{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T08:55:39Z","timestamp":1775638539176,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":32,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642147111","type":"print"},{"value":"9783642147128","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010]]},"DOI":"10.1007\/978-3-642-14712-8_7","type":"book-chapter","created":{"date-parts":[[2010,7,29]],"date-time":"2010-07-29T09:17:50Z","timestamp":1280395070000},"page":"109-123","source":"Crossref","is-referenced-by-count":56,"title":["New Software Speed Records for Cryptographic Pairings"],"prefix":"10.1007","author":[{"given":"Michael","family":"Naehrig","sequence":"first","affiliation":[]},{"given":"Ruben","family":"Niederhagen","sequence":"additional","affiliation":[]},{"given":"Peter","family":"Schwabe","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"7_CR1","unstructured":"The GNU MP bignum library, http:\/\/gmplib.org\/ (accessed March 31, 2010)"},{"key":"7_CR2","unstructured":"MPFQ - a finite field library, http:\/\/mpfq.gforge.inria.fr\/ (accessed March 31, 2010)"},{"key":"7_CR3","unstructured":"Ar\u00e8ne, C., Lange, T., Naehrig, M., Ritzenthaler, C.: Faster pairing computation. Cryptology ePrint Archive, Report 2009\/155, to appear in the Journal of Number Theory (2010), http:\/\/eprint.iacr.org\/2009\/155\/"},{"key":"7_CR4","unstructured":"Barker, E., Barker, W., Burr, W., Polk, W., Smid, M.: Recommendation for key management - part 1: General (revised). Published as NIST Special Publication 800-57 (2007), http:\/\/csrc.nist.gov\/groups\/ST\/toolkit\/documents\/SP800-57Part1_3-8-07.pdf"},{"key":"7_CR5","unstructured":"Barreto, P.S.L.M.: A survey on craptological pairing algorithms. Journal of Craptology\u00a07 (2010), http:\/\/www.anagram.com\/~jcrap\/Volume_7\/Pairings.pdf"},{"issue":"3","key":"7_CR6","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1007\/s10623-006-9033-6","volume":"42","author":"P.S.L.M. Barreto","year":"2007","unstructured":"Barreto, P.S.L.M., Galbraith, S.D., \u00d3\u2019 h\u00c9igeartaigh, C., Scott, M.: Efficient pairing computation on supersingular abelian varieties. Designs, Codes and Cryptography\u00a042(3), 239\u2013271 (2007)","journal-title":"Designs, Codes and Cryptography"},{"key":"7_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1007\/3-540-45708-9_23","volume-title":"Advances in Cryptology - CRYPTO 2002","author":"P.S.L.M. Barreto","year":"2002","unstructured":"Barreto, P.S.L.M., Kim, H.Y., Lynn, B., Scott, M.: Efficient algorithms for pairing-based cryptosystems. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol.\u00a02442, pp. 354\u2013368. Springer, Heidelberg (2002)"},{"issue":"4","key":"7_CR8","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/s00145-004-0311-z","volume":"17","author":"P.S.L.M. Barreto","year":"2004","unstructured":"Barreto, P.S.L.M., Lynn, B., Scott, M.: Efficient implementation of pairing-based cryptosystems. Journal of Cryptology\u00a017(4), 321\u2013334 (2004)","journal-title":"Journal of Cryptology"},{"key":"7_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1007\/11693383_22","volume-title":"Selected Areas in Cryptography","author":"P.S.L.M. Barreto","year":"2006","unstructured":"Barreto, P.S.L.M., Naehrig, M.: Pairing-friendly elliptic curves of prime order. In: Preneel, B., Tavares, S. (eds.) SAC 2005. LNCS, vol.\u00a03897, pp. 319\u2013331. Springer, Heidelberg (2006)"},{"key":"7_CR10","unstructured":"Bernstein, D.J.: qhasm: tools to help write high-speed software, http:\/\/cr.yp.to\/qhasm.html (accessed March 31, 2010)"},{"key":"7_CR11","unstructured":"Bernstein, D.J.: Floating-point arithmetic and message authentication, Document ID: dabadd3095644704c5cbe9690ea3738e (2004), http:\/\/cr.yp.to\/papers.html#hash127"},{"key":"7_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/11745853_14","volume-title":"Public Key Cryptography - PKC 2006","author":"D.J. Bernstein","year":"2006","unstructured":"Bernstein, D.J.: Curve25519: new Diffie-Hellman speed records. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T.G. (eds.) PKC 2006. LNCS, vol.\u00a03958, pp. 207\u2013228. Springer, Heidelberg (2006) Document ID: 4230efdfa673480fc079449d90f322c0, http:\/\/cr.yp.to\/papers.html#curve25519"},{"key":"7_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1007\/978-3-540-24676-3_30","volume-title":"Advances in Cryptology - EUROCRYPT 2004","author":"D. Boneh","year":"2004","unstructured":"Boneh, D., Di Crescenzo, G., Ostrovsky, R., Persiano, G.: Public key encryption with keyword search. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol.\u00a03027, pp. 506\u2013522. Springer, Heidelberg (2004)"},{"key":"7_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/978-3-540-73489-5_10","volume-title":"Pairing-Based Cryptography \u2013 Pairing 2007","author":"A.J. Devegili","year":"2007","unstructured":"Devegili, A.J., Scott, M., Dahab, R.: Implementing cryptographic pairings over Barreto-Naehrig curves. In: Takagi, T., Okamoto, T., Okamoto, E., Okamoto, T. (eds.) Pairing 2007. LNCS, vol.\u00a04575, pp. 197\u2013207. Springer, Heidelberg (2007)"},{"key":"7_CR15","unstructured":"Smart, N. (ed): ECRYPT2 yearly report on algorithms and keysizes (2008-2009). Technical report, ECRYPT II \u2013 European Network of Excellence in Cryptology, EU FP7, ICT-2007-216676 (2009) (published as deliverable D.SPA.7), http:\/\/www.ecrypt.eu.org\/documents\/D.SPA.7.pdf"},{"key":"7_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1007\/978-3-642-04138-9_18","volume-title":"Cryptographic Hardware and Embedded Systems - CHES 2009","author":"J. Fan","year":"2009","unstructured":"Fan, J., Vercauteren, F., Verbauwhede, I.: Faster $\\mathbb{F}_p$ -arithmetic for cryptographic pairings on Barreto-Naehrig curves. In: Clavier, C., Gaj, K. (eds.) CHES 2009. LNCS, vol.\u00a05747, pp. 240\u2013253. Springer, Heidelberg (2009), http:\/\/www.cosic.esat.kuleuven.be\/publications\/article-1256.pdf"},{"key":"7_CR17","unstructured":"Fog, A.: Software optimization ressources (2010), http:\/\/www.agner.org\/optimize\/ (accessed March 31, 2010)"},{"issue":"2","key":"7_CR18","doi-asserted-by":"publisher","first-page":"224","DOI":"10.1007\/s00145-009-9048-z","volume":"23","author":"D. Freeman","year":"2010","unstructured":"Freeman, D., Scott, M., Teske, E.: A taxonomy of pairing-friendly elliptic curves. Journal of Cryptology\u00a023(2), 224\u2013280 (2010)","journal-title":"Journal of Cryptology"},{"key":"7_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1007\/978-3-642-04159-4_3","volume-title":"Selected Areas in Cryptography","author":"P. Grabher","year":"2009","unstructured":"Grabher, P., Gro\u00dfsch\u00e4dl, J., Page, D.: On software parallel implementation of cryptographic pairings. In: Avanzi, R.M., Keliher, L., Sica, F. (eds.) SAC 2008. LNCS, vol.\u00a05381, pp. 34\u201349. Springer, Heidelberg (2009)"},{"key":"7_CR20","doi-asserted-by":"crossref","unstructured":"Granger, R., Scott, M.: Faster squaring in the cyclotomic subgroup of sixth degree extensions. In: Nguyen, P., Pointcheval, D. (eds.) PKC 2010. LNCS, vol.\u00a06056, pp. 209\u2013223. Springer, Heidelberg (2010), http:\/\/eprint.iacr.org\/2009\/565\/","DOI":"10.1007\/978-3-642-13013-7_13"},{"key":"7_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1007\/978-3-540-78967-3_24","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2008","author":"J. Groth","year":"2008","unstructured":"Groth, J., Sahai, A.: Efficient non-interactive proof systems for bilinear groups. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol.\u00a04965, pp. 415\u2013432. Springer, Heidelberg (2008)"},{"key":"7_CR22","volume-title":"Identity-Based Cryptography","author":"D. Hankerson","year":"2008","unstructured":"Hankerson, D., Menezes, A., Scott, M.: Software implementation of pairings. In: Joye, M., Neven, G. (eds.) Identity-Based Cryptography. IOS Press, Amsterdam (2008), http:\/\/www.math.uwaterloo.ca\/~ajmeneze\/publications\/pairings_software.pdf"},{"key":"7_CR23","doi-asserted-by":"publisher","first-page":"4595","DOI":"10.1109\/TIT.2006.881709","volume":"52","author":"F. He\u00df","year":"2006","unstructured":"He\u00df, F., Smart, N.P., Vercauteren, F.: The eta pairing revisited. IEEE Transactions on Information Theory\u00a052, 4595\u20134602 (2006)","journal-title":"IEEE Transactions on Information Theory"},{"key":"7_CR24","unstructured":"Lee, E., Lee, H.-S., Park, C.-M.: Efficient and generalized pairing computation on abelian varieties. Cryptology ePrint Archive, Report 2008\/040 (2008), http:\/\/eprint.iacr.org\/2008\/040\/"},{"key":"7_CR25","unstructured":"Shamus\u00a0Software Ltd. Multiprecision integer and rational arithmetic C\/C++ library, http:\/\/www.shamus.ie\/ (accessed March 31, 2010)"},{"key":"7_CR26","unstructured":"Miller, V.S.: Short programs for functions on curves (Unpublished manuscript) (1986), http:\/\/crypto.stanford.edu\/miller\/miller.pdf"},{"key":"7_CR27","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/s00145-004-0315-8","volume":"17","author":"V.S. Miller","year":"2004","unstructured":"Miller, V.S.: The Weil pairing, and its efficient calculation. Journal of Cryptology\u00a017, 235\u2013261 (2004)","journal-title":"Journal of Cryptology"},{"key":"7_CR28","unstructured":"Naehrig, M.: Constructive and Computational Aspects of Cryptographic Pairings. PhD thesis, Technische Universiteit Eindhoven (2009), http:\/\/www.cryptojedi.org\/users\/michael\/data\/thesis\/2009-05-13-diss.pdf"},{"key":"7_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1007\/978-3-540-68164-9_25","volume-title":"Progress in Cryptology \u2013 AFRICACRYPT 2008","author":"M. Naehrig","year":"2008","unstructured":"Naehrig, M., Barreto, P.S.L.M., Schwabe, P.: On compressible pairings and their computation. In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol.\u00a05023, pp. 371\u2013388. Springer, Heidelberg (2008)"},{"key":"7_CR30","unstructured":"Scott, M.: Personal communication (March 2010)"},{"key":"7_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1007\/978-3-642-03298-1_6","volume-title":"Pairing-Based Cryptography \u2013 Pairing 2009","author":"M. Scott","year":"2009","unstructured":"Scott, M., Benger, N., Charlemagne, M., Dominguez Perez, L.J., Kachisa, E.J.: On the final exponentiation for calculating pairings on ordinary elliptic curves. In: Shacham, H. (ed.) Pairing 2009. LNCS, vol.\u00a05671, pp. 78\u201388. Springer, Heidelberg (2009)"},{"key":"7_CR32","doi-asserted-by":"crossref","unstructured":"Vercauteren, F.: Optimal pairings. IEEE Transactions on Information Theory\u00a056(1) (2010)","DOI":"10.1109\/TIT.2009.2034881"}],"container-title":["Lecture Notes in Computer Science","Progress in Cryptology \u2013 LATINCRYPT 2010"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-14712-8_7.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,24]],"date-time":"2020-11-24T02:56:41Z","timestamp":1606186601000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-14712-8_7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"ISBN":["9783642147111","9783642147128"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-14712-8_7","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010]]}}}