0|0|0|0|0|0,0*00 |0|0|0|0|0|0|0|0|

  

0|0|0|0|0|0|000*)

  

(*010 |0|0|0|0|0|0|0|0|000* |0*00 |0*** |*00* |?|0*** |?,

  

1*00 |0|0|0|0|0|0|000* |0*00 |0*** |*00* |?|0*** |?|?|?) \(\nrightarrow \)

  

(0|0|0|0|0|0|0|0|0|0|0|0|0|0|0|0,0*00 |0|0|0|0|0|0|0|0|

  

0|0|0|0|0|0|000*)