{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T23:19:23Z","timestamp":1773962363531,"version":"3.50.1"},"reference-count":19,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2022,2,4]],"date-time":"2022-02-04T00:00:00Z","timestamp":1643932800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,5,19]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper proposes a new method to find high-probability truncated differentials using matrix muliplication. For Markov cipher with similar round function, suppose that the transition probability matrix of round function is $\\mathcal{D}$, then $\\mathcal{D}^{r}$ contains all the differential probabilities of an $r$-round block cipher. To reduce the matrix dimension, we consider the word-oriented truncated differential and the truncated transition probability matrix $\\mathcal{T}$. Regardless of the effect of the $S$-box, we focus on whether there is a non-zero difference on one cell instead of the value of the difference. In this case, the matrix dimension reduces significantly and we can calculate $\\mathcal{T}^{r}$ using a workstation. Then all the $r$-round truncated differential probabilities can be found from $\\mathcal{T}^{r}$. And the probability in $\\mathcal{T}^{r}$ is the probability of the whole truncated differential hull but not a single or several truncated differential characteristics. Besides, we make a more accurate probability estimation of the truncated differential of lightweight block cipher. Combined with the truncated differential hull, we found some longer truncated differential distinguishers. And as $\\mathcal{T}^{r}$ stores all the truncated differential probabilities, we can also find all the impossible truncated differentials.<\/jats:p>","DOI":"10.1093\/comjnl\/bxab213","type":"journal-article","created":{"date-parts":[[2022,1,28]],"date-time":"2022-01-28T12:09:42Z","timestamp":1643371782000},"page":"1069-1082","source":"Crossref","is-referenced-by-count":5,"title":["A New Method To Find All The High-Probability Word-Oriented Truncated Differentials: Application To <tt>Midori<\/tt>, <tt>SKINNY<\/tt> And <tt>CRAFT<\/tt>"],"prefix":"10.1093","volume":"66","author":[{"given":"Hao","family":"Guo","sequence":"first","affiliation":[{"name":"State Key Laboratory of Information Security , Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093 , China"},{"name":"School of Cyber Security , University of Chinese Academy of Sciences, Beijing 100049 , China"},{"name":"School of Cryptology , University of Chinese Academy of Sciences, Beijing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiyu","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Security , Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093 , China"},{"name":"School of Cyber Security , University of Chinese Academy of Sciences, Beijing 100049 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qianqian","family":"Yang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Security , Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093 , China"},{"name":"School of Cyber Security , University of Chinese Academy of Sciences, Beijing 100049 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"Hu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Information Security , Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093 , China"},{"name":"School of Cyber Security , University of Chinese Academy of Sciences, Beijing 100049 , China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiyuan","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering , Huizhou University"},{"name":"Henan Key Laboratory of Network Cryptography Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2022,2,4]]},"reference":[{"key":"2023052000434648400_ref1","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/BF00630563","article-title":"Differential cryptanalysis of DES-like cryptosystems","volume":"4","author":"Biham","year":"1991","journal-title":"Journal of CRYPTOLOGY"},{"key":"2023052000434648400_ref2","first-page":"196","article-title":"Truncated and higher order differentials","volume-title":"Fast Software Encryption: Second International Workshop. 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