{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T04:37:51Z","timestamp":1780634271561,"version":"3.54.1"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2011,9,25]],"date-time":"2011-09-25T00:00:00Z","timestamp":1316908800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Cryptogr Eng"],"published-print":{"date-parts":[[2011,11]]},"DOI":"10.1007\/s13389-011-0017-8","type":"journal-article","created":{"date-parts":[[2011,9,24]],"date-time":"2011-09-24T11:25:44Z","timestamp":1316863544000},"page":"187-199","source":"Crossref","is-referenced-by-count":32,"title":["Speeding scalar multiplication over binary elliptic curves using the new carry-less multiplication instruction"],"prefix":"10.1007","volume":"1","author":[{"given":"Jonathan","family":"Taverne","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Armando","family":"Faz-Hern\u00e1ndez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Diego F.","family":"Aranha","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francisco","family":"Rodr\u00edguez-Henr\u00edquez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Darrel","family":"Hankerson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Julio","family":"L\u00f3pez","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2011,9,25]]},"reference":[{"issue":"3","key":"17_CR1","first-page":"481","volume":"14","author":"O. Ahmadi","year":"2008","unstructured":"Ahmadi O., Hankerson D., Rodr\u00edguez-Henr\u00edquez F.: Parallel formulations of scalar multiplication on Koblitz curves. J. UCS 14(3), 481\u2013504 (2008)","journal-title":"J. UCS"},{"key":"17_CR2","doi-asserted-by":"crossref","unstructured":"Aranha, D.F., L\u00f3pez, J., Hankerson, D.: Efficient software implementation of binary field arithmetic using vector instruction sets. In: Abdalla, M., Barreto, P.S.L.M. (eds.) The First International Conference on Cryptology and Information Security (LATINCRYPT 2010). Lecture Notes in Computer Science, vol. 6212, pp. 144\u2013161 (2010)","DOI":"10.1007\/978-3-642-14712-8_9"},{"key":"17_CR3","doi-asserted-by":"crossref","unstructured":"Avanzi, R.M.: Another look at square roots (and other less common operations) in fields of even characteristic. In: Adams, C.M., Miri, A., Wiener, M.J. (eds.) 14th International Workshop on Selected Areas in Cryptography (SAC 2007). Lecture Notes in Computer Science, vol. 4876, pp. 138\u2013154. Springer (2007)","DOI":"10.1007\/978-3-540-77360-3_10"},{"key":"17_CR4","doi-asserted-by":"crossref","unstructured":"Bellare, M. (ed.): Advances in Cryptology\u2014CRYPTO 2000. Lecture Notes in Computer Science, vol. 1880. Springer (2000)","DOI":"10.1007\/3-540-44598-6"},{"key":"17_CR5","doi-asserted-by":"crossref","unstructured":"Bernstein, D., Lange, T.: Analysis and optimization of elliptic-curve single-scalar multiplication. In: Proceedings 8th International Conference on Finite Fields and Applications (Fq8), vol. 461, pp. 1\u201320. AMS (2008)","DOI":"10.1090\/conm\/461\/08979"},{"key":"17_CR6","doi-asserted-by":"crossref","unstructured":"Bernstein, D.J.: Batch Binary Edwards. In: Halevi, S. (ed.) Advances in Cryptology\u2014CRYPTO 2009. Lecture Notes in Computer Science, vol. 5677, pp. 317\u2013336. Springer (2009)","DOI":"10.1007\/978-3-642-03356-8_19"},{"key":"17_CR7","unstructured":"Bernstein, D.J., Lange, T. (eds.) eBACS: ECRYPT Benchmarking of Cryptographic Systems. http:\/\/bench.cr.yp.to . Accessed 25 Aug 2011"},{"key":"17_CR8","doi-asserted-by":"crossref","unstructured":"Beuchat, J.-L., D\u00edaz, J., Mitsunari, S., Okamoto, E., Rodr\u00edguez-Henr\u00edquez, F., Teruya, T.: High-speed software implementation of the optimal ate pairing over Barreto-Naehrig curves. In: Joye, M., Miyaji, A., Otsuka, A. (eds.) Pairing-Based Cryptography\u2014Pairing 2010. Lecture Notes in Computer Science, vol. 6487, pp. 21\u201339 (2010)","DOI":"10.1007\/978-3-642-17455-1_2"},{"issue":"5","key":"17_CR9","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1016\/j.ipl.2005.05.013","volume":"95","author":"I.F. Blake","year":"2005","unstructured":"Blake I.F., Murty V.K., Xu G.: A note on window \u03c4-NAF algorithm. Inf. Process. Lett. 95(5), 496\u2013502 (2005)","journal-title":"Inf. Process. Lett."},{"key":"17_CR10","doi-asserted-by":"crossref","unstructured":"Bodrato, M.: Towards optimal Toom-Cook multiplication for univariate and multivariate polynomials in characteristic 2 and 0. In: Carlet, C., Sunar, B. (eds.) Arithmetic of Finite Fields (WAIFI 2007). Lecture Notes in Computer Science, vol. 4547, pp. 116\u2013133. Springer (2007)","DOI":"10.1007\/978-3-540-73074-3_10"},{"key":"17_CR11","doi-asserted-by":"crossref","unstructured":"Bos, J.W., Kleinjung, T., Niederhagen, R., Schwabe, P.: ECC2K-130 on Cell CPUs. In: Bernstein, D.J., Lange, T. (eds.) 3rd International Conference on Cryptology in Africa (AFRICACRYPT 2010). Lecture Notes in Computer Science, vol. 6055, pp. 225\u2013242. Springer (2010)","DOI":"10.1007\/978-3-642-12678-9_14"},{"issue":"4","key":"17_CR12","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1147\/sj.294.0526","volume":"29","author":"P.G. Comba","year":"1990","unstructured":"Comba P.G.: Exponentiation cryptosystems on the IBM PC. IBM Syst. J. 29(4), 526\u2013538 (1990)","journal-title":"IBM Syst. J."},{"key":"17_CR13","doi-asserted-by":"crossref","unstructured":"Dahmen, E., Okeya, K., Schepers, D.: Affine precomputation with sole inversion in elliptic curve cryptography. In: Pieprzyk, J., Ghodosi, H., Dawson, E. (eds.) Information Security and Privacy (ACISP 2007). Lecture Notes in Computer Science, vol. 4586, pp. 245\u2013258. Springer (2007)","DOI":"10.1007\/978-3-540-73458-1_19"},{"key":"17_CR14","unstructured":"Firasta, N., Buxton, M., Jinbo, P., Nasri, K., Kuo, S.: Intel AVX: new frontiers in performance improvement and energy efficiency. White paper. http:\/\/software.intel.com\/"},{"key":"17_CR15","unstructured":"Fog, A.: Instruction tables: list of instruction latencies, throughputs and micro-operation breakdowns for Intel, AMD and VIA CPUs. http:\/\/www.agner.org\/optimize\/instruction_tables.pdf . Accessed 01 Mar 2011"},{"issue":"8","key":"17_CR16","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.1109\/TC.2004.43","volume":"53","author":"K. Fong","year":"2004","unstructured":"Fong K., Hankerson D., L\u00f3pez J., Menezes A.: Field inversion and point halving revisited. IEEE Trans. Comput. 53(8), 1047\u20131059 (2004)","journal-title":"IEEE Trans. Comput."},{"key":"17_CR17","unstructured":"Grabher, P., Gro\u00dfsch\u00e4dl, J., Page, D.: On software parallel implementation of cryptographic pairings. Cryptology ePrint Archive, Report 2008\/205. http:\/\/eprint.iacr.org\/ (2008)"},{"issue":"2","key":"17_CR18","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1023\/A:1013860532636","volume":"25","author":"J. Guajardo","year":"2002","unstructured":"Guajardo J., Paar C.: Itoh-Tsujii inversion in standard basis and its application in cryptography and codes. Des. Codes Cryptogr. 25(2), 207\u2013216 (2002)","journal-title":"Des. Codes Cryptogr."},{"key":"17_CR19","unstructured":"Gueron, S.: Intel Advanced Encryption Standard (AES) Instructions Set. White paper. http:\/\/software.intel.com\/"},{"key":"17_CR20","unstructured":"Gueron, S., Kounavis, M.E.: Carry-less multiplication and its usage for computing the GCM mode. White paper. http:\/\/software.intel.com\/"},{"key":"17_CR21","volume-title":"Guide to Elliptic Curve Cryptography","author":"D. Hankerson","year":"2004","unstructured":"Hankerson D., Menezes A.J., Vanstone S.: Guide to Elliptic Curve Cryptography. Springer, Secaucus (2004)"},{"key":"17_CR22","unstructured":"Hu, Z., Longa P., Xu, M.: Implementing 4-dimensional GLV method on GLS elliptic curves with j-invariant 0. Des. Codes Cryptogr. (to appear)"},{"key":"17_CR23","unstructured":"Intel.: Intel SSE4 Programming Reference. Technical Report. http:\/\/software.intel.com\/"},{"issue":"3","key":"17_CR24","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/0890-5401(88)90024-7","volume":"78","author":"T. Itoh","year":"1988","unstructured":"Itoh T., Tsujii S.: A fast algorithm for computing multiplicative inverses in GF (2 m ) using normal bases. Inf. Comput. 78(3), 171\u2013177 (1988)","journal-title":"Inf. Comput."},{"key":"17_CR25","unstructured":"J\u00e4rvinen, K., Optimized FPGA-based elliptic curve cryptography processor for high-speed applications. Integr. VLSI J. (to appear)"},{"issue":"9","key":"17_CR26","doi-asserted-by":"crossref","first-page":"1162","DOI":"10.1109\/TVLSI.2008.2000728","volume":"16","author":"K.U. J\u00e4rvinen","year":"2008","unstructured":"J\u00e4rvinen K.U., Skytt\u00e4 J.: On parallelization of high-speed processors for elliptic curve cryptography. IEEE Trans. VLSI Syst. 16(9), 1162\u20131175 (2008)","journal-title":"IEEE Trans. VLSI Syst."},{"issue":"2","key":"17_CR27","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.micpro.2008.08.002","volume":"33","author":"K.U. J\u00e4rvinen","year":"2009","unstructured":"J\u00e4rvinen K.U., Skytt\u00e4 J.: Fast point multiplication on Koblitz curves: Parallelization method and implementations. Microprocess. Microsyst. Embedded Hardware Des. 33(2), 106\u2013116 (2009)","journal-title":"Microprocess. Microsyst. Embedded Hardware Des."},{"key":"17_CR28","unstructured":"Karatsuba, A., Ofman, Y.: Multiplication of many-digital numbers by automatic computers. Doklady Akad. Nauk SSSR 145, 293\u2013294 (1962). Translation in Physics-Doklady 7, 595\u2013596 (1963)"},{"key":"17_CR29","unstructured":"Kim, K.H., Kim, S.I.: A new method for speeding up arithmetic on elliptic curves over binary fields. Cryptology ePrint Archive, Report 2007\/181. http:\/\/eprint.iacr.org\/ (2007)"},{"key":"17_CR30","doi-asserted-by":"crossref","unstructured":"King, B. Rubin, B.: Improvements to the point halving algorithm. In: Wang, H., Pieprzyk, J., Varadharajan, V. (eds.) 9th Australasian Conference on Information Security and Privacy (ACISP 2004). Lecture Notes in Computer Science, vol. 3108, pp. 262\u2013276. Springer (2004)","DOI":"10.1007\/978-3-540-27800-9_23"},{"key":"17_CR31","doi-asserted-by":"crossref","unstructured":"Knudsen, E.: Elliptic scalar multiplication using point halving. In: Lam, K., Okamoto, E. (eds.) Advances in Cryptology\u2014ASIACRYPT \u201999. Lecture Notes in Computer Science, vol. 1716, pp. 135\u2013149. Springer (1999)","DOI":"10.1007\/978-3-540-48000-6_12"},{"key":"17_CR32","doi-asserted-by":"crossref","unstructured":"Koblitz, N.: CM-curves with good cryptographic properties. In: Feigenbaum, J. (ed.) Advances in Cryptology\u2014CRYPTO \u201991. Lecture Notes in Computer Science, vol. 576, pp. 279\u2013287. Springer (1992)","DOI":"10.1007\/3-540-46766-1_22"},{"key":"17_CR33","unstructured":"Lomont, C.: Introduction to Intel advanced vector extensions. Intel Software Network. http:\/\/software.intel.com\/file\/37205 (2011)"},{"key":"17_CR34","doi-asserted-by":"crossref","unstructured":"Longa, P., Gebotys, C.H.: Efficient techniques for high-speed elliptic curve cryptography. In: Mangard, S., Standaert, F.-X. (eds.) Cryptographic Hardware and Embedded Systems (CHES 2010). Lecture Notes in Computer Science, vol. 6225, pp. 80\u201394. Springer (2010)","DOI":"10.1007\/978-3-642-15031-9_6"},{"key":"17_CR35","doi-asserted-by":"crossref","unstructured":"L\u00f3pez, J., Dahab, R.: Fast multiplication on elliptic curves over GF (2 m )without precomputation. In: Ko\u00e7, \u00c7.K., Paar, C. (eds.) First International Workshop on Cryptographic Hardware and Embedded Systems (CHES 99). Lecture Notes in Computer Science, vol. 1717, pp. 316\u2013327. Springer (1999)","DOI":"10.1007\/3-540-48059-5_27"},{"key":"17_CR36","doi-asserted-by":"crossref","unstructured":"L\u00f3pez, J., Dahab, R.: High-speed software multiplication in GF(2 m ). In: Roy, B.K., Okamoto, E. (eds.) 1st International Conference in Cryptology in India (INDOCRYPT 2000). Lecture Notes in Computer Science, vol. 1977, pp. 203\u2013212. Springer (2000)","DOI":"10.1007\/3-540-44495-5_18"},{"key":"17_CR37","doi-asserted-by":"crossref","unstructured":"Lutz, J., Hasan, M.A.: High performance FPGA based elliptic curve cryptographic co-processor. In: International Conference on Information Technology: Coding and Computing (ITCC\u201904), vol. 2, pp. 486\u2013492. IEEE Computer Society (2004)","DOI":"10.1109\/ITCC.2004.1286701"},{"issue":"3","key":"17_CR38","doi-asserted-by":"crossref","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 Trans. Comput. 54(3), 362\u2013369 (2005)","journal-title":"IEEE Trans. Comput."},{"key":"17_CR39","unstructured":"National Institute of Standards and Technology (NIST).: Recommended Elliptic Curves for Federal Government Use. NIST Special Publication. http:\/\/csrc.nist.gov\/csrc\/fedstandards.html . Accessed July 1999"},{"key":"17_CR40","unstructured":"Schroeppel, R.: Elliptic curves: Twice as fast! Presentation at the CRYPTO 2000 [4] Rump Session (2000)"},{"issue":"2-3","key":"17_CR41","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1023\/A:1008306223194","volume":"19","author":"J.A. Solinas","year":"2000","unstructured":"Solinas J.A.: Efficient arithmetic on Koblitz curves. Des. Codes Cryptogr. 19(2-3), 195\u2013249 (2000)","journal-title":"Des. Codes Cryptogr."},{"key":"17_CR42","doi-asserted-by":"crossref","unstructured":"Taverne, J., Faz-Hern\u00e1ndez, A., Aranha, D.F., Rodr\u00edguez-Henr\u00edquez, F., Hankerson, D., L\u00f3pez, J.: Software implementation of binary elliptic curves: impact of the carry-less multiplier on scalar multiplication. In: International Workshop on Cryptographic Hardware and Embedded Systems (CHES 2011). Lecture Notes in Computer Science, vol. 6917, Springer, New York (2011)","DOI":"10.1007\/978-3-642-23951-9_8"},{"key":"17_CR43","doi-asserted-by":"crossref","unstructured":"Wall, D.W.: Limits of instruction-level parallelism. In: 4th International Conference on Architectural Support for Programming Languages and Operating System (ASPLOS 91), pp. 176\u2013188. ACM, New York (1991)","DOI":"10.1145\/106972.106991"},{"issue":"1","key":"17_CR44","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1145\/216585.216588","volume":"23","author":"W.A. Wulf","year":"1995","unstructured":"Wulf W.A., McKee S.A.: Hitting the memory wall: implications of the obvious. SIGARCH Comput. Architect. News 23(1), 20\u201324 (1995)","journal-title":"SIGARCH Comput. Architect. News"}],"container-title":["Journal of Cryptographic Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13389-011-0017-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s13389-011-0017-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s13389-011-0017-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,7]],"date-time":"2021-12-07T09:54:35Z","timestamp":1638870875000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s13389-011-0017-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,9,25]]},"references-count":44,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2011,11]]}},"alternative-id":["17"],"URL":"https:\/\/doi.org\/10.1007\/s13389-011-0017-8","relation":{},"ISSN":["2190-8508","2190-8516"],"issn-type":[{"value":"2190-8508","type":"print"},{"value":"2190-8516","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,9,25]]}}}