{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:36:50Z","timestamp":1764981410507,"version":"3.46.0"},"reference-count":27,"publisher":"Walter de Gruyter GmbH","issue":"2","license":[{"start":{"date-parts":[[2017,5,11]],"date-time":"2017-05-11T00:00:00Z","timestamp":1494460800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,6,1]]},"abstract":"Abstract<\/jats:title>\n \n In this paper, we observe simple yet subtle interconnections among design theory, coding theory and cryptography.\nMaximum distance separable (MDS) matrices have applications not only in coding theory but are also\nof great importance in the design of block ciphers and hash functions. It is nontrivial\nto find MDS matrices which could be used in lightweight cryptography. In the SAC 2004 paper [12], Junod and Vaudenay considered bi-regular matrices which are useful objects to build MDS matrices. Bi-regular matrices are those matrices all of whose entries are nonzero and all of whose\n \n \n \n \n 2<\/m:mn>\n \u00d7<\/m:mo>\n 2<\/m:mn>\n <\/m:mrow>\n <\/m:math>\n {2\\times 2}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n submatrices are nonsingular. Therefore MDS matrices are bi-regular matrices, but the converse is not true. They proposed the constructions of efficient MDS matrices by studying\nthe two major aspects of a\n \n \n \n \n d<\/m:mi>\n \u00d7<\/m:mo>\n d<\/m:mi>\n <\/m:mrow>\n <\/m:math>\n {d\\times d}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n bi-regular matrix\n M<\/jats:italic>\n , namely\n \n \n \n \n \n v<\/m:mi>\n 1<\/m:mn>\n <\/m:msub>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n M<\/m:mi>\n )<\/m:mo>\n <\/m:mrow>\n <\/m:mrow>\n <\/m:math>\n {v_{1}(M)}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , i.e. the number of occurrences of 1 in\n M<\/jats:italic>\n , and\n \n \n \n \n \n c<\/m:mi>\n 1<\/m:mn>\n <\/m:msub>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n M<\/m:mi>\n )<\/m:mo>\n <\/m:mrow>\n <\/m:mrow>\n <\/m:math>\n {c_{1}(M)}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , i.e. the number of distinct elements in\n M<\/jats:italic>\n other than 1. They calculated the maximum number of ones that can occur in a\n \n \n \n \n d<\/m:mi>\n \u00d7<\/m:mo>\n d<\/m:mi>\n <\/m:mrow>\n <\/m:math>\n {d\\times d}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n bi-regular matrices, i.e.\n \n \n \n \n v<\/m:mi>\n 1<\/m:mn>\n \n d<\/m:mi>\n ,<\/m:mo>\n d<\/m:mi>\n <\/m:mrow>\n <\/m:msubsup>\n <\/m:math>\n {v_{1}^{d,d}}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n for\n d<\/jats:italic>\n up to 8, but with their approach, finding\n \n \n \n \n v<\/m:mi>\n 1<\/m:mn>\n \n d<\/m:mi>\n ,<\/m:mo>\n d<\/m:mi>\n <\/m:mrow>\n <\/m:msubsup>\n <\/m:math>\n {v_{1}^{d,d}}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n for\n \n \n \n \n d<\/m:mi>\n \u2265<\/m:mo>\n 9<\/m:mn>\n <\/m:mrow>\n <\/m:math>\n {d\\geq 9}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n seems difficult.\n <\/jats:p>\n \n In this paper, we explore the connection between the maximum number of ones in bi-regular matrices\nand the incidence matrices of Balanced Incomplete Block Design (BIBD).\nIn this paper, tools are developed to compute\n \n \n \n \n v<\/m:mi>\n 1<\/m:mn>\n \n d<\/m:mi>\n ,<\/m:mo>\n d<\/m:mi>\n <\/m:mrow>\n <\/m:msubsup>\n <\/m:math>\n {v_{1}^{d,d}}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n for arbitrary\n d<\/jats:italic>\n .\nUsing these results, we construct a restrictive version of\n \n \n \n \n d<\/m:mi>\n \u00d7<\/m:mo>\n d<\/m:mi>\n <\/m:mrow>\n <\/m:math>\n {d\\times d}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n bi-regular matrices, introducing by calling almost-bi-regular matrices, having\n \n \n \n \n v<\/m:mi>\n 1<\/m:mn>\n \n d<\/m:mi>\n ,<\/m:mo>\n d<\/m:mi>\n <\/m:mrow>\n <\/m:msubsup>\n <\/m:math>\n {v_{1}^{d,d}}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n ones\nfor\n \n \n \n \n d<\/m:mi>\n \u2264<\/m:mo>\n 21<\/m:mn>\n <\/m:mrow>\n <\/m:math>\n {d\\leq 21}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n . Since, the number of ones in any\n \n \n \n \n d<\/m:mi>\n \u00d7<\/m:mo>\n d<\/m:mi>\n <\/m:mrow>\n <\/m:math>\n {d\\times d}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n MDS matrix cannot exceed the maximum number of ones in a\n \n \n \n \n d<\/m:mi>\n \u00d7<\/m:mo>\n d<\/m:mi>\n <\/m:mrow>\n <\/m:math>\n {d\\times d}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n bi-regular matrix, our results provide an upper bound on the number of ones in any\n \n \n \n \n d<\/m:mi>\n \u00d7<\/m:mo>\n d<\/m:mi>\n <\/m:mrow>\n <\/m:math>\n {d\\times d}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n MDS matrix.\n <\/jats:p>\n \n We observe an interesting connection between Latin squares and bi-regular matrices and\nstudy the conditions under which a Latin square becomes a bi-regular matrix and finally\nconstruct MDS matrices from Latin squares.\nAlso a lower bound of\n \n \n \n \n \n c<\/m:mi>\n 1<\/m:mn>\n <\/m:msub>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n M<\/m:mi>\n )<\/m:mo>\n <\/m:mrow>\n <\/m:mrow>\n <\/m:math>\n {c_{1}(M)}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n is computed for\n \n \n \n \n d<\/m:mi>\n \u00d7<\/m:mo>\n d<\/m:mi>\n <\/m:mrow>\n <\/m:math>\n {d\\times d}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n bi-regular matrices\n M<\/jats:italic>\n such that\n \n \n \n \n \n \n v<\/m:mi>\n 1<\/m:mn>\n <\/m:msub>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n M<\/m:mi>\n )<\/m:mo>\n <\/m:mrow>\n <\/m:mrow>\n =<\/m:mo>\n \n v<\/m:mi>\n 1<\/m:mn>\n \n d<\/m:mi>\n ,<\/m:mo>\n d<\/m:mi>\n <\/m:mrow>\n <\/m:msubsup>\n <\/m:mrow>\n <\/m:math>\n {v_{1}(M)=v_{1}^{d,d}}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , where\n \n \n \n \n d<\/m:mi>\n =<\/m:mo>\n \n \n q<\/m:mi>\n 2<\/m:mn>\n <\/m:msup>\n +<\/m:mo>\n q<\/m:mi>\n +<\/m:mo>\n 1<\/m:mn>\n <\/m:mrow>\n <\/m:mrow>\n <\/m:math>\n {d=q^{2}+q+1}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n and\n q<\/jats:italic>\n is any prime power.\nFinally,\n \n \n \n \n d<\/m:mi>\n \u00d7<\/m:mo>\n d<\/m:mi>\n <\/m:mrow>\n <\/m:math>\n {d\\times d}<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n efficient MDS matrices are constructed for\n d<\/jats:italic>\n up to 8\nfrom bi-regular matrices having maximum number of ones and\nminimum number of other distinct elements for lightweight applications.\n <\/jats:p>","DOI":"10.1515\/jmc-2016-0013","type":"journal-article","created":{"date-parts":[[2017,5,11]],"date-time":"2017-05-11T08:45:40Z","timestamp":1494492340000},"page":"85-116","source":"Crossref","is-referenced-by-count":3,"title":["Applications of design theory for the constructions of MDS matrices for lightweight cryptography"],"prefix":"10.1515","volume":"11","author":[{"given":"Kishan Chand","family":"Gupta","sequence":"first","affiliation":[{"name":"Applied Statistics Unit , Indian Statistical Institute , 203, B.T. Road , Kolkata 700108 , India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sumit Kumar","family":"Pandey","sequence":"additional","affiliation":[{"name":"School of Physical and Mathematical Sciences , Nanyang Technological University , Singapore , Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Indranil Ghosh","family":"Ray","sequence":"additional","affiliation":[{"name":"Applied Statistics Unit , Indian Statistical Institute , 203, B.T. Road , Kolkata 700108 , India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2017,5,11]]},"reference":[{"key":"2025120600314652419_j_jmc-2016-0013_ref_001_w2aab3b7e1182b1b6b1ab2b2b1Aa","doi-asserted-by":"crossref","unstructured":"D. Augot and M. Finiasz,\nDirect construction of recursive MDS diffusion layers using shortened BCH codes,\nFast Software Encryption (FSE 2014),\nLecture Notes in Comput. Sci. 8540,\nSpringer, Berlin (2015), 3\u201317.","DOI":"10.1007\/978-3-662-46706-0_1"},{"key":"2025120600314652419_j_jmc-2016-0013_ref_002_w2aab3b7e1182b1b6b1ab2b2b2Aa","unstructured":"P. Barreto and V. Rijmen,\nThe Khazad legacy-level block cipher,\nsubmission to the NESSIE Project (2000), http:\/\/cryptonessie.org."},{"key":"2025120600314652419_j_jmc-2016-0013_ref_003_w2aab3b7e1182b1b6b1ab2b2b3Aa","doi-asserted-by":"crossref","unstructured":"P. S. L. M. Barreto and V. Rijmen,\nWhirlpool,\nEncyclopedia of Cryptography and Security. Second Edition,\nSpringer, New York (2011), 1384\u20131385.","DOI":"10.1007\/978-1-4419-5906-5_626"},{"key":"2025120600314652419_j_jmc-2016-0013_ref_004_w2aab3b7e1182b1b6b1ab2b2b4Aa","doi-asserted-by":"crossref","unstructured":"J. Daemen, L. R. Knudsen and V. Rijmen,\nThe block cipher square,\nFast Software Encryption (FSE 1997),\nLecture Notes in Comput. Sci. 1267,\nSpringer, Berlin (1997), 149\u2013165.","DOI":"10.1007\/BFb0052343"},{"key":"2025120600314652419_j_jmc-2016-0013_ref_005_w2aab3b7e1182b1b6b1ab2b2b5Aa","doi-asserted-by":"crossref","unstructured":"J. Daemen and V. Rijmen,\nThe Design of Rijndael: AES \u2013 The Advanced Encryption Standard,\nSpringer, Berlin, 2002.","DOI":"10.1007\/978-3-662-04722-4_1"},{"key":"2025120600314652419_j_jmc-2016-0013_ref_006_w2aab3b7e1182b1b6b1ab2b2b6Aa","unstructured":"G. D. Filho, P. Barreto and V. Rijmen,\nThe Maelstrom-0 hash function,\nProceedings of the 6th Brazilian Symposium on Information and Computer Systems Security (2006);\navailable at http:\/\/www.lbd.dcc.ufmg.br\/colecoes\/sbseg\/2006\/0017.pdf."},{"key":"2025120600314652419_j_jmc-2016-0013_ref_007_w2aab3b7e1182b1b6b1ab2b2b7Aa","unstructured":"P. Gauravaram, L. R. Knudsen, K. Matusiewicz, F. Mendel, C. Rechberger, M. Schlaffer and S. Thomsen,\nGr\u00f8stl \u2013 A SHA-3 candidate,\nsubmission to NIST (2008), http:\/\/www.groestl.info."},{"key":"2025120600314652419_j_jmc-2016-0013_ref_008_w2aab3b7e1182b1b6b1ab2b2b8Aa","doi-asserted-by":"crossref","unstructured":"J. Guo, T. Peyrin and A. Poschmann,\nThe PHOTON family of lightweight hash functions,\nAdvances in Cryptology (CRYPTO 2011),\nLecture Notes in Comput. Sci. 6841,\nSpringer, Berlin (2011), 222\u2013239.","DOI":"10.1007\/978-3-642-22792-9_13"},{"key":"2025120600314652419_j_jmc-2016-0013_ref_009_w2aab3b7e1182b1b6b1ab2b2b9Aa","doi-asserted-by":"crossref","unstructured":"K. C. Gupta and I. G. Ray,\nOn constructions of involutory MDS matrices,\nProgress in Cryptology (AFRICACRYPT 2013),\nLecture Notes in Comput. Sci. 7918,\nSpringer, Berlin (2013), 43\u201360.","DOI":"10.1007\/978-3-642-38553-7_3"},{"key":"2025120600314652419_j_jmc-2016-0013_ref_010_w2aab3b7e1182b1b6b1ab2b2c10Aa","doi-asserted-by":"crossref","unstructured":"K. C. Gupta and I. G. Ray,\nOn constructions of MDS matrices from companion matrices for lightweight cryptography,\nSecurity Engineering and Intelligence Informatics (CD-ARES 2013),\nLecture Notes in Comput. Sci. 8128,\nSpringer, Berlin (2013), 29\u201343.","DOI":"10.1007\/978-3-642-40588-4_3"},{"key":"2025120600314652419_j_jmc-2016-0013_ref_011_w2aab3b7e1182b1b6b1ab2b2c11Aa","doi-asserted-by":"crossref","unstructured":"K. C. Gupta and I. G. Ray,\nOn constructions of circulant MDS matrices for lightweight cryptography,\nInformation Security Practice and Experience (ISPEC 2014),\nLecture Notes in Comput. Sci. 8434,\nSpringer, Berlin (2014), 564\u2013576.","DOI":"10.1007\/978-3-319-06320-1_41"},{"key":"2025120600314652419_j_jmc-2016-0013_ref_012_w2aab3b7e1182b1b6b1ab2b2c12Aa","doi-asserted-by":"crossref","unstructured":"P. Junod and S. Vaudenay,\nPerfect diffusion primitives for block ciphers building efficient MDS matrices,\nSelected Areas in Cryptography (Waterloo 2004),\nLecture Notes in Comput. Sci. 3357,\nSpringer, Berlin (2005), 84\u201399.","DOI":"10.1007\/978-3-540-30564-4_6"},{"key":"2025120600314652419_j_jmc-2016-0013_ref_013_w2aab3b7e1182b1b6b1ab2b2c13Aa","doi-asserted-by":"crossref","unstructured":"J. Lacan and J. Fimes,\nSystematic MDS erasure codes based on Vandermonde matrices,\nIEEE Commun. Lett. 8 (2004), no. 9, 570\u2013572.","DOI":"10.1109\/LCOMM.2004.833807"},{"key":"2025120600314652419_j_jmc-2016-0013_ref_014_w2aab3b7e1182b1b6b1ab2b2c14Aa","unstructured":"F. J. MacWilliams and N. J. A. Sloane,\nThe Theory of Error Correcting Codes,\nNorth Holland, Amsterdam, 1986."},{"key":"2025120600314652419_j_jmc-2016-0013_ref_015_w2aab3b7e1182b1b6b1ab2b2c15Aa","unstructured":"J. Nakahara, Jr. and E. Abrahao,\nA new involutory MDS matrix for the AES,\nInt. J. Netw. Secur. 9 (2009), no. 2, 109\u2013116."},{"key":"2025120600314652419_j_jmc-2016-0013_ref_016_w2aab3b7e1182b1b6b1ab2b2c16Aa","doi-asserted-by":"crossref","unstructured":"V. Rijmen, J. Daemen, B. Preneel, A. Bosselaers and E. D. Win,\nThe cipher SHARK,\nFast Software Encryption (FSE 1996),\nLecture Notes in Comput. Sci. 1039,\nSpringer, Berlin (1996), 99\u2013112.","DOI":"10.1007\/3-540-60865-6_47"},{"key":"2025120600314652419_j_jmc-2016-0013_ref_017_w2aab3b7e1182b1b6b1ab2b2c17Aa","doi-asserted-by":"crossref","unstructured":"M. Sajadieh, M. Dakhilalian, H. Mala and B. Omoomi,\nOn construction of involutory MDS matrices from Vandermonde matrices in GF\u2062(2q){{\\rm GF}(2^{q})},\nDes. Codes Cryptogr. 64 (2012), no. 3, 287\u2013308.","DOI":"10.1007\/s10623-011-9578-x"},{"key":"2025120600314652419_j_jmc-2016-0013_ref_018_w2aab3b7e1182b1b6b1ab2b2c18Aa","doi-asserted-by":"crossref","unstructured":"M. Sajadieh, M. Dakhilalian, H. Mala and P. Sepehrdad,\nRecursive diffusion layers for block ciphers and hash functions,\nFast Software Encryption (FSE 2012),\nLecture Notes in Comput. Sci. 7549,\nSpringer, Berlin (2012), 385\u2013401.","DOI":"10.1007\/978-3-642-34047-5_22"},{"key":"2025120600314652419_j_jmc-2016-0013_ref_019_w2aab3b7e1182b1b6b1ab2b2c19Aa","unstructured":"B. Schneier, J. Kelsey, D. Whiting, D. Wagner, C. Hall and N. Ferguson,\nTwofish: A 128-bit block cipher,\nFirst Advanced Encryption Standard (AES) Candidate Conference,\nNational Institute for Standards and Technology, Gaithersburg (1998);\navailable at https:\/\/www.schneier.com\/academic\/paperfiles\/paper-twofish-paper.pdf."},{"key":"2025120600314652419_j_jmc-2016-0013_ref_020_w2aab3b7e1182b1b6b1ab2b2c20Aa","unstructured":"B. Schneier, J. Kelsey, D. Whiting, D. Wagner, C. Hall and N. Ferguson,\nThe Twofish Encryption Algorithm,\nJohn Wiley & Sons, New York, 1999."},{"key":"2025120600314652419_j_jmc-2016-0013_ref_021_w2aab3b7e1182b1b6b1ab2b2c21Aa","unstructured":"T. Shiraj and K. Shibutani,\nOn the diffusion matrix employed in the Whirlpool hashing function,\npreprint (2003), https:\/\/www.cosic.esat.kuleuven.be\/nessie\/reports\/phase2\/whirlpool-20030311.pdf."},{"key":"2025120600314652419_j_jmc-2016-0013_ref_022_w2aab3b7e1182b1b6b1ab2b2c22Aa","unstructured":"D. R. Stinson,\nCryptography: Theory and Practice,\nCRC Press, Boca Raton, 1995."},{"key":"2025120600314652419_j_jmc-2016-0013_ref_023_w2aab3b7e1182b1b6b1ab2b2c23Aa","unstructured":"D. R. Stinson,\nCombinatorial Designs: Constructions and Analysis,\nSpringer, New York, 2003."},{"key":"2025120600314652419_j_jmc-2016-0013_ref_024_w2aab3b7e1182b1b6b1ab2b2c24Aa","doi-asserted-by":"crossref","unstructured":"D. Watanabe, S. Furuya, H. Yoshida, K. Takaragi and B. Preneel,\nA new keystream generator MUGI,\nFast Software Encryption (FSE 2002),\nLecture Notes in Comput. Sci. 2365,\nSpringer, Berlin (2002), 179\u2013194.","DOI":"10.1007\/3-540-45661-9_14"},{"key":"2025120600314652419_j_jmc-2016-0013_ref_025_w2aab3b7e1182b1b6b1ab2b2c25Aa","doi-asserted-by":"crossref","unstructured":"S. Wu, M. Wang and W. Wu,\nRecursive diffusion layers for (lightweight) block ciphers and hash functions,\nSelected Areas in Cryptography (SAC 2012),\nLecture Notes in Comput. Sci. 7707,\nSpringer, Berlin (2013), 355\u2013371.","DOI":"10.1007\/978-3-642-35999-6_23"},{"key":"2025120600314652419_j_jmc-2016-0013_ref_026_w2aab3b7e1182b1b6b1ab2b2c26Aa","unstructured":"A. M. Youssef, S. Mister and S. E. Tavares,\nOn the design of linear transformations for substitution permutation encryption networks,\nWorkshop on Selected Areas in Cryptography (SAC 1997),\nCarleton University, Ottawa (1997), 40\u201348."},{"key":"2025120600314652419_j_jmc-2016-0013_ref_027_w2aab3b7e1182b1b6b1ab2b2c27Aa","unstructured":"Sony Corporation,\nThe 128-bit block cipher CLEFIA\nAlgorithm Specification (2007), http:\/\/www.sony.co.jp\/Products\/cryptography\/clefia\/download\/data\/clefia-spec-1.0.pdf."}],"container-title":["Journal of Mathematical Cryptology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.degruyter.com\/view\/j\/jmc.2017.11.issue-2\/jmc-2016-0013\/jmc-2016-0013.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2016-0013\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2016-0013\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T00:33:51Z","timestamp":1764981231000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/jmc-2016-0013\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,5,11]]},"references-count":27,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,5,16]]},"published-print":{"date-parts":[[2017,6,1]]}},"alternative-id":["10.1515\/jmc-2016-0013"],"URL":"https:\/\/doi.org\/10.1515\/jmc-2016-0013","relation":{},"ISSN":["1862-2984","1862-2976"],"issn-type":[{"type":"electronic","value":"1862-2984"},{"type":"print","value":"1862-2976"}],"subject":[],"published":{"date-parts":[[2017,5,11]]}}}