{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T12:26:40Z","timestamp":1773232000149,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":20,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642316616","type":"print"},{"value":"9783642316623","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2012]]},"DOI":"10.1007\/978-3-642-31662-3_12","type":"book-chapter","created":{"date-parts":[[2012,7,2]],"date-time":"2012-07-02T10:10:20Z","timestamp":1341223820000},"page":"168-186","source":"Crossref","is-referenced-by-count":9,"title":["Finding Optimal Formulae for Bilinear Maps"],"prefix":"10.1007","author":[{"given":"Razvan","family":"Barbulescu","sequence":"first","affiliation":[]},{"given":"J\u00e9r\u00e9mie","family":"Detrey","sequence":"additional","affiliation":[]},{"given":"Nicolas","family":"Estibals","sequence":"additional","affiliation":[]},{"given":"Paul","family":"Zimmermann","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"12_CR1","unstructured":"Albrecht, M.R.: The M4RIE library for dense linear algebra over small fields with even characteristic (2011) (preprint), \n                    \n                      http:\/\/arxiv.org\/abs\/1111.6900"},{"key":"12_CR2","unstructured":"Artin, M.: Algebra. Prentice-Hall, Inc. (1991)"},{"key":"12_CR3","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/S0885-064X(02)00007-9","volume":"19","author":"M. Bl\u00e4ser","year":"2003","unstructured":"Bl\u00e4ser, M.: On the complexity of the multiplication of matrices of small formats. Journal of Complexity\u00a019, 43\u201360 (2003)","journal-title":"Journal of Complexity"},{"key":"12_CR4","doi-asserted-by":"crossref","unstructured":"B\u00fcrgisser, P., Clausen, M., Shokrollahi, M.: Algebraic complexity theory, vol. 315. Springer (1997)","DOI":"10.1007\/978-3-662-03338-8"},{"issue":"4","key":"12_CR5","doi-asserted-by":"publisher","first-page":"572","DOI":"10.1109\/TC.2008.207","volume":"58","author":"M. Cenk","year":"2009","unstructured":"Cenk, M., \u00d6zbudak, F.: Improved polynomial multiplication formulas over \n                    \n                      \n                    \n                    ${\\mathbb F}_2$\n                   using Chinese remainder theorem. IEEE Trans. Comput.\u00a058(4), 572\u2013576 (2009)","journal-title":"IEEE Trans. Comput."},{"key":"12_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"406","DOI":"10.1007\/978-3-540-68164-9_27","volume-title":"Progress in Cryptology \u2013 AFRICACRYPT 2008","author":"M. Cenk","year":"2008","unstructured":"Cenk, M., \u00d6zbudak, F.: Efficient Multiplication in \n                    \n                      \n                    \n                    ${\\mathbb F}_{3^{\\ell m}}$\n                  , m\u2009\u2265\u20091 and 5\u2009\u2264\u2009\u2113\u2009\u2264\u200918. In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol.\u00a05023, pp. 406\u2013414. Springer, Heidelberg (2008)"},{"key":"12_CR7","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1016\/j.jco.2009.11.002","volume":"26","author":"M. Cenk","year":"2010","unstructured":"Cenk, M., \u00d6zbudak, F.: On multiplication in finite fields. J. Complexity\u00a026, 172\u2013186 (2010)","journal-title":"J. Complexity"},{"key":"12_CR8","doi-asserted-by":"publisher","first-page":"3451","DOI":"10.1016\/j.tcs.2011.02.031","volume":"412","author":"M. Cenk","year":"2011","unstructured":"Cenk, M., \u00d6zbudak, F.: Multiplication of polynomials modulo x\n                  \n                    n\n                  . Theoret. Comput. Sci.\u00a0412, 3451\u20133462 (2011)","journal-title":"Theoret. Comput. Sci."},{"key":"12_CR9","doi-asserted-by":"crossref","unstructured":"Chung, J., Hasan, M.A.: Asymmetric squaring formulae. In: Kornerup, P., Muller, J.M. (eds.) Proc. ARITH 18, pp. 113\u2013122 (2007)","DOI":"10.1109\/ARITH.2007.11"},{"issue":"3","key":"12_CR10","doi-asserted-by":"publisher","first-page":"1254","DOI":"10.1137\/060661569","volume":"30","author":"P. Comon","year":"2008","unstructured":"Comon, P., Golub, G., Lim, L., Mourrain, B.: Symmetric tensors and symmetric tensor rank. SIAM J. Matrix Anal. & Appl.\u00a030(3), 1254\u20131279 (2008)","journal-title":"SIAM J. Matrix Anal. & Appl."},{"key":"12_CR11","unstructured":"Courtois, N.T., Bard, G.V., Hulme, D.: A new general-purpose method to multiply 3 \u00d73 matrices using only 23 multiplications (2011) (preprint), \n                    \n                      http:\/\/arxiv.org\/abs\/1108.2830"},{"issue":"5","key":"12_CR12","doi-asserted-by":"publisher","first-page":"716","DOI":"10.1109\/TC.2007.1024","volume":"56","author":"H. Fan","year":"2007","unstructured":"Fan, H., Hasan, A.: Comments on five, six, and seven-term Karatsuba-like formulae. IEEE Trans. Comput.\u00a056(5), 716\u2013717 (2007)","journal-title":"IEEE Trans. Comput."},{"issue":"6","key":"12_CR13","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1007\/s00200-003-0144-2","volume":"14","author":"G. Hanrot","year":"2004","unstructured":"Hanrot, G., Quercia, M., Zimmermann, P.: The middle product algorithm, I. Speeding up the division and square root of power series. Appl. Algebra Engrg. Comm. Comput.\u00a014(6), 415\u2013438 (2004)","journal-title":"Appl. Algebra Engrg. Comm. Comput."},{"issue":"4","key":"12_CR14","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1016\/0196-6774(90)90014-6","volume":"11","author":"J. Hastad","year":"1990","unstructured":"Hastad, J.: Tensor rank is NP-complete. J. Algorithms\u00a011(4), 644\u2013654 (1990)","journal-title":"J. Algorithms"},{"issue":"2","key":"12_CR15","first-page":"293","volume":"145","author":"A.A. Karatsuba","year":"1962","unstructured":"Karatsuba, A.A., Ofman, Y.: Multiplication of multi-digit numbers on automata. Doklady Akad. Nauk SSSR\u00a0145(2), 293\u2013294 (1962) (in Russian); translation in Soviet Physics-Doklady 7, 595\u2013596 (1963)","journal-title":"Doklady Akad. Nauk SSSR"},{"issue":"3","key":"12_CR16","doi-asserted-by":"publisher","first-page":"362","DOI":"10.1109\/TC.2005.49","volume":"54","author":"P. Montgomery","year":"2005","unstructured":"Montgomery, P.: Five, six, and seven-term Karatsuba-like formulae. IEEE Trans. Comput.\u00a054(3), 362\u2013369 (2005)","journal-title":"IEEE Trans. Comput."},{"issue":"1","key":"12_CR17","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/s002000000037","volume":"11","author":"T. Mulders","year":"2000","unstructured":"Mulders, T.: On short multiplications and divisions. Appl. Algebra Engrg. Comm. Comput.\u00a011(1), 69\u201388 (2000)","journal-title":"Appl. Algebra Engrg. Comm. Comput."},{"key":"12_CR18","doi-asserted-by":"publisher","first-page":"2052","DOI":"10.1016\/j.laa.2008.06.004","volume":"429","author":"I. Oseledets","year":"2008","unstructured":"Oseledets, I.: Optimal Karatsuba-like formulae for certain bilinear forms in GF(2). Linear Algebra and its Applications\u00a0429, 2052\u20132066 (2008)","journal-title":"Linear Algebra and its Applications"},{"issue":"4","key":"12_CR19","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1007\/BF02165411","volume":"13","author":"V. Strassen","year":"1969","unstructured":"Strassen, V.: Gaussian elimination is not optimal. Numerische Mathematik\u00a013(4), 354\u2013356 (1969)","journal-title":"Numerische Mathematik"},{"key":"12_CR20","first-page":"714","volume":"3","author":"A. Toom","year":"1963","unstructured":"Toom, A.: The complexity of a scheme of functional elements realizing the multiplication of integers. Soviet Mathematics Doklady\u00a03, 714\u2013716 (1963)","journal-title":"Soviet Mathematics Doklady"}],"container-title":["Lecture Notes in Computer Science","Arithmetic of Finite Fields"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-31662-3_12.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,4]],"date-time":"2021-05-04T11:42:57Z","timestamp":1620128577000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-31662-3_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"ISBN":["9783642316616","9783642316623"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-31662-3_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012]]}}}