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Yal\u00e7in, \u201cBlock ciphers \u2014 Focus on the linear layer (feat. PRIDE),\u201d Advances in Cryptology-CRYPTO 2014-34th Annual Cryptology Conference, Santa Barbara, CA, USA, Aug. 2014, Proceedings, Part I, pp.57-76, 2014. 10.1007\/978-3-662-44371-2_4","DOI":"10.1007\/978-3-662-44371-2_4"},{"key":"2","doi-asserted-by":"crossref","unstructured":"[2] D. Augot and M. Finiasz, \u201cDirect construction of recursive MDS diffusion layers using shortened BCH codes, Fast Software Encryption-21st International Workshop, FSE 2014, London, UK, March 2014. Revised Selected Papers, pp.3-17, 2014. 10.1007\/978-3-662-46706-0_1","DOI":"10.1007\/978-3-662-46706-0_1"},{"key":"3","doi-asserted-by":"publisher","unstructured":"[3] R. Avanzi, \u201cThe QARMA block cipher family. Almost MDS matrices over rings with zero divisors, nearly symmetric even-mansour constructions with non-involutory central rounds, and search heuristics for low-latency s-boxes,\u201d IACR Trans. Symmetric Cryptol., vol.2017, no.1, pp.4-44, 2017. 10.46586\/tosc.v2017.i1.4-44","DOI":"10.46586\/tosc.v2017.i1.4-44"},{"key":"4","doi-asserted-by":"crossref","unstructured":"[4] S. Banik, A. Bogdanov, T. Isobe, K. Shibutani, H. Hiwatari, T. Akishita, and F. Regazzoni, \u201cMidori: A block cipher for low energy,\u201d ASIACRYPT (2), T. Iwata and J.H. Cheon, eds., volume 9453 of Lecture Notes in Computer Science, pp.411-436, Springer, 2015. 10.1007\/978-3-662-48800-3_17","DOI":"10.1007\/978-3-662-48800-3_17"},{"key":"5","doi-asserted-by":"crossref","unstructured":"[5] S. Banik, A. Bogdanov, and F. Regazzoni, \u201cExploring energy efficiency of lightweight block ciphers,\u201d SAC, O. Dunkelman and L. Keliher, eds., volume 9566 of Lecture Notes in Computer Science, pp.178-194, Springer, 2015. 10.1007\/978-3-319-31301-6_10","DOI":"10.1007\/978-3-319-31301-6_10"},{"key":"6","doi-asserted-by":"crossref","unstructured":"[6] J. Borghoff, A. Canteaut, T. G\u00fcneysu, E.B. Kavun, M. Knezevic, L.R. Knudsen, G. Leander, V. Nikov, C. Paar, C. Rechberger, P. Rombouts, S.S. Thomsen, and T. Yal\u00e7in, PRINCE \u2014 A low-latency block cipher for pervasive computing applications \u2014 Extended abstract,\u201d ASIACRYPT, X. Wang and K. Sako, eds., volume 7658 of Lecture Notes in Computer Science, pp.208-225, Springer, 2012. 10.1007\/978-3-642-34961-4_14","DOI":"10.1007\/978-3-642-34961-4_14"},{"key":"7","doi-asserted-by":"crossref","unstructured":"[7] S. Banik, Y. Funabiki, and T. Isobe, \u201cMore results on shortest linear programs,\u201d Advances in Information and Computer Security-14th International Workshop on Security, IWSEC 2019, Tokyo, Japan, Aug. 2019, Proceedings, pp.109-128, 2019. 10.1007\/978-3-030-26834-3_7","DOI":"10.1007\/978-3-030-26834-3_7"},{"key":"8","doi-asserted-by":"crossref","unstructured":"[8] C. Beierle, J. Jean, S. K\u00f6lbl, G. Leander, A. Moradi, T. Peyrin, Y. Sasaki, P. Sasdrich, and S.M. Sim, \u201cThe SKINNY family of block ciphers and its low-latency variant MANTIS,\u201d Advances in Cryptology-CRYPTO 2016-36th Annual International Cryptology Conference, Santa Barbara, CA, USA, Aug. 2016, Proceedings, Part II, pp.123-153, 2016. 10.1007\/978-3-662-53008-5_5","DOI":"10.1007\/978-3-662-53008-5_5"},{"key":"9","doi-asserted-by":"crossref","unstructured":"[9] C. Beierle, T. Kranz, and G. Leander, \u201cLightweight multiplication in <i>GF<\/i>(2<i><sup>n<\/sup><\/i>) with applications to MDS matrices,\u201d Advances in Cryptology-CRYPTO 2016-36th Annual International Cryptology Conference, Santa Barbara, CA, USA, Aug. 2016, Proceedings, Part I, pp.625-653, 2016. 10.1007\/978-3-662-53018-4_23","DOI":"10.1007\/978-3-662-53018-4_23"},{"key":"10","doi-asserted-by":"crossref","unstructured":"[10] J. Boyar, P. Matthews, and R. Peralta, \u201cOn the shortest linear straight-line program for computing linear forms,\u201d Mathematical Foundations of Computer Science 2008, 33rd International Symposium, MFCS 2008, Torun, Poland, Aug. 2008, Proceedings, pp.168-179, 2008. 10.1007\/978-3-540-85238-4_13","DOI":"10.1007\/978-3-540-85238-4_13"},{"key":"11","doi-asserted-by":"publisher","unstructured":"[11] P.S.L.M. Barreto, V. Nikov, S. Nikova, V. Rijmen, and E. Tischhauser, \u201cWhirlwind: A new cryptographic hash function,\u201d Des. Codes Cryptography, vol.56, no.2-3, pp.141-162, 2010. 10.1007\/s10623-010-9391-y","DOI":"10.1007\/s10623-010-9391-y"},{"key":"12","doi-asserted-by":"crossref","unstructured":"[12] J. Boyar and R. Peralta, \u201cA new combinational logic minimization technique with applications to cryptology,\u201d Experimental Algorithms, 9th International Symposium, SEA 2010, Ischia Island, Naples, Italy, May 2010. Proceedings, pp.178-189, 2010. 10.1007\/978-3-642-13193-6_16","DOI":"10.1007\/978-3-642-13193-6_16"},{"key":"13","unstructured":"[13] J. Boyar and R. Peralta, \u201cC++ implementation of slp algorithm,\u201d 2018. Available at http:\/\/www.imada.sdu.dk~joan\/xor\/Improved2.cc"},{"key":"14","unstructured":"[14] P.S.L.M. Barreto and V. Rijmen, \u201cThe anubis block cipher, 2000. Submission to NESSIE project. Available at https:\/\/www.cosic.esat.kuleuven.be\/nessie\/workshop\/submissions\/anubis.zip"},{"key":"15","unstructured":"[15] P.S.L.M. Barreto and V. Rijmen, \u201cThe khazad legacy-level block cipher,\u201d 2000. Submission to NESSIE project. Available at https:\/\/www.cosic.esat.kuleuven.be\/nessie\/workshop\/submissions\/khazad.zip"},{"key":"16","doi-asserted-by":"crossref","unstructured":"[16] P.S.L.M. Barreto and V. Rijmen, \u201cWhirlpool,\u201d Encyclopedia of Cryptography and Security, 2nd ed., pp.1384-1385. 2011. 10.1007\/978-1-4419-5906-5_626","DOI":"10.1007\/978-1-4419-5906-5_626"},{"key":"17","doi-asserted-by":"crossref","unstructured":"[17] C. Cid, S. Murphy, and M.J.B. Robshaw, \u201cSmall scale variants of the AES,\u201d Fast Software Encryption: 12th International Workshop, FSE 2005, Paris, France, Feb. 2005, Revised Selected Papers, pp.145-162, 2005. 10.1007\/b137506","DOI":"10.1007\/11502760_10"},{"key":"18","doi-asserted-by":"crossref","unstructured":"[18] J. Daemen and V. Rijmen, The Design of Rijndael: AES-The Advanced Encryption Standard, Springer Verlag, Berlin, Heidelberg, New York, 2002. 10.1007\/978-3-662-60769-5","DOI":"10.1007\/978-3-662-04722-4_1"},{"key":"19","doi-asserted-by":"crossref","unstructured":"[19] C. Fuhs and P. Schneider-Kamp, \u201cSynthesizing shortest linear straight-line programs over GF(2) using SAT,\u201d Theory and Applications of Satisfiability Testing-SAT 2010, 13th International Conference, SAT 2010, Edinburgh, UK, July 2010. Proceedings, pp.71-84, 2010. 10.1007\/978-3-642-14186-7_8","DOI":"10.1007\/978-3-642-14186-7_8"},{"key":"20","unstructured":"[20] P. Gauravaram, L.R. Knudsen, K. Matusiewicz, F. Mendel, C. Rechberger, M. Schl\u00e4ffer, and S.S. Thomsen, \u201cGr\u00f8stl-a SHA-3 candidate,\u201d Symmetric Cryptography, 11.01.-16.01.2009, 2009."},{"key":"21","doi-asserted-by":"crossref","unstructured":"[21] J. Guo, T. Peyrin, and A. Poschmann, \u201cThe PHOTON family of lightweight hash functions,\u201d Advances in Cryptology-CRYPTO 2011-31st Annual Cryptology Conference, Santa Barbara, CA, USA, Aug. 2011. Proceedings, pp.222-239, 2011. 10.1007\/978-3-642-22792-9_13","DOI":"10.1007\/978-3-642-22792-9_13"},{"key":"22","doi-asserted-by":"crossref","unstructured":"[22] J. Guo, T. Peyrin, A. Poschmann, and M.J.B. Robshaw, The LED block cipher,\u201d CHES, B. Preneel and T. Takagi, eds., volume 6917 of Lecture Notes in Computer Science, pp.326-341, Springer, 2011. 10.1007\/978-3-642-23951-9_22","DOI":"10.1007\/978-3-642-23951-9_22"},{"key":"23","doi-asserted-by":"publisher","unstructured":"[23] K.C. Gupta, S.K. Pandey, and A. Venkateswarlu, \u201cTowards a general construction of recursive MDS diffusion layers,\u201d Des. Codes Cryptogr., vol.82, no.1-2, pp.179-195, 2017. 10.1007\/s10623-016-0261-0","DOI":"10.1007\/s10623-016-0261-0"},{"key":"24","doi-asserted-by":"publisher","unstructured":"[24] K.C. Gupta and I.G. Ray, \u201cCryptographically significant MDS matrices based on circulant and circulant-like matrices for lightweight applications,\u201d Cryptogr. Commun., vol.7, no.2, pp.257-287, 2015. 10.1007\/s12095-014-0116-3","DOI":"10.1007\/s12095-014-0116-3"},{"key":"25","doi-asserted-by":"crossref","unstructured":"[25] J. Jean, A. Moradi, T. Peyrin, and P. 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Vaudenay, \u201cFOX: A new family of block ciphers,\u201d Selected Areas in Cryptography, 11th International Workshop, SAC 2004, Waterloo, Canada, Aug. 2004, Revised Selected Papers, pp.114-129, 2004. 10.1007\/978-3-540-30564-4_8","DOI":"10.1007\/978-3-540-30564-4_8"},{"key":"29","doi-asserted-by":"crossref","unstructured":"[29] D. Kwon, J. Kim, S. Park, S.H. Sung, Y. Sohn, J.H. Song, Y. Yeom, E.-J. Yoon, S. Lee, J. Lee, S. Chee, D. Han, and J. Hong, \u201cNew block cipher: ARIA,\u201d Information Security and Cryptology-ICISC 2003, 6th International Conference, Seoul, Korea, Nov. 2003, Revised Papers, pp.432-445, 2003. 10.1007\/978-3-540-24691-6_32","DOI":"10.1007\/978-3-540-24691-6_32"},{"key":"30","unstructured":"[30] T. Kranz, G. Leander, K. Stoffelen, and F. Wiemer, Github repository: Shorter linear SLPS for MDS matrices, 2018. Available at https:\/\/github.com\/rub-hgi\/shorter_linear_slps_for_mds_matrices"},{"key":"31","doi-asserted-by":"publisher","unstructured":"[31] T. Kranz, G. Leander, K. Stoffelen, and F. Wiemer, \u201cShorter linear straight-line programs for MDS matrices,\u201d IACR Trans. Symmetric Cryptol., vol.2018, no.4, pp.188-211, 2018. 10.46586\/tosc.v2017.i4.188-211","DOI":"10.46586\/tosc.v2017.i4.188-211"},{"key":"32","doi-asserted-by":"crossref","unstructured":"[32] M. Liu and S.M. Sim, \u201cLightweight MDS generalized circulant matrices,\u201d Fast Software Encryption-23rd International Conference, FSE 2016, Bochum, Germany, March 2016, Revised Selected Papers, pp.101-120, 2016. 10.1007\/978-3-662-52993-5_6","DOI":"10.1007\/978-3-662-52993-5_6"},{"key":"33","doi-asserted-by":"publisher","unstructured":"[33] S. Li, S. Sun, C. Li, Z. Wei, and L. Hu, \u201cConstructing low-latency involutory MDS matrices with lightweight circuits, IACR Trans. Symmetric Cryptol., vol.2019, no.1, pp.84-117, 2019. 10.46586\/tosc.v2019.i1.84-117","DOI":"10.46586\/tosc.v2019.i1.84-117"},{"key":"34","doi-asserted-by":"crossref","unstructured":"[34] Y. Li and M. Wang, \u201cOn the construction of lightweight circulant involutory MDS matrices,\u201d Fast Software Encryption-23rd International Conference, FSE 2016, Bochum, Germany, March 2016, Revised Selected Papers, pp.121-139, 2016. 10.1007\/978-3-662-52993-5_7","DOI":"10.1007\/978-3-662-52993-5_7"},{"key":"35","unstructured":"[35] C. Paar, \u201cOptimized arithmetic for reed-solomon encoders,\u201d Proc. IEEE International Symposium on Information Theory, p.250, June 1997. 10.1109\/isit.1997.613165"},{"key":"36","doi-asserted-by":"crossref","unstructured":"[36] S.M. Sim, K. Khoo, F.E. Oggier, and T. Peyrin, \u201cLightweight MDS involution matrices,\u201d Fast Software Encryption-22nd International Workshop, FSE 2015, Istanbul, Turkey, March 2015, Revised Selected Papers, pp.471-493, 2015. 10.1007\/978-3-662-48116-5_23","DOI":"10.1007\/978-3-662-48116-5_23"},{"key":"37","unstructured":"[37] B. Schneier, J. Kelsey, D. Whiting, D. Wagner, C. Hall, and N. Ferguson, \u201cTwofish: A 128-bit block cipher,\u201d 1998. Available at https:\/\/www.schneier.com\/academic\/paperfiles\/paper-twofish-paper.pdf"},{"key":"38","doi-asserted-by":"publisher","unstructured":"[38] S. Sarkar and H. Syed, \u201cLightweight diffusion layer: Importance of toeplitz matrices,\u201d IACR Trans. Symmetric Cryptol., vol.2016, no.1, pp.95-113, 2016. 10.46586\/tosc.v2016.i1.95-113","DOI":"10.46586\/tosc.v2016.i1.95-113"},{"key":"39","unstructured":"[39] S. Sarkar and H. Syed, \u201cAnalysis of toeplitz MDS matrices,\u201d Information Security and Privacy-22nd Australasian Conference, ACISP 2017, Auckland, New Zealand, July 2017, Proceedings, Part II, pp.3-18, 2017. 10.1007\/978-3-319-59870-3_1"},{"key":"40","doi-asserted-by":"publisher","unstructured":"[40] T. Shirai, K. Shibutani, T. Akishita, S. Moriai, and T. Iwata, The 128-Bit blockcipher CLEFIA (Extended abstract),\u201d FSE, A. Biryukov, ed., volume 4593 of Lecture Notes in Computer Science, pp.181-195, Springer, 2007. 10.1007\/978-3-540-74619-5_12","DOI":"10.1007\/978-3-540-74619-5_12"},{"key":"41","doi-asserted-by":"crossref","unstructured":"[41] K. 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