{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T13:00:17Z","timestamp":1772283617466,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":20,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540773597","type":"print"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-77360-3_12","type":"book-chapter","created":{"date-parts":[[2007,12,1]],"date-time":"2007-12-01T03:04:18Z","timestamp":1196478258000},"page":"173-183","source":"Crossref","is-referenced-by-count":18,"title":["Explicit Formulas for Efficient Multiplication in $\\mathbb{F}_{3^{6m}}$"],"prefix":"10.1007","author":[{"given":"Elisa","family":"Gorla","sequence":"first","affiliation":[]},{"given":"Christoph","family":"Puttmann","sequence":"additional","affiliation":[]},{"given":"Jamshid","family":"Shokrollahi","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"12_CR1","volume-title":"Seminumerical Algorithms","author":"D.E. Knuth","year":"1998","unstructured":"Knuth, D.E.: The Art of Computer Programming. In: Seminumerical Algorithms, 3rd edn., vol.\u00a02, Addison-Wesley, Reading\u00a0MA (1998), First edition (1969)","edition":"3"},{"key":"12_CR2","unstructured":"von\u00a0zur Gathen, J., Gerhard, J.: Modern Computer Algebra, 2nd edn. Cambridge University Press, Cambridge (2003), First edition (1999)"},{"key":"12_CR3","unstructured":"Department, U.S.: of Commerce \/ National Institute of Standards and Technology: Digital Signature Standard (DSS), Federal Information Processings Standards Publication 186-2 (January 2000)"},{"key":"12_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1007\/BFb0055748","volume-title":"Advances in Cryptology - CRYPTO \u201998","author":"D.V. Bailey","year":"1998","unstructured":"Bailey, D.V., Paar, C.: Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol.\u00a01462, pp. 472\u2013485. Springer, Heidelberg (1998)"},{"key":"12_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1007\/978-3-540-24654-1_23","volume-title":"Selected Areas in Cryptography","author":"R.M. Avanzi","year":"2004","unstructured":"Avanzi, R.M., Mih\u0103ilescu, P.: Generic Efficient Arithmetic Algorithms for PAFFs (Processor Adequate Finite Fields) and Related Algebraic Structures (Extended Abstract. In: Matsui, M., Zuccherato, R.J. (eds.) SAC 2003. LNCS, vol.\u00a03006, pp. 320\u2013334. Springer, Heidelberg (2004)"},{"key":"12_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/978-3-540-40061-5_7","volume-title":"Advances in Cryptology - ASIACRYPT 2003","author":"I. Duursma","year":"2003","unstructured":"Duursma, I., Lee, H.: Tate-Pairing Implementations for Tripartite Key Agreement. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol.\u00a02894, pp. 111\u2013123. Springer, Heidelberg (2003)"},{"key":"12_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"412","DOI":"10.1007\/11545262_30","volume-title":"Cryptographic Hardware and Embedded Systems \u2013 CHES 2005","author":"T. Kerins","year":"2005","unstructured":"Kerins, T., Marnane, W.P., Popovici, E.M., Barreto, P.S.L.M.: Efficient Hardware for the Tate Pairing Calculation in Characteristic Three. In: Rao, J.R., Sunar, B. (eds.) CHES 2005. LNCS, vol.\u00a03659, pp. 412\u2013426. Springer, Heidelberg (2005)"},{"issue":"7","key":"12_CR8","first-page":"595","volume":"7","author":"A. Karatsuba","year":"1963","unstructured":"Karatsuba, A., Ofman, Y.: Multiplication of Multidigit Numbers on Automata. Soviet Physics\u2013Doklady\u00a07(7), 595\u2013596 (1963) Translated from Doklady Akademii Nauk SSSR 145(2), 293\u2013294 (July 1962)","journal-title":"Soviet Physics\u2013Doklady"},{"key":"12_CR9","unstructured":"Paar, C.: Efficient VLSI Architectures for Bit-Parallel Computation in Galois Fields. PhD thesis, Institute for Experimental Mathematics, University of Essen, Essen, Germany (June 1994)"},{"key":"12_CR10","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1109\/TIT.1977.1055735","volume":"IT-23","author":"A. Lempel","year":"1977","unstructured":"Lempel, A., Winograd, S.: A New Approach to Error-Correcting Codes. IEEE Transactions on Information Theory\u00a0IT-23, 503\u2013508 (1977)","journal-title":"IEEE Transactions on Information Theory"},{"key":"12_CR11","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970364","volume-title":"Arithmetic Complexity of Computations","author":"S. Winograd","year":"1980","unstructured":"Winograd, S.: Arithmetic Complexity of Computations, vol.\u00a033. SIAM, Philadelphia (1980)"},{"key":"12_CR12","series-title":"Grundlehren der mathematischen Wissenschaften","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03338-8","volume-title":"Algebraic Complexity Theory","author":"P. B\u00fcrgisser","year":"1997","unstructured":"B\u00fcrgisser, P., Clausen, M., Shokrollahi, M.A.: Algebraic Complexity Theory. Grundlehren der mathematischen Wissenschaften, vol.\u00a0315. Springer, Heidelberg (1997)"},{"issue":"9","key":"12_CR13","doi-asserted-by":"publisher","first-page":"1167","DOI":"10.1109\/TC.2006.136","volume":"55","author":"J.C. Bajard","year":"2006","unstructured":"Bajard, J.C., Imbert, L., Negre, C.: Arithmetic Operations in Finite Fields of Medium Prime Characteristic Using the Lagrange Representation. IEEE Transactions on Computers\u00a055(9), 1167\u20131177 (2006)","journal-title":"IEEE Transactions on Computers"},{"key":"12_CR14","volume-title":"Fast Algorithms for Digital Signal Processing","author":"R.E. Blahut","year":"1985","unstructured":"Blahut, R.E.: Fast Algorithms for Digital Signal Processing. Addison-Wesley, Reading\u00a0MA (1985)"},{"key":"12_CR15","doi-asserted-by":"publisher","first-page":"297","DOI":"10.2307\/2003354","volume":"19","author":"J.W. Cooley","year":"1965","unstructured":"Cooley, J.W., Tukey, J.W.: An Algorithm for the Machine Computation of the Complex Fourier Series. Mathematics of Computation\u00a019, 297\u2013331 (1965)","journal-title":"Mathematics of Computation"},{"key":"12_CR16","unstructured":"Loan, C.V.: Computational Frameworks for the Fast Fourier Transform. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1992)"},{"key":"12_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/11693383_25","volume-title":"Selected Areas in Cryptography","author":"J. Gathen von zur","year":"2006","unstructured":"von zur Gathen, J., Shokrollahi, J.: Efficient FPGA-based Karatsuba Multipliers for Polynomials over \n                  \n                    \n                  \n                  $\\mathbb{F}_{2}$\n                . In: Preneel, B., Tavares, S. (eds.) SAC 2005. LNCS, vol.\u00a03897, pp. 359\u2013369. Springer, Heidelberg (2006)"},{"issue":"3","key":"12_CR18","doi-asserted-by":"publisher","first-page":"362","DOI":"10.1109\/TC.2005.49","volume":"54","author":"P.L. Montgomery","year":"2005","unstructured":"Montgomery, P.L.: Five, Six, and Seven-Term Karatsuba-Like Formulae. IEEE Transactions on Computers\u00a054(3), 362\u2013369 (2005)","journal-title":"IEEE Transactions on Computers"},{"key":"12_CR19","unstructured":"Shoup, V.: NTL: A library for doing number theory, \n                  \n                    http:\/\/www.shoup.net\/ntl"},{"key":"12_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/978-3-540-40061-5_7","volume-title":"Advances in Cryptology - ASIACRYPT 2003","author":"I. Duursma","year":"2003","unstructured":"Duursma, I., Lee, H.S.: Tate Pairing Implementation for Hyperelliptic Curves \n                  \n                    \n                  \n                  $y\\sp 2=x\\sp p-x+d$\n                . In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol.\u00a02894, pp. 111\u2013123. Springer, Heidelberg (2003)"}],"container-title":["Lecture Notes in Computer Science","Selected Areas in Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-77360-3_12.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T07:09:28Z","timestamp":1619507368000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-77360-3_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540773597"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-77360-3_12","relation":{},"subject":[]}}