{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,27]],"date-time":"2025-05-27T22:24:43Z","timestamp":1748384683044,"version":"3.40.4"},"publisher-location":"Berlin, Heidelberg","reference-count":98,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783662434130"},{"type":"electronic","value":"9783662434147"}],"license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-3-662-43414-7_1","type":"book-chapter","created":{"date-parts":[[2014,5,20]],"date-time":"2014-05-20T14:57:06Z","timestamp":1400597826000},"page":"3-25","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["The Realm of the Pairings"],"prefix":"10.1007","author":[{"given":"Diego F.","family":"Aranha","sequence":"first","affiliation":[]},{"given":"Paulo S. L. M.","family":"Barreto","sequence":"additional","affiliation":[]},{"given":"Patrick","family":"Longa","sequence":"additional","affiliation":[]},{"given":"Jefferson E.","family":"Ricardini","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,5,21]]},"reference":[{"key":"1_CR1","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/978-3-642-36334-4_13","volume-title":"Pairing 2012","author":"T Acar","year":"2013","unstructured":"Acar, T., Lauter, K., Naehrig, M., Shumow, D.: Affine pairings on ARM. In: Abdalla, M., Lange, T. (eds.) Pairing 2012. LNCS, vol. 7708, pp. 203\u2013209. Springer, Heidelberg (2013)"},{"key":"1_CR2","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/978-3-642-36334-4_11","volume-title":"Pairing 2012","author":"DF Aranha","year":"2013","unstructured":"Aranha, D.F., Fuentes-Casta\u00f1eda, L., Knapp, E., Menezes, A., Rodr\u00edguez-Henr\u00edquez, F.: Implementing pairings at the 192-bit security level. In: Abdalla, M., Lange, T. (eds.) Pairing 2012. LNCS, vol. 7708, pp. 177\u2013195. Springer, Heidelberg (2013)"},{"key":"1_CR3","unstructured":"Aranha, D.F., Gouv\u00eaa, C.P.L.: RELIC is an Efficient LIbrary for Cryptography. http:\/\/code.google.com\/p\/relic-toolkit\/"},{"key":"1_CR4","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1007\/978-3-642-20465-4_5","volume-title":"EUROCRYPT 2011","author":"DF Aranha","year":"2011","unstructured":"Aranha, D.F., Karabina, K., Longa, P., Gebotys, C.H., L\u00f3pez, J.: Faster explicit formulas for computing pairings over ordinary curves. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 48\u201368. Springer, Heidelberg (2011)"},{"key":"1_CR5","doi-asserted-by":"crossref","unstructured":"Balfanz, D., Durfee, G., Shankar, N., Smetters, D.K., Staddon, J., Wong, H.C.: Secret handshakes from pairing-based key agreements. In: IEEE Symposium on Security and Privacy - S&P 2003, Berkeley, USA, pp. 180\u2013196. IEEE Computer Society (2003)","DOI":"10.1109\/SECPRI.2003.1199336"},{"key":"1_CR6","unstructured":"Barbulescu, R., Gaudry, P., Joux, A., Thom\u00e9, E.: A quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic. Cryptology ePrint Archive, Report 2013\/400 (2013). http:\/\/eprint.iacr.org\/2013\/400"},{"issue":"3","key":"1_CR7","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1007\/s10623-006-9033-6","volume":"42","author":"PSLM Barreto","year":"2007","unstructured":"Barreto, P.S.L.M., Galbraith, S.D., \u00d3h\u00c9igeartaigh, C., Scott, M.: Efficient pairing computation on supersingular abelian varieties. Des. Codes Crypt. 42(3), 239\u2013271 (2007)","journal-title":"Des. Codes Crypt."},{"key":"1_CR8","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1007\/3-540-45708-9_23","volume-title":"CRYPTO 2002","author":"PSLM 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. 2442, pp. 354\u2013369. Springer, Heidelberg (2002)"},{"key":"1_CR9","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1007\/11593447_28","volume-title":"ASIACRYPT 2005","author":"PSLM Barreto","year":"2005","unstructured":"Barreto, P.S.L.M., Libert, B., McCullagh, N., Quisquater, J.-J.: Efficient and provably-secure identity-based signatures and signcryption from bilinear maps. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 515\u2013532. Springer, Heidelberg (2005)"},{"key":"1_CR10","series-title":"LNCS","first-page":"257","volume-title":"SCN 2002","author":"PSLM Barreto","year":"2003","unstructured":"Barreto, P.S.L.M., Lynn, B., Scott, M.: Constructing elliptic curves with prescribed embedding degrees. In: Cimato, S., Galdi, C., Persiano, G. (eds.) SCN 2002. LNCS, vol. 2576, pp. 257\u2013267. Springer, Heidelberg (2003)"},{"key":"1_CR11","series-title":"LNCS","first-page":"17","volume-title":"SAC 2003","author":"PSLM Barreto","year":"2004","unstructured":"Barreto, P.S.L.M., Lynn, B., Scott, M.: On the selection of pairing-friendly groups. In: Matsui, M., Zuccherato, R.J. (eds.) SAC 2003. LNCS, vol. 3006, pp. 17\u201325. Springer, Heidelberg (2004)"},{"key":"1_CR12","series-title":"LNCS","first-page":"319","volume-title":"SAC 2005","author":"PSLM 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. 3897, pp. 319\u2013331. Springer, Heidelberg (2006)"},{"key":"1_CR13","series-title":"LNCS","first-page":"180","volume-title":"WAIFI 2010","author":"N Benger","year":"2010","unstructured":"Benger, N., Scott, M.: Constructing tower extensions of finite fields for implementation of pairing-based cryptography. In: Hasan, M.A., Helleseth, T. (eds.) WAIFI 2010. LNCS, vol. 6087, pp. 180\u2013195. Springer, Heidelberg (2010)"},{"key":"1_CR14","series-title":"LNCS","first-page":"310","volume-title":"CT-RSA 2013","author":"K Benson","year":"2013","unstructured":"Benson, K., Shacham, H., Waters, B.: The $$k$$ -BDH assumption family: bilinear map cryptography from progressively weaker assumptions. In: Dawson, E. (ed.) CT-RSA 2013. LNCS, vol. 7779, pp. 310\u2013325. Springer, Heidelberg (2013)"},{"key":"1_CR15","series-title":"LNCS","first-page":"21","volume-title":"Pairing 2010","author":"J-L Beuchat","year":"2010","unstructured":"Beuchat, J.-L., Gonz\u00e1lez-D\u00edaz, J.E., Mitsunari, S., Okamoto, E., Rodr\u00edguez-Henr\u00edquez, F., Teruya, T.: High-speed software implementation of the optimal ate pairing over Barreto\u2013Naehrig curves. In: Joye, M., Miyaji, A., Otsuka, A. (eds.) Pairing 2010. LNCS, vol. 6487, pp. 21\u201339. Springer, Heidelberg (2010)"},{"key":"1_CR16","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1007\/978-3-540-24676-3_4","volume-title":"EUROCRYPT 2004","author":"D Boneh","year":"2004","unstructured":"Boneh, D., Boyen, X.: Short signatures without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 56\u201373. Springer, Heidelberg (2004)"},{"key":"1_CR17","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1007\/3-540-44647-8_13","volume-title":"CRYPTO 2001","author":"D Boneh","year":"2001","unstructured":"Boneh, D., Franklin, M.: Identity-based encryption from the Weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213\u2013229. Springer, Heidelberg (2001)"},{"issue":"3","key":"1_CR18","doi-asserted-by":"publisher","first-page":"586","DOI":"10.1137\/S0097539701398521","volume":"32","author":"D Boneh","year":"2003","unstructured":"Boneh, D., Franklin, M.: Identity-based encryption from the Weil pairing. SIAM J. Comput. 32(3), 586\u2013615 (2003)","journal-title":"SIAM J. Comput."},{"key":"1_CR19","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1007\/3-540-39200-9_26","volume-title":"EUROCRYPT 2003","author":"D Boneh","year":"2003","unstructured":"Boneh, D., Gentry, C., Lynn, B., Shacham, H.: Aggregate and verifiably encrypted signatures from bilinear maps. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 416\u2013432. Springer, Heidelberg (2003)"},{"key":"1_CR20","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1007\/3-540-45682-1_30","volume-title":"ASIACRYPT 2001","author":"D Boneh","year":"2001","unstructured":"Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514\u2013532. Springer, Heidelberg (2001)"},{"key":"1_CR21","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1007\/978-3-540-45146-4_23","volume-title":"CRYPTO 2003","author":"X Boyen","year":"2003","unstructured":"Boyen, X.: Multipurpose identity-based signcryption: A swiss army knife for identity-based cryptography. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 383\u2013399. Springer, Heidelberg (2003)"},{"key":"1_CR22","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1007\/11818175_17","volume-title":"CRYPTO 2006","author":"X Boyen","year":"2006","unstructured":"Boyen, X., Waters, B.: Anonymous hierarchical identity-based encryption (without random oracles). In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 290\u2013307. Springer, Heidelberg (2006)"},{"issue":"1","key":"1_CR23","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/s10623-004-3808-4","volume":"37","author":"F Brezing","year":"2005","unstructured":"Brezing, F., Weng, A.: Elliptic curves suitable for pairing based cryptography. Des. Codes Crypt. 37(1), 133\u2013141 (2005)","journal-title":"Des. Codes Crypt."},{"key":"1_CR24","series-title":"LNCS","first-page":"18","volume-title":"PKC 2003","author":"JC Cha","year":"2002","unstructured":"Cha, J.C., Cheon, J.H.: An identity-based signature from gap Diffie-Hellman groups. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 18\u201330. Springer, Heidelberg (2002)"},{"issue":"4","key":"1_CR25","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1007\/s10207-006-0011-9","volume":"6","author":"L Chen","year":"2007","unstructured":"Chen, L., Cheng, Z., Smart, N.P.: Identity-based key agreement protocols from pairings. Int. J. Inf. Secur. 6(4), 213\u2013241 (2007)","journal-title":"Int. J. Inf. Secur."},{"issue":"6","key":"1_CR26","doi-asserted-by":"publisher","first-page":"892","DOI":"10.1007\/s11767-005-0065-2","volume":"23","author":"X Chen","year":"2006","unstructured":"Chen, X., Zhang, F., Kim, K.: New ID-based group signature from pairings. J. Electron. (China) 23(6), 892\u2013900 (2006)","journal-title":"J. Electron. (China)"},{"key":"1_CR27","series-title":"LNCS","first-page":"200","volume-title":"ACISP 2010","author":"X Chen","year":"2010","unstructured":"Chen, X., Zhang, F., Susilo, W., Tian, H., Li, J., Kim, K.: Identity-based chameleon hash scheme without key exposure. In: Steinfeld, R., Hawkes, P. (eds.) ACISP 2010. LNCS, vol. 6168, pp. 200\u2013215. Springer, Heidelberg (2010)"},{"key":"1_CR28","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/11761679_1","volume-title":"EUROCRYPT 2006","author":"JH Cheon","year":"2006","unstructured":"Cheon, J.H.: Security analysis of the strong Diffie-Hellman problem. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 1\u201311. Springer, Heidelberg (2006)"},{"issue":"3","key":"1_CR29","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1007\/s00145-009-9047-0","volume":"23","author":"JH Cheon","year":"2010","unstructured":"Cheon, J.H.: Discrete logarithm problems with auxiliary inputs. J. Cryptology 23(3), 457\u2013476 (2010)","journal-title":"J. Cryptology"},{"key":"1_CR30","series-title":"LNCS","first-page":"421","volume-title":"CHES 2011","author":"RCC Cheung","year":"2011","unstructured":"Cheung, R.C.C., Duquesne, S., Fan, J., Guillermin, N., Verbauwhede, I., Yao, G.X.: FPGA implementation of pairings using residue number system and lazy reduction. In: Preneel, B., Takagi, T. (eds.) CHES 2011. LNCS, vol. 6917, pp. 421\u2013441. Springer, Heidelberg (2011)"},{"key":"1_CR31","doi-asserted-by":"crossref","unstructured":"Chung, J., Hasan, M.: Asymmetric squaring formulae. In: 18th IEEE Symposium on Computer Arithmetic - ARITH-18 2007, pp. 113\u2013122 (2007)","DOI":"10.1109\/ARITH.2007.11"},{"key":"1_CR32","unstructured":"Cocks, C., Pinch, R.G.E.: Identity-based cryptosystems based on the Weil pairing (2001) (unpublished manuscript)"},{"issue":"4","key":"1_CR33","doi-asserted-by":"publisher","first-page":"526","DOI":"10.1147\/sj.294.0526","volume":"29","author":"PG 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":"1_CR34","unstructured":"Costello, C.: Particularly friendly members of family trees. Cryptology ePrint Archive, Report 2012\/072 (2012). http:\/\/eprint.iacr.org\/"},{"key":"1_CR35","series-title":"LNCS","first-page":"224","volume-title":"PKC 2010","author":"C Costello","year":"2010","unstructured":"Costello, C., Lange, T., Naehrig, M.: Faster pairing computations on curves with high-degree twists. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 224\u2013242. Springer, Heidelberg (2010)"},{"key":"1_CR36","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1007\/978-3-642-25578-6_23","volume-title":"INDOCRYPT 2011","author":"C Costello","year":"2011","unstructured":"Costello, C., Lauter, K., Naehrig, M.: Attractive subfamilies of BLS curves for implementing high-security pairings. In: Bernstein, D.J., Chatterjee, S. (eds.) INDOCRYPT 2011. LNCS, vol. 7107, pp. 320\u2013342. Springer, Heidelberg (2011)"},{"key":"1_CR37","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9316-0","volume-title":"Prime Numbers: A Computational Perspective","author":"R Crandall","year":"2001","unstructured":"Crandall, R., Pomerance, C.: Prime Numbers: A Computational Perspective. Springer, Berlin (2001)"},{"key":"1_CR38","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/978-3-540-73489-5_10","volume-title":"Pairing 2007","author":"AJ Devegili","year":"2007","unstructured":"Devegili, A.J., Scott, M., Dahab, R.: Implementing cryptographic pairings over Barreto-Naehrig curves. In: Takagi, T., Okamoto, E., Okamoto, T., Okamoto, T. (eds.) Pairing 2007. LNCS, vol. 4575, pp. 197\u2013207. Springer, Heidelberg (2007)"},{"issue":"2","key":"1_CR39","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/s00145-004-0219-7","volume":"18","author":"R Dupont","year":"2005","unstructured":"Dupont, R., Enge, A., Morain, F.: Building curves with arbitrary small MOV degree over finite prime fields. J. Cryptology 18(2), 79\u201389 (2005)","journal-title":"J. Cryptology"},{"key":"1_CR40","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/978-3-540-40061-5_7","volume-title":"ASIACRYPT 2003","author":"I Duursma","year":"2003","unstructured":"Duursma, I., Lee, H.-S.: Tate pairing implementation for hyperelliptic curves $$y^{2}=x^{p}-x+d$$ . In: Laih, C.S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 111\u2013123. Springer, Heidelberg (2003)"},{"issue":"5","key":"1_CR41","doi-asserted-by":"publisher","first-page":"676","DOI":"10.1109\/TC.2011.78","volume":"61","author":"J Fan","year":"2012","unstructured":"Fan, J., Vercauteren, F., Verbauwhede, I.: Efficient hardware implementation of $$\\mathbb{F}_p$$ -arithmetic for pairing-friendly curves. IEEE Trans. Comput. 61(5), 676\u2013685 (2012)","journal-title":"IEEE Trans. Comput."},{"key":"1_CR42","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-33481-8_1","volume-title":"LatinCrypt 2012","author":"P-A Fouque","year":"2012","unstructured":"Fouque, P.-A., Tibouchi, M.: Indifferentiable hashing to Barreto-Naehrig curves. In: Hevia, A., Neven, G. (eds.) LatinCrypt 2012. LNCS, vol. 7533, pp. 1\u201317. Springer, Heidelberg (2012)"},{"key":"1_CR43","series-title":"LNCS","first-page":"452","volume-title":"ANTS 2006","author":"D Freeman","year":"2006","unstructured":"Freeman, D.: Constructing pairing-friendly elliptic curves with embedding degree 10. In: Hess, F., Pauli, S., Pohst, M. (eds.) ANTS 2006. LNCS, vol. 4076, pp. 452\u2013465. Springer, Heidelberg (2006)"},{"issue":"2","key":"1_CR44","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. J. Cryptology 23(2), 224\u2013280 (2010)","journal-title":"J. Cryptology"},{"issue":"5","key":"1_CR45","doi-asserted-by":"publisher","first-page":"1717","DOI":"10.1109\/18.771254","volume":"45","author":"G Frey","year":"1999","unstructured":"Frey, G., M\u00fcller, M., R\u00fcck, H.: The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems. IEEE Trans. Inf. Theory 45(5), 1717\u20131719 (1999)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1_CR46","first-page":"865","volume":"62","author":"G Frey","year":"1994","unstructured":"Frey, G., R\u00fcck, H.G.: A remark concerning $$m$$ -divisibility and the discrete logarithm problem in the divisor class group of curves. Math. Comput. 62, 865\u2013874 (1994)","journal-title":"Math. Comput."},{"key":"1_CR47","series-title":"LNCS","first-page":"412","volume-title":"SAC 2011","author":"L Fuentes-Casta\u00f1eda","year":"2012","unstructured":"Fuentes-Casta\u00f1eda, L., Knapp, E., Rodr\u00edguez-Henr\u00edquez, F.: Faster hashing to $${\\mathbb{G}}_2$$ . In: Miri, A., Vaudenay, S. (eds.) SAC 2011. LNCS, vol. 7118, pp. 412\u2013430. Springer, Heidelberg (2012)"},{"key":"1_CR48","series-title":"LNCS","first-page":"324","volume-title":"ANTS 2002","author":"SD Galbraith","year":"2002","unstructured":"Galbraith, S.D., Harrison, K., Soldera, D.: Implementing the Tate pairing. In: Fieker, C., Kohel, D.R. (eds.) ANTS 2002. LNCS, vol. 2369, pp. 324\u2013337. Springer, Heidelberg (2002)"},{"key":"1_CR49","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1007\/3-540-45682-1_29","volume-title":"ASIACRYPT 2001","author":"SD Galbraith","year":"2001","unstructured":"Galbraith, S.D.: Supersingular curves in cryptography. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 495\u2013513. Springer, Heidelberg (2001)"},{"issue":"16","key":"1_CR50","doi-asserted-by":"publisher","first-page":"3113","DOI":"10.1016\/j.dam.2007.12.010","volume":"156","author":"SD Galbraith","year":"2008","unstructured":"Galbraith, S.D., Paterson, K.G., Smart, N.P.: Pairings for cryptographers. Discrete Appl. Math. 156(16), 3113\u20133121 (2008)","journal-title":"Discrete Appl. Math."},{"key":"1_CR51","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"548","DOI":"10.1007\/3-540-36178-2_34","volume-title":"ASIACRYPT 2002","author":"C Gentry","year":"2002","unstructured":"Gentry, C., Silverberg, A.: Hierarchical ID-based cryptography. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 548\u2013566. Springer, Heidelberg (2002)"},{"key":"1_CR52","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1007\/978-3-642-10628-6_17","volume-title":"INDOCRYPT 2009","author":"CPL Gouv\u00eaa","year":"2009","unstructured":"Gouv\u00eaa, C.P.L., L\u00f3pez, J.: Software implementation of pairing-based cryptography on sensor networks using the MSP430 microcontroller. In: Roy, B., Sendrier, N. (eds.) INDOCRYPT 2009. LNCS, vol. 5922, pp. 248\u2013262. Springer, Heidelberg (2009)"},{"key":"1_CR53","series-title":"LNCS","first-page":"149","volume-title":"SAC 2012","author":"G Grewal","year":"2013","unstructured":"Grewal, G., Azarderakhsh, R., Longa, P., Hu, S., Jao, D.: Efficient implementation of bilinear pairings on ARM processors. In: Knudsen, L.R., Wu, H. (eds.) SAC 2012. LNCS, vol. 7707, pp. 149\u2013165. Springer, Heidelberg (2013)"},{"key":"1_CR54","unstructured":"Hankerson, D., Menezes, A., Scott, M.: Software implementation of pairings. In: Identity-Based Cryptography, ch. 12, pp. 188\u2013206. IOS Press, Amsterdam (2008)"},{"key":"1_CR55","doi-asserted-by":"publisher","first-page":"4595","DOI":"10.1109\/TIT.2006.881709","volume":"52","author":"F Hess","year":"2006","unstructured":"Hess, F., Smart, N., Vercauteren, F.: The eta pairing revisited. IEEE Trans. Inf. Theory 52, 4595\u20134602 (2006)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1_CR56","series-title":"LNCS","first-page":"385","volume-title":"ANTS 2000","author":"A Joux","year":"2000","unstructured":"Joux, A.: A one-round protocol for tripartite Diffie-Hellman. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 385\u2013394. Springer, Heidelberg (2000)"},{"key":"1_CR57","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1007\/978-3-540-85538-5_9","volume-title":"Pairing 2008","author":"EJ Kachisa","year":"2008","unstructured":"Kachisa, E.J., Schaefer, E.F., Scott, M.: Constructing Brezing-Weng pairing-friendly elliptic curves using elements in the cyclotomic field. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol. 5209, pp. 126\u2013135. Springer, Heidelberg (2008)"},{"key":"1_CR58","series-title":"LNCS","first-page":"102","volume-title":"ANTS-VIII 2008","author":"K Karabina","year":"2008","unstructured":"Karabina, K., Teske, E.: On prime-order elliptic curves with embedding degrees $$k$$ = 3, 4, and 6. In: van der Poorten, A.J., Stein, A. (eds.) ANTS-VIII 2008. LNCS, vol. 5011, pp. 102\u2013117. Springer, Heidelberg (2008)"},{"key":"1_CR59","series-title":"LNCS","first-page":"1","volume-title":"Pairing 2010","author":"K Lauter","year":"2010","unstructured":"Lauter, K., Montgomery, P.L., Naehrig, M.: An analysis of affine coordinates for pairing computation. In: Joye, M., Miyaji, A., Otsuka, A. (eds.) Pairing 2010. LNCS, vol. 6487, pp. 1\u201320. Springer, Heidelberg (2010)"},{"issue":"4","key":"1_CR60","doi-asserted-by":"publisher","first-page":"1793","DOI":"10.1109\/TIT.2009.2013048","volume":"55","author":"E Lee","year":"2009","unstructured":"Lee, E., Lee, H.-S., Park, C.-M.: Efficient and generalized pairing computation on abelian varieties. IEEE Trans. Inf. Theory 55(4), 1793\u20131803 (2009)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1_CR61","doi-asserted-by":"crossref","unstructured":"Libert, B., Quisquater. J.-J.: New identity based signcryption schemes from pairings. In: Information Theory Workshop - ITW 2003, pp. 155\u2013158. IEEE (2003)","DOI":"10.1109\/ITW.2003.1216718"},{"key":"1_CR62","unstructured":"Longa, P.: High-speed elliptic curve and pairing-based cryptography. Ph.D. thesis, University of Waterloo, April 2011"},{"issue":"4","key":"1_CR63","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1007\/s00145-006-0544-0","volume":"19","author":"F Luca","year":"2006","unstructured":"Luca, F., Shparlinski, I.E.: Elliptic curves with low embedding degree. J. Cryptology 19(4), 553\u2013562 (2006)","journal-title":"J. Cryptology"},{"key":"1_CR64","series-title":"LNCS","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1007\/978-3-540-77272-9_18","volume-title":"Cryptography and Coding 2007","author":"S Matsuda","year":"2007","unstructured":"Matsuda, S., Kanayama, N., Hess, F., Okamoto, E.: Optimised versions of the ate and twisted ate pairings. In: Galbraith, S.D. (ed.) Cryptography and Coding 2007. LNCS, vol. 4887, pp. 302\u2013312. Springer, Heidelberg (2007)"},{"key":"1_CR65","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-3198-2","volume-title":"Elliptic Curve Public Key Cryptosystems","author":"AJ Menezes","year":"1993","unstructured":"Menezes, A.J.: Elliptic Curve Public Key Cryptosystems. Kluwer Academic Publishers, Boston (1993)"},{"key":"1_CR66","doi-asserted-by":"publisher","first-page":"1639","DOI":"10.1109\/18.259647","volume":"39","author":"AJ Menezes","year":"1993","unstructured":"Menezes, A.J., Okamoto, T., Vanstone, S.A.: Reducing elliptic curve logarithms to logarithms in a finite field. IEEE Trans. Inf. Theory 39, 1639\u20131646 (1993)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1_CR67","unstructured":"Miller, V.S.: Short programs for functions on curves. IBM Thomas J. Watson Research Center Report (1986). http:\/\/crypto.stanford.edu\/miller\/miller.pdf"},{"issue":"4","key":"1_CR68","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/s00145-004-0315-8","volume":"17","author":"VS Miller","year":"2004","unstructured":"Miller, V.S.: The Weil pairing, and its efficient calculation. J. Cryptology 17(4), 235\u2013261 (2004)","journal-title":"J. Cryptology"},{"key":"1_CR69","unstructured":"Mitsunari, S.: A fast implementation of the optimal ate pairing over BN curve on Intel Haswell processor. Cryptology ePrint Archive, Report 2013\/362 (2013). http:\/\/eprint.iacr.org\/"},{"issue":"2","key":"1_CR70","first-page":"481","volume":"E85\u2013A","author":"S Mitsunari","year":"2002","unstructured":"Mitsunari, S., Sakai, R., Kasahara, M.: A new traitor tracing. IEICE Trans. Fundam. E85\u2013A(2), 481\u2013484 (2002)","journal-title":"IEICE Trans. Fundam."},{"issue":"5","key":"1_CR71","first-page":"1234","volume":"E84\u2013A","author":"A Miyaji","year":"2001","unstructured":"Miyaji, A., Nakabayashi, M., Takano, S.: New explicit conditions of elliptic curve traces for FR-reduction. IEICE Trans. Fundam. E84\u2013A(5), 1234\u20131243 (2001)","journal-title":"IEICE Trans. Fundam."},{"issue":"170","key":"1_CR72","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1090\/S0025-5718-1985-0777282-X","volume":"44","author":"PL Montgomery","year":"1985","unstructured":"Montgomery, P.L.: Modular multiplication without trial division. Math. Comput. 44(170), 519\u2013521 (1985)","journal-title":"Math. Comput."},{"key":"1_CR73","series-title":"LNCS","first-page":"186","volume-title":"Pairing 2013","author":"Y Mori","year":"2014","unstructured":"Mori, Y., Akagi, S., Nogami, Y., Shirase, M.: Pseudo 8-sparse multiplication for efficient ate-based pairing on Barreto-Naehrig curve. In: Cao, Z., Zhang, F. (eds.) Pairing 2013. LNCS, vol. 8365, pp. 186\u2013198. Springer, Heidelberg (2014)"},{"key":"1_CR74","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1007\/978-3-540-68164-9_25","volume-title":"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. 5023, pp. 371\u2013388. Springer, Heidelberg (2008)"},{"key":"1_CR75","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/978-3-642-14712-8_7","volume-title":"LATINCRYPT 2010","author":"M Naehrig","year":"2010","unstructured":"Naehrig, M., Niederhagen, R., Schwabe, P.: New software speed records for cryptographic pairings. In: Abdalla, M., Barreto, P.S.L.M. (eds.) LATINCRYPT 2010. LNCS, vol. 6212, pp. 109\u2013123. Springer, Heidelberg (2010)"},{"key":"1_CR76","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1007\/978-3-540-85538-5_13","volume-title":"Pairing 2008","author":"Y Nogami","year":"2008","unstructured":"Nogami, Y., Akane, M., Sakemi, Y., Kato, H., Morikawa, Y.: Integer variable $$\\chi$$ \u2013based ate pairing. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol. 5209, pp. 178\u2013191. Springer, Heidelberg (2008)"},{"key":"1_CR77","series-title":"LNCS","first-page":"104","volume-title":"PKC 2001","author":"T Okamoto","year":"2001","unstructured":"Okamoto, T., Pointcheval, D.: The gap-problems: a new class of problems for the security of cryptographic schemes. In: Kim, K. (ed.) PKC 2001. LNCS, vol. 1992, pp. 104\u2013118. Springer, Heidelberg (2001)"},{"key":"1_CR78","unstructured":"Ozturk, E., Guilford, J., Gopal, V.: Large integer squaring on intel architecture processors. Intel white paper (2013)"},{"key":"1_CR79","unstructured":"Ozturk, E., Guilford, J., Gopal, V., Feghali, W.: New instructions supporting large integer arithmetic on intel architecture processors. Intel white paper (2012)"},{"issue":"8","key":"1_CR80","doi-asserted-by":"publisher","first-page":"1319","DOI":"10.1016\/j.jss.2011.03.083","volume":"84","author":"GCCF Pereira","year":"2011","unstructured":"Pereira, G.C.C.F., Simpl\u00edcio Jr, M.A., Naehrig, M., Barreto, P.S.L.M.: A family of implementation-friendly BN elliptic curves. J. Syst. Softw. 84(8), 1319\u20131326 (2011)","journal-title":"J. Syst. Softw."},{"key":"1_CR81","first-page":"918","volume":"32","author":"JM Pollard","year":"1978","unstructured":"Pollard, J.M.: Monte Carlo methods for index computation (mod $$p$$ ). Math. Comput. 32, 918\u2013924 (1978)","journal-title":"Math. Comput."},{"key":"1_CR82","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"336","DOI":"10.1007\/3-540-45708-9_22","volume-title":"CRYPTO 2002","author":"K Rubin","year":"2002","unstructured":"Rubin, K., Silverberg, A.: Supersingular abelian varieties in cryptology. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 336\u2013353. Springer, Heidelberg (2002)"},{"key":"1_CR83","unstructured":"Sakai, R., Kasahara, M.: Cryptosystems based on pairing over elliptic curve. In: Symposium on Cryptography and Information Security - SCIS 2003, pp. 8C-1, January 2003"},{"key":"1_CR84","unstructured":"Sakai, R., Ohgishi, K., Kasahara, M.: Cryptosystems based on pairing. In: Symposium on Cryptography and Information Security - SCIS 2000, Okinawa, Japan, January 2000"},{"key":"1_CR85","unstructured":"Scott, M.: A note on twists for pairing friendly curves (2009). ftp:\/\/ftp.computing.dcu.ie\/pub\/resources\/crypto\/twists.pdf"},{"key":"1_CR86","series-title":"LNCS","first-page":"296","volume-title":"IMACC 2011","author":"M Scott","year":"2011","unstructured":"Scott, M.: On the efficient implementation of pairing-based protocols. In: Chen, L. (ed.) IMACC 2011. LNCS, vol. 7089, pp. 296\u2013308. Springer, Heidelberg (2011)"},{"key":"1_CR87","unstructured":"Scott, M.: Unbalancing pairing-based key exchange protocols. Cryptology ePrint Archive, Report 2013\/688 (2013). http:\/\/eprint.iacr.org\/2013\/688"},{"key":"1_CR88","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1007\/978-3-540-28628-8_9","volume-title":"CRYPTO 2004","author":"M Scott","year":"2004","unstructured":"Scott, M., Barreto, P.S.L.M.: Compressed pairings. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 140\u2013156. Springer, Heidelberg (2004)"},{"key":"1_CR89","series-title":"LNCS","first-page":"78","volume-title":"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., Waters, B. (eds.) Pairing 2009. LNCS, vol. 5671, pp. 78\u201388. Springer, Heidelberg (2009)"},{"key":"1_CR90","unstructured":"Shirase, M.: Barreto-Naehrig curve with fixed coefficient. IACR ePrint Archive, report 2010\/134 (2010). http:\/\/eprint.iacr.org\/2010\/134"},{"key":"1_CR91","series-title":"Graduate Texts in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-1920-8","volume-title":"The Arithmetic of Elliptic Curves","author":"JH Silverman","year":"1986","unstructured":"Silverman, J.H.: The Arithmetic of Elliptic Curves. Graduate Texts in Mathematics, vol. 106. Springer, Berlin (1986)"},{"issue":"278","key":"1_CR92","doi-asserted-by":"publisher","first-page":"1093","DOI":"10.1090\/S0025-5718-2011-02543-3","volume":"81","author":"JJ Urroz","year":"2012","unstructured":"Urroz, J.J., Luca, F., Shparlinski, I.: On the number of isogeny classes of pairing-friendly elliptic curves and statistics of MNT curves. Math. Comput. 81(278), 1093\u20131110 (2012)","journal-title":"Math. Comput."},{"issue":"1","key":"1_CR93","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1109\/TIT.2009.2034881","volume":"56","author":"F Vercauteren","year":"2010","unstructured":"Vercauteren, F.: Optimal pairings. IEEE Trans. Inf. Theory 56(1), 455\u2013461 (2010)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"1_CR94","first-page":"592","volume":"210","author":"A Weil","year":"1940","unstructured":"Weil, A.: Sur les fonctions alg\u00e9briques \u00e0 corps de constantes fini. Comptes Rendus de l\u2019Acad\u00e9mie des Sciences 210, 592\u2013594 (1940)","journal-title":"Comptes Rendus de l\u2019Acad\u00e9mie des Sciences"},{"key":"1_CR95","unstructured":"Zavattoni, E., Dom\u00ednguez-P\u00e9rez, L.J., Mitsunari, S., S\u00e1nchez, A.H., Teruya, T., Rodr\u00edguez-Henr\u00edquez, F.: Software implementation of attribute-based encryption (2013). http:\/\/sandia.cs.cinvestav.mx\/index.php?n=Site.CPABE"},{"key":"1_CR96","unstructured":"Zhang, F., Chen, X.: Yet another short signatures without random oracles from bilinear pairings. IACR Cryptology ePrint Archive, report 2005\/230 (2005)"},{"key":"1_CR97","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1007\/3-540-36178-2_33","volume-title":"ASIACRYPT 2002","author":"F Zhang","year":"2002","unstructured":"Zhang, F., Kim, K.: ID-based blind signature and ring signature from pairings. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 533\u2013547. Springer, Heidelberg (2002)"},{"key":"1_CR98","series-title":"LNCS","first-page":"277","volume-title":"PKC 2004","author":"F Zhang","year":"2004","unstructured":"Zhang, F., Safavi-Naini, R., Susilo, W.: An efficient signature scheme from bilinear pairings and its applications. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 277\u2013290. Springer, Heidelberg (2004)"}],"container-title":["Lecture Notes in Computer Science","Selected Areas in Cryptography -- SAC 2013"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-43414-7_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,2]],"date-time":"2025-05-02T23:59:07Z","timestamp":1746230347000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-43414-7_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783662434130","9783662434147"],"references-count":98,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-43414-7_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2014]]},"assertion":[{"value":"21 May 2014","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}