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We propose an algorithm which can greatly reduce the searching complexity to find such trails efficiently since the search space exponentially expands to find impossible differentials with multiple active bits. There is another situation leading to the contradiction in impossible differentials except for miss-in-the-middle. We show how the contradiction happens and conclude the precondition of it defined as miss-from-the-middle. It makes our results more comprehensive by applying these two approach simultaneously. This paper gives for the first time impossible differential characteristics with multiple active bits for SIMON and SIMECK, leading to a great increase in the number. The results can be verified not only by covering the state-of-art, but also by the MILP model.<\/jats:p>","DOI":"10.1186\/s42400-021-00081-x","type":"journal-article","created":{"date-parts":[[2021,6,2]],"date-time":"2021-06-02T00:04:21Z","timestamp":1622592261000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Searching for impossible subspace trails and improved impossible differential characteristics for SIMON-like block ciphers"],"prefix":"10.1186","volume":"4","author":[{"given":"Xuzi","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6567-9216","authenticated-orcid":false,"given":"Baofeng","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Hou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dongdai","family":"Lin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,6,2]]},"reference":[{"key":"81_CR1","doi-asserted-by":"publisher","unstructured":"Abdelraheem, MA, Alizadeh J, AlKhzaimi HA, Aref MR, Bagheri N, Gauravaram P (2015) Improved linear cryptanalysis of reduced-round SIMON-32 and SIMON-48. 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