{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T15:57:56Z","timestamp":1772467076765,"version":"3.50.1"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2021,5,3]],"date-time":"2021-05-03T00:00:00Z","timestamp":1620000000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,5,3]],"date-time":"2021-05-03T00:00:00Z","timestamp":1620000000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2021,7]]},"DOI":"10.1007\/s10623-021-00876-6","type":"journal-article","created":{"date-parts":[[2021,5,3]],"date-time":"2021-05-03T18:04:48Z","timestamp":1620065088000},"page":"1433-1452","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Construction of $${\\text {MDS}}$$ matrices from generalized Feistel structures"],"prefix":"10.1007","volume":"89","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1445-1593","authenticated-orcid":false,"given":"Mahdi","family":"Sajadieh","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4495-7616","authenticated-orcid":false,"given":"Mohsen","family":"Mousavi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,5,3]]},"reference":[{"key":"876_CR1","doi-asserted-by":"crossref","unstructured":"Augot D., Finiasz M.: Direct construction of recursive MDS diffusion layers using shortened BCH codes. In: FSE, vol. 8540, pp. 3\u201317. Springer, Berlin (2014).","DOI":"10.1007\/978-3-662-46706-0_1"},{"key":"876_CR2","doi-asserted-by":"crossref","unstructured":"Banik S., Bogdanov A., Isobe T., Shibutani K., Hiwatari H. et\u00a0al.: Midori: a block cipher for low energy. In: International Conference on the Theory and Application of Cryptology and Information Security, vol. 9453, pp. 411\u2013436. Springer, Berlin (2015).","DOI":"10.1007\/978-3-662-48800-3_17"},{"key":"876_CR3","doi-asserted-by":"crossref","unstructured":"Banik S., Funabiki Y., Isobe T.: More results on shortest linear programs. In: International Workshop on Security, vol. 11689, pp. 109\u2013128. Springer, Berlin (2019).","DOI":"10.1007\/978-3-030-26834-3_7"},{"key":"876_CR4","doi-asserted-by":"crossref","unstructured":"Beierle C., \u00a0Kranz T., Leander G.: Lightweight multiplication in GF$$(2^n)$$ with applications to MDS matrices. In: CRYPTO, vol. 9814, pp. 625\u2013653. Springer, Berlin (2016).","DOI":"10.1007\/978-3-662-53018-4_23"},{"key":"876_CR5","doi-asserted-by":"crossref","unstructured":"Berger T.P., Minier M., Thomas G.: Extended Generalized Feistel Networks using Matrix Representation. In: SAC, vol. 8282, pp. 289\u2013305. Springer, Berlin (2014).","DOI":"10.1007\/978-3-662-43414-7_15"},{"issue":"1","key":"876_CR6","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1109\/18.746771","volume":"45","author":"M Blaum","year":"1999","unstructured":"Blaum M., Roth R.M.: On lowest density MDS codes. IEEE Trans. Inf. Theory 45(1), 46\u201359 (1999).","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"876_CR7","doi-asserted-by":"publisher","first-page":"264","DOI":"10.46586\/tosc.v2019.i1.264-301","volume":"2019","author":"V Cauchois","year":"2019","unstructured":"Cauchois V., Gomez C., Thomas G.: General diffusion analysis: how to find optimal permutations for generalized type-II Feistel schemes. IACR Trans. Symmetric Cryptol. 2019(1), 264\u2013301 (2019).","journal-title":"IACR Trans. Symmetric Cryptol."},{"issue":"2\u20133","key":"876_CR8","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1007\/s10623-018-0520-3","volume":"87","author":"V Cauchois","year":"2019","unstructured":"Cauchois V., Loidreau P.: On circulant involutory MDS matrices. Des. Codes Cryptogr. 87(2\u20133), 249\u2013260 (2019).","journal-title":"Des. Codes Cryptogr."},{"key":"876_CR9","volume-title":"The Design of Rijndael AES-The Advanced Encryption Standard","author":"J Daemen","year":"2013","unstructured":"Daemen J., Rijmen V.: The Design of Rijndael AES-The Advanced Encryption Standard. Springer, Berlin (2013)."},{"issue":"2","key":"876_CR10","doi-asserted-by":"publisher","first-page":"218","DOI":"10.46586\/tosc.v2019.i2.218-240","volume":"2019","author":"P Derbez","year":"2019","unstructured":"Derbez P., Fouque P.A., Lambin B., Mollimard V.: Efficient search for optimal diffusion layers of generalized Feistel networks. IACR Trans. Symmetric Cryptol. 2019(2), 218\u2013240 (2019).","journal-title":"IACR Trans. Symmetric Cryptol."},{"issue":"2","key":"876_CR11","first-page":"48","volume":"2017","author":"S Duval","year":"2017","unstructured":"Duval S., Leurent G.: MDS matrices with lightweight circuits. IACR Trans. Symmetric Cryptol. 2017(2), 48\u201378 (2017).","journal-title":"IACR Trans. Symmetric Cryptol."},{"key":"876_CR12","doi-asserted-by":"crossref","unstructured":"Guo J., Peyrin T., Poschmann A.: The PHOTON family of lightweight hash functions. In: CRYPTO, vol. 684, pp. 222\u2013239. Springer, Berlin (2011).","DOI":"10.1007\/978-3-642-22792-9_13"},{"issue":"4","key":"876_CR13","doi-asserted-by":"publisher","first-page":"779","DOI":"10.3934\/amc.2019045","volume":"13","author":"KC Gupta","year":"2019","unstructured":"Gupta K.C., Pandey S.K., Ray I.G., Samanta S.: Cryptographically significant MDS matrices over finite fields: a brief survey and some generalized results. Adv. Math. Commun. 13(4), 779\u2013843 (2019).","journal-title":"Adv. Math. Commun."},{"issue":"1\u20132","key":"876_CR14","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s10623-016-0233-4","volume":"82","author":"KC Gupta","year":"2017","unstructured":"Gupta K.C., Pandey S.K., Venkateswarlu A.: On the direct construction of recursive MDS matrices. Des. Codes Cryptogr. 82(1\u20132), 77\u201394 (2017).","journal-title":"Des. Codes Cryptogr."},{"issue":"1\u20132","key":"876_CR15","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1007\/s10623-016-0261-0","volume":"82","author":"KC Gupta","year":"2017","unstructured":"Gupta K.C., Pandey S.K., Venkateswarlu A.: Towards a general construction of recursive MDS diffusion layers. Des. Codes Cryptogr. 82(1\u20132), 179\u2013195 (2017).","journal-title":"Des. Codes Cryptogr."},{"issue":"2\u20133","key":"876_CR16","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1007\/s10623-018-0582-2","volume":"87","author":"KC Gupta","year":"2019","unstructured":"Gupta K.C., Pandey S.K., Venkateswarlu A.: Almost involutory recursive MDS diffusion layers. Des. Codes Cryptogr. 87(2\u20133), 609\u2013626 (2019).","journal-title":"Des. Codes Cryptogr."},{"key":"876_CR17","doi-asserted-by":"crossref","unstructured":"Gupta K.C., Ray I.G.: On constructions of involutory MDS matrices. In: AFRICACRYPT, vol. 7918, pp. 43\u201360. Springer, Berlin (2013).","DOI":"10.1007\/978-3-642-38553-7_3"},{"key":"876_CR18","volume-title":"Matrix Analysis","author":"RA Horn","year":"2013","unstructured":"Horn R.A., Johnson C.R.: Matrix Analysis. Cambridge University Press, Cambridge (2013)."},{"issue":"4","key":"876_CR19","doi-asserted-by":"publisher","first-page":"130","DOI":"10.46586\/tosc.v2017.i4.130-168","volume":"2017","author":"J Jean","year":"2017","unstructured":"Jean J., Peyrin T., Sim S.M., Tourteaux J.: Optimizing implementations of lightweight building blocks. IACR Trans. Symmetric Cryptol. 2017(4), 130\u2013168 (2017).","journal-title":"IACR Trans. Symmetric Cryptol."},{"issue":"3","key":"876_CR20","doi-asserted-by":"publisher","first-page":"231","DOI":"10.46586\/tosc.v2019.i3.231-256","volume":"2019","author":"A Kesarwani","year":"2019","unstructured":"Kesarwani A., Sarkar S., Venkateswarlu A.: Exhaustive search for various types of MDS matrices. IACR Trans. Symmetric Cryptol. 2019(3), 231\u2013256 (2019).","journal-title":"IACR Trans. Symmetric Cryptol."},{"key":"876_CR21","doi-asserted-by":"crossref","unstructured":"Khoo K., \u00a0Peyrin T., Poschmann A.Y., \u00a0Yap H.: FOAM: Searching for Hardware-Optimal SPN Structures and Components with a Fair Comparison. In: CHES, vol. 8731, pp. 433\u2013450. Springer, Berlin (2014).","DOI":"10.1007\/978-3-662-44709-3_24"},{"key":"876_CR22","doi-asserted-by":"crossref","unstructured":"Kolsch L.: XOR-Counts and Lightweight Multiplication with Fixed Elements in Binary Finite Fields. In: EUROCRYPT, vol. 11476, pp. 285\u2013312. Springer, Berlin (2019).","DOI":"10.1007\/978-3-030-17653-2_10"},{"issue":"4","key":"876_CR23","doi-asserted-by":"publisher","first-page":"188","DOI":"10.46586\/tosc.v2017.i4.188-211","volume":"2017","author":"H Kranz","year":"2017","unstructured":"Kranz H., Leander G., Stoffelen K., Wiemer F.: Shorter linear straight-line programs for MDS matrices. IACR Trans. Symmetric Cryptol. 2017(4), 188\u2013211 (2017).","journal-title":"IACR Trans. Symmetric Cryptol."},{"issue":"1","key":"876_CR24","doi-asserted-by":"publisher","first-page":"129","DOI":"10.46586\/tosc.v2017.i1.129-155","volume":"2017","author":"C Li","year":"2017","unstructured":"Li C., Wang Q.: Design of lightweight linear diffusion layers from near-MDS matrices. IACR Trans. Symmetric Cryptol. 2017(1), 129\u2013155 (2017).","journal-title":"IACR Trans. Symmetric Cryptol."},{"issue":"1","key":"876_CR25","doi-asserted-by":"publisher","first-page":"84","DOI":"10.46586\/tosc.v2019.i1.84-117","volume":"2019","author":"S Li","year":"2019","unstructured":"Li S., Sun S., Li C., Wei Z., Hu L.: Constructing low-latency involutory MDS matrices with lightweight circuits. IACR Trans. Symmetric Cryptol. 2019(1), 84\u2013117 (2019).","journal-title":"IACR Trans. Symmetric Cryptol."},{"key":"876_CR26","doi-asserted-by":"crossref","unstructured":"Li Y., Wang M.: On the Construction of Lightweight Circulant Involutory MDS Matrices. In: FSE, vol. 9783, pp. 121\u2013139. Springer, Berlin (2016).","DOI":"10.1007\/978-3-662-52993-5_7"},{"key":"876_CR27","doi-asserted-by":"crossref","unstructured":"Liu M., Sim S.M.: Lightweight MDS Generalized Circulant Matrices. In: FSE, vol. 9783, pp. 101\u2013120. Springer, Berlin (2016).","DOI":"10.1007\/978-3-662-52993-5_6"},{"key":"876_CR28","doi-asserted-by":"crossref","unstructured":"Mesnager S., Kim K.H., Jo D., Choe J., Han M., Lee D.N.: A proof of the Beierle-Kranz-Leander conjecture related to lightweight multiplication in $${\\mathbb{F}}_{2^n}$$. Des. Codes Cryptogr., pp. 1\u201312 (2019).","DOI":"10.1007\/s10623-019-00665-2"},{"issue":"4","key":"876_CR29","doi-asserted-by":"publisher","first-page":"348","DOI":"10.1049\/iet-ifs.2017.0156","volume":"12","author":"MK Pehlivano\u011flu","year":"2018","unstructured":"Pehlivano\u011flu M.K., Sakall\u0131 M.T., Akleylek S., Duru N., Rijmen V.: Generalisation of Hadamard matrix to generate involutory MDS matrices for lightweight cryptography. IET Inf. Secur. 12(4), 348\u2013355 (2018).","journal-title":"IET Inf. Secur."},{"issue":"3","key":"876_CR30","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1007\/s10623-011-9578-x","volume":"64","author":"M Sajadieh","year":"2012","unstructured":"Sajadieh M., Dakhilalian M., Mala H., Omoomi B.: On construction of involutory MDS matrices from Vandermonde matrices in GF$$(2^q)$$. Des. Codes Cryptogr. 64(3), 287\u2013308 (2012).","journal-title":"Des. Codes Cryptogr."},{"key":"876_CR31","doi-asserted-by":"crossref","unstructured":"Sajadieh M., \u00a0Dakhilalian M., \u00a0Mala H., \u00a0Sepehrdad P.: Efficient diffusion layers for block ciphers and hash functions. In: FSE, vol. 7549, pp. 385\u2013401. Springer, Berlin (2012).","DOI":"10.1007\/978-3-642-34047-5_22"},{"key":"876_CR32","doi-asserted-by":"crossref","unstructured":"Sarkar S., Syed H.: Lightweight Diffusion Layer: Importance of Toeplitz Matrices. In: FSE, vol. 2016, pp. 95\u2013113. Springer, Berlin (2016).","DOI":"10.46586\/tosc.v2016.i1.95-113"},{"key":"876_CR33","doi-asserted-by":"crossref","unstructured":"Shibutani K.: On the Diffusion of Generalized Feistel Structures Regarding Differential and Linear Cryptanalysis. In: SAC, vol. 6544, pp. 211\u2013228. Springer, Berlin (2011).","DOI":"10.1007\/978-3-642-19574-7_15"},{"key":"876_CR34","doi-asserted-by":"crossref","unstructured":"Sim S.M., \u00a0Khoo K., \u00a0Oggier F., \u00a0Peyrin T.: Lightweight MDS Involution Matrices. In: FSE, vol. 9054, pp. 471\u2013493. Springer, Berlin (2015).","DOI":"10.1007\/978-3-662-48116-5_23"},{"key":"876_CR35","doi-asserted-by":"crossref","unstructured":"Tan Q.Q., Peyrin T.: Improved Heuristics for Short Linear Programs. In: Cryptology ePrint Archive, pp. 1\u201325. IACR (2019).","DOI":"10.46586\/tches.v2020.i1.203-230"},{"key":"876_CR36","doi-asserted-by":"crossref","unstructured":"Toh D., Teo J., Khoo K., Sim S.M.: Lightweight MDS Serial-Type Matrices with Minimal Fixed XOR Count. In: AFRICACRYPT, vol. 10831, pp. 51\u201371. Springer, Berlin (2018).","DOI":"10.1007\/978-3-319-89339-6_4"},{"key":"876_CR37","doi-asserted-by":"crossref","unstructured":"Wu S., Wang M., \u00a0Wu W.: Recursive Diffusion Layers for (Lightweight) Block Ciphers and Hash Functions. In: SAC, vol. 7707, pp. 355\u2013371. Springer, Berlin (2012).","DOI":"10.1007\/978-3-642-35999-6_23"},{"key":"876_CR38","unstructured":"Youssef A.M., \u00a0Mister S., Tavares S.E.: On the design of linear transformations for substitution permutation encryption networks. In: SAC, pp. 40\u201348 (1997)."},{"key":"876_CR39","doi-asserted-by":"crossref","unstructured":"Zheng Y., Matsumoto T., \u00a0Imai H.: On the Construction of Block Ciphers Provably Secure and Not Relying on Any Unproved Hypotheses. In: Conference on the Theory and Application of Cryptology, vol. 435, pp. 461\u2013480. Springer, Berlin (1989).","DOI":"10.1007\/0-387-34805-0_42"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-021-00876-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-021-00876-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-021-00876-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,14]],"date-time":"2021-06-14T19:32:09Z","timestamp":1623699129000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-021-00876-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,3]]},"references-count":39,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2021,7]]}},"alternative-id":["876"],"URL":"https:\/\/doi.org\/10.1007\/s10623-021-00876-6","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,3]]},"assertion":[{"value":"30 September 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 April 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 April 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 May 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}