{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:20:11Z","timestamp":1759638011253,"version":"3.40.3"},"publisher-location":"Cham","reference-count":29,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319403663"},{"type":"electronic","value":"9783319403670"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-40367-0_17","type":"book-chapter","created":{"date-parts":[[2016,6,29]],"date-time":"2016-06-29T14:53:42Z","timestamp":1467212022000},"page":"269-284","source":"Crossref","is-referenced-by-count":1,"title":["Generalized Hardness Assumption for Self-bilinear Map with Auxiliary Information"],"prefix":"10.1007","author":[{"given":"Takashi","family":"Yamakawa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Goichiro","family":"Hanaoka","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Noboru","family":"Kunihiro","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,6,30]]},"reference":[{"key":"17_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"446","DOI":"10.1007\/978-3-662-49096-9_19","volume-title":"Theory of Cryptography","author":"MR Albrecht","year":"2016","unstructured":"Albrecht, M.R., Farshim, P., Hofheinz, D., Larraia, E., Paterson, K.G.: Multilinear maps from obfuscation. In: Kushilevitz, E., et al. (eds.) TCC 2016-A. LNCS, vol. 9562, pp. 446\u2013473. Springer, Heidelberg (2016). doi: 10.1007\/978-3-662-49096-9_19"},{"key":"17_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/3-540-44647-8_1","volume-title":"Advances in Cryptology - CRYPTO 2001","author":"B Barak","year":"2001","unstructured":"Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S.P., Yang, K.: On the (im)possibility of obfuscating programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1\u201318. Springer, Heidelberg (2001)"},{"key":"17_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/978-3-540-24676-3_14","volume-title":"Advances in Cryptology - EUROCRYPT 2004","author":"D Boneh","year":"2004","unstructured":"Boneh, D., Boyen, X.: Efficient selective-ID secure identity-based encryption without random oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223\u2013238. Springer, Heidelberg (2004)"},{"key":"17_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/3-540-44647-8_13","volume-title":"Advances in Cryptology - 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)"},{"key":"17_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/978-3-642-20465-4_10","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2011","author":"D Boneh","year":"2011","unstructured":"Boneh, D., Freeman, D.M.: Homomorphic signatures for polynomial functions. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 149\u2013168. Springer, Heidelberg (2011)"},{"key":"17_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1007\/978-3-642-55220-5_30","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2014","author":"D Boneh","year":"2014","unstructured":"Boneh, D., Gentry, C., Gorbunov, S., Halevi, S., Nikolaenko, V., Segev, G., Vaikuntanathan, V., Vinayagamurthy, D.: Fully key-homomorphic encryption, arithmetic circuit ABE and compact garbled circuits. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 533\u2013556. Springer, Heidelberg (2014)"},{"key":"17_CR7","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1090\/conm\/324\/05731","volume":"324","author":"D Boneh","year":"2002","unstructured":"Boneh, D., Silverberg, A.: Applications of multilinear forms to cryptography. Contemporary Mathematics 324, 71\u201390 (2002)","journal-title":"Contemporary Mathematics"},{"key":"17_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1007\/978-3-662-44371-2_12","volume-title":"Advances in Cryptology \u2013 CRYPTO 2014","author":"D Boneh","year":"2014","unstructured":"Boneh, D., Waters, B., Zhandry, M.: Low overhead broadcast encryption from multilinear maps. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 206\u2013223. Springer, Heidelberg (2014)"},{"key":"17_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/978-3-662-44371-2_21","volume-title":"Advances in Cryptology \u2013 CRYPTO 2014","author":"D Catalano","year":"2014","unstructured":"Catalano, D., Fiore, D., Warinschi, B.: Homomorphic signatures with efficient verification for polynomial functions. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 371\u2013389. Springer, Heidelberg (2014)"},{"key":"17_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"509","DOI":"10.1007\/978-3-662-49890-3_20","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2016","author":"JH Cheon","year":"2016","unstructured":"Cheon, J.H., Fouque, P.-A., Lee, C., Minaud, B., Ryu, H.: Cryptanalysis of the new CLT multilinear map over the integers. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9665, pp. 509\u2013536. Springer, Heidelberg (2016). doi: 10.1007\/978-3-662-49890-3_20"},{"key":"17_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/978-3-662-46800-5_1","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2015","author":"JH Cheon","year":"2015","unstructured":"Cheon, J.H., Han, K., Lee, C., Ryu, H., Stehl\u00e9, D.: Cryptanalysis of the multilinear map over the integers. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 3\u201312. Springer, Heidelberg (2015)"},{"issue":"2","key":"17_CR12","doi-asserted-by":"crossref","first-page":"303","DOI":"10.4134\/BKMS.2009.46.2.303","volume":"46","author":"JH Cheon","year":"2009","unstructured":"Cheon, J.H., Lee, D.H.: A note on self-bilinear maps. Bull. Korean Math. Soc. 46(2), 303\u2013309 (2009)","journal-title":"Bull. Korean Math. Soc."},{"key":"17_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1007\/978-3-642-40041-4_26","volume-title":"Advances in Cryptology \u2013 CRYPTO 2013","author":"J-S Coron","year":"2013","unstructured":"Coron, J.-S., Lepoint, T., Tibouchi, M.: Practical multilinear maps over the integers. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 476\u2013493. Springer, Heidelberg (2013)"},{"key":"17_CR14","first-page":"267","volume":"1","author":"J-S Coron","year":"2015","unstructured":"Coron, J.-S., Lepoint, T., Tibouchi, M.: New multilinear maps over the integers. CRYPTO 1, 267\u2013286 (2015)","journal-title":"CRYPTO"},{"key":"17_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-3-642-38348-9_1","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2013","author":"S Garg","year":"2013","unstructured":"Garg, S., Gentry, C., Halevi, S.: Candidate multilinear maps from ideal lattices. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 1\u201317. Springer, Heidelberg (2013)"},{"key":"17_CR16","doi-asserted-by":"crossref","unstructured":"Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: FOCS, pp. 40\u201349 (2013)","DOI":"10.1109\/FOCS.2013.13"},{"key":"17_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/978-3-642-40084-1_27","volume-title":"Advances in Cryptology \u2013 CRYPTO 2013","author":"S Garg","year":"2013","unstructured":"Garg, S., Gentry, C., Halevi, S., Sahai, A., Waters, B.: Attribute-based encryption for circuits from multilinear maps. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 479\u2013499. Springer, Heidelberg (2013)"},{"key":"17_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1007\/978-3-662-46497-7_20","volume-title":"Theory of Cryptography","author":"C Gentry","year":"2015","unstructured":"Gentry, C., Gorbunov, S., Halevi, S.: Graph-induced multilinear maps from lattices. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 498\u2013527. Springer, Heidelberg (2015)"},{"key":"17_CR19","doi-asserted-by":"crossref","unstructured":"Gorbunov, S., Vaikuntanathan, V., Wichs, D.: Leveled fully homomorphic signatures from standard lattices. In: STOC 2015, 469\u2013477 (2015)","DOI":"10.1145\/2746539.2746576"},{"key":"17_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/11761679_21","volume-title":"Advances in Cryptology - EUROCRYPT 2006","author":"J Groth","year":"2006","unstructured":"Groth, J., Ostrovsky, R., Sahai, A.: Perfect non-interactive zero knowledge for NP. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 339\u2013358. Springer, Heidelberg (2006)"},{"key":"17_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","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. 4965, pp. 415\u2013432. Springer, Heidelberg (2008)"},{"key":"17_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1007\/978-3-642-03356-8_37","volume-title":"Advances in Cryptology - CRYPTO 2009","author":"D Hofheinz","year":"2009","unstructured":"Hofheinz, D., Kiltz, E.: The group of signed quadratic residues and applications. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 637\u2013653. Springer, Heidelberg (2009)"},{"key":"17_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1007\/978-3-662-49890-3_21","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2016","author":"Y Hu","year":"2016","unstructured":"Hu, Y., Jia, H.: Cryptanalysis of GGH map. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9665, pp. 537\u2013565. Springer, Heidelberg (2016). doi: 10.1007\/978-3-662-49890-3_21"},{"key":"17_CR24","unstructured":"Lee, C., Cheon, J.H., Jeong, J.: An algorithm for ntru problems and cryptanalysis of the ggh multilinear map without an encoding of zero. Cryptology ePrint Archive, Report 2016\/139 (2016). https:\/\/2.zoppoz.workers.dev:443\/http\/eprint.iacr.org\/"},{"key":"17_CR25","unstructured":"Miles, E., Sahai, A., Zhandry, M.: Annihilation attacks for multilinear maps: Cryptanalysis of indistinguishability obfuscation over ggh13. Cryptology ePrint Archive, Report 2016\/147 (2016). https:\/\/2.zoppoz.workers.dev:443\/http\/eprint.iacr.org\/"},{"key":"17_CR26","unstructured":"Paneth, O., Sahai, A.: On the equivalence of obfuscation and multilinear maps. Cryptology ePrint Archive, Report 2015\/791 (2015). https:\/\/2.zoppoz.workers.dev:443\/http\/eprint.iacr.org\/"},{"key":"17_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/11426639_27","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2005","author":"A Sahai","year":"2005","unstructured":"Sahai, A., Waters, B.: Fuzzy identity-based encryption. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457\u2013473. Springer, Heidelberg (2005)"},{"key":"17_CR28","unstructured":"Xie, X., Xue, R.: Bounded fully homomorphic signature schemes. Cryptology ePrint Archive, Report 2014\/420 (2014). https:\/\/2.zoppoz.workers.dev:443\/http\/eprint.iacr.org\/"},{"key":"17_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1007\/978-3-662-44381-1_6","volume-title":"Advances in Cryptology \u2013 CRYPTO 2014","author":"T Yamakawa","year":"2014","unstructured":"Yamakawa, T., Yamada, S., Hanaoka, G., Kunihiro, N.: Self-bilinear map on unknown order groups from indistinguishability obfuscation and its applications. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 90\u2013107. Springer, Heidelberg (2014)"}],"container-title":["Lecture Notes in Computer Science","Information Security and Privacy"],"original-title":[],"link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-40367-0_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,24]],"date-time":"2017-06-24T13:27:50Z","timestamp":1498310870000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/http\/link.springer.com\/10.1007\/978-3-319-40367-0_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319403663","9783319403670"],"references-count":29,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1007\/978-3-319-40367-0_17","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2016]]}}}