Security analysis of SIMECK block cipher against related-key impossible differential

SIMECK is a family of lightweight block ciphers that relies on Feistel structure. Being proposed at CHES in 2015, the round function of SIMECK is slightly modified from SIMON. A cipher in this family with K-bit key and n-bit block is called SIMECK n / K , for n / K ∈ { 32 / 64 , 48 / 96 , 64 / 128 } . SIMECK has already received a number of third-party analyses. However, the security level on SIMECK against the related-key impossible differential has never been evaluated. In this paper, we consider related-key impossible differential distinguishers for the variants of SIMECK. We first propose some distinguishers on SIMECK using the miss-in-the-middle approach. More specifically, 15/16/19-round related-key impossible differential distinguishers on SIMECK32/48/64 are presented first while the best previously known results were 11/15/17-round on SIMECK32/48/64 in the single-key setting. Afterwards, thanks to MILP approach, we automatically prove that these characteristics are the best related-key impossible differentials of SIMECK when we limit the input and output differences to 1 active bit.