{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,8]],"date-time":"2024-09-08T12:31:05Z","timestamp":1725798665152},"publisher-location":"Berlin, Heidelberg","reference-count":23,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783662444641"},{"type":"electronic","value":"9783662444658"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-3-662-44465-8_12","type":"book-chapter","created":{"date-parts":[[2014,8,12]],"date-time":"2014-08-12T06:33:02Z","timestamp":1407825182000},"page":"130-140","source":"Crossref","is-referenced-by-count":2,"title":["The Relationship between Multiplicative Complexity and Nonlinearity"],"prefix":"10.1007","author":[{"given":"Joan","family":"Boyar","sequence":"first","affiliation":[]},{"given":"Magnus Gausdal","family":"Find","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"12_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/978-3-642-38233-8_6","volume-title":"Algorithms and Complexity","author":"J. Boyar","year":"2013","unstructured":"Boyar, J., Find, M., Peralta, R.: Four measures of nonlinearity. In: Spirakis, P.G., Serna, M. (eds.) CIAC 2013. LNCS, vol.\u00a07878, pp. 61\u201372. Springer, Heidelberg (2013), eprint with correction available at the Cryptology ePrint Archive, Report 2013\/633 (2013), \n                    \n                      http:\/\/eprint.iacr.org\/"},{"issue":"1","key":"12_CR2","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1016\/S0304-3975(99)00182-6","volume":"235","author":"J. Boyar","year":"2000","unstructured":"Boyar, J., Peralta, R., Pochuev, D.: On the multiplicative complexity of Boolean functions over the basis (\n                    \n                      \n                    \n                    $\\land$\n                  , \u2295, 1). Theor. Comput. Sci.\u00a0235(1), 43\u201357 (2000)","journal-title":"Theor. Comput. Sci."},{"issue":"5","key":"12_CR3","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1109\/TC.1980.1675583","volume":"29","author":"M.R. Brown","year":"1980","unstructured":"Brown, M.R., Dobkin, D.P.: An improved lower bound on polynomial multiplication. IEEE Trans. Computers\u00a029(5), 337\u2013340 (1980)","journal-title":"IEEE Trans. Computers"},{"issue":"3","key":"12_CR4","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1007\/s00037-006-0215-4","volume":"15","author":"N.H. Bshouty","year":"2006","unstructured":"Bshouty, N.H., Kaminski, M.: Polynomial multiplication over finite fields: from quadratic to straight-line complexity. Computational Complexity\u00a015(3), 252\u2013262 (2006)","journal-title":"Computational Complexity"},{"doi-asserted-by":"crossref","unstructured":"B\u00fcrgisser, P., Clausen, M., Shokrollahi, M.A.: Algebraic Complexity Theory. Grundlehren der mathematischen Wissenschaften, vol.\u00a0315. Springer (1997)","key":"12_CR5","DOI":"10.1007\/978-3-662-03338-8"},{"key":"12_CR6","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1017\/CBO9780511780448.011","volume-title":"Boolean Models and Methods in Mathematics, Computer Science, and Engineering","author":"C. Carlet","year":"2010","unstructured":"Carlet, C.: Boolean functions for cryptography and error correcting codes. In: Crama, Y., Hammer, P.L. (eds.) Boolean Models and Methods in Mathematics, Computer Science, and Engineering, ch. 8, pp. 257\u2013397. Cambridge University Press, Cambridge (2010)"},{"key":"12_CR7","doi-asserted-by":"publisher","first-page":"398","DOI":"10.1017\/CBO9780511780448.012","volume-title":"Boolean Models and Methods in Mathematics, Computer Science, and Engineering","author":"C. Carlet","year":"2010","unstructured":"Carlet, C.: Vectorial Boolean functions for cryptography. In: Crama, Y., Hammer, P.L. (eds.) Boolean Models and Methods in Mathematics, Computer Science, and Engineering, ch. 9, pp. 398\u2013469. Cambridge Univ. Press, Cambridge (2010)"},{"key":"12_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1007\/BFb0053450","volume-title":"Advances in Cryptology - EUROCRYPT \u201994","author":"F. Chabaud","year":"1995","unstructured":"Chabaud, F., Vaudenay, S.: Links between differential and linear cryptanalysis. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol.\u00a0950, pp. 356\u2013365. Springer, Heidelberg (1995)"},{"doi-asserted-by":"crossref","unstructured":"Daemen, J., Rijmen, V.: The Design of Rijndael: AES-The Advanced Encryption Standard. Security and Cryptology. Springer (2002)","key":"12_CR9","DOI":"10.1007\/978-3-662-04722-4"},{"doi-asserted-by":"crossref","unstructured":"Jukna, S.: Extremal Combinatorics: with Applications in Computer Science, 2nd edn. Texts in Theoretical Computer Science. Springer (2011)","key":"12_CR10","DOI":"10.1007\/978-3-642-17364-6"},{"key":"12_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-24508-4","volume-title":"Boolean Function Complexity: Advances and Frontiers","author":"S. Jukna","year":"2012","unstructured":"Jukna, S.: Boolean Function Complexity: Advances and Frontiers. Springer, Heidelberg (2012)"},{"issue":"1","key":"12_CR12","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1145\/58562.59306","volume":"36","author":"M. Kaminski","year":"1989","unstructured":"Kaminski, M., Bshouty, N.H.: Multiplicative complexity of polynomial multiplication over finite fields. J. ACM\u00a036(1), 150\u2013170 (1989)","journal-title":"J. ACM"},{"key":"12_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"486","DOI":"10.1007\/978-3-540-70583-3_40","volume-title":"Automata, Languages and Programming","author":"V. Kolesnikov","year":"2008","unstructured":"Kolesnikov, V., Schneider, T.: Improved garbled circuit: Free XOR gates and applications. In: Aceto, L., Damg\u00e5rd, I., Goldberg, L.A., Halld\u00f3rsson, M.M., Ing\u00f3lfsd\u00f3ttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol.\u00a05126, pp. 486\u2013498. Springer, Heidelberg (2008)"},{"doi-asserted-by":"crossref","unstructured":"Komargodski, I., Raz, R., Tal, A.: Improved average-case lower bounds for demorgan formula size. In: FOCS, pp. 588\u2013597 (2013)","key":"12_CR14","DOI":"10.1109\/FOCS.2013.69"},{"key":"12_CR15","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1016\/0304-3975(83)90108-1","volume":"22","author":"A. Lempel","year":"1983","unstructured":"Lempel, A., Seroussi, G., Winograd, S.: On the complexity of multiplication in finite fields. Theor. Comput. Sci.\u00a022, 285\u2013296 (1983)","journal-title":"Theor. Comput. Sci."},{"issue":"2","key":"12_CR16","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1109\/TIT.1977.1055688","volume":"23","author":"R.J. McEliece","year":"1977","unstructured":"McEliece, R.J., Rodemich, E.R., Rumsey Jr., H., Welch, L.R.: New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities. IEEE Trans. Inform. Theory\u00a023(2), 157\u2013166 (1977)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"2","key":"12_CR17","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1016\/0304-3975(92)90235-8","volume":"102","author":"R. Mirwald","year":"1992","unstructured":"Mirwald, R., Schnorr, C.P.: The multiplicative complexity of quadratic Boolean forms. Theor. Comput. Sci.\u00a0102(2), 307\u2013328 (1992)","journal-title":"Theor. Comput. Sci."},{"key":"12_CR18","first-page":"123","volume":"8","author":"E.I. Nechiporuk","year":"1962","unstructured":"Nechiporuk, E.I.: On the complexity of schemes in some bases containing nontrivial elements with zero weights. Problemy Kibernetiki\u00a08, 123\u2013160 (1962) (in Russian)","journal-title":"Problemy Kibernetiki"},{"key":"12_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/3-540-51083-4_47","volume-title":"Applied Algebra, Algebraic Algorithms and Error-Correcting Codes","author":"C.P. Schnorr","year":"1989","unstructured":"Schnorr, C.P.: The multiplicative complexity of Boolean functions. In: Mora, T. (ed.) AAECC 1988. LNCS, vol.\u00a0357, pp. 45\u201358. Springer, Heidelberg (1989)"},{"unstructured":"Sloane, N., MacWilliams, F.: The Theory of Error Correcting Codes. North-Holland Math. Library 16 (1977)","key":"12_CR20"},{"issue":"3","key":"12_CR21","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1007\/BF01436566","volume":"20","author":"V. Strassen","year":"1973","unstructured":"Strassen, V.: Die berechnungskomplexit\u00e4t von elementarsymmetrischen funktionen und von interpolationskoeffizienten. Numerische Mathematik\u00a020(3), 238\u2013251 (1973)","journal-title":"Numerische Mathematik"},{"key":"12_CR22","first-page":"184","volume":"264","author":"V. Strassen","year":"1973","unstructured":"Strassen, V.: Vermeidung von Divisionen. Journal f\u00fcr die reine und angewandte Mathematik\u00a0264, 184\u2013202 (1973)","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"},{"doi-asserted-by":"crossref","unstructured":"Vaikuntanathan, V.: Computing blindfolded: New developments in fully homomorphic encryption. In: Ostrovsky, R. (ed.) FOCS, pp. 5\u201316. IEEE (2011)","key":"12_CR23","DOI":"10.1109\/FOCS.2011.98"}],"container-title":["Lecture Notes in Computer Science","Mathematical Foundations of Computer Science 2014"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-44465-8_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,27]],"date-time":"2019-05-27T11:06:37Z","timestamp":1558955197000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-44465-8_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783662444641","9783662444658"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-44465-8_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2014]]}}}