{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T04:56:30Z","timestamp":1764132990918,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":37,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783662493830"},{"type":"electronic","value":"9783662493847"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"vor","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":[[2016]]},"DOI":"10.1007\/978-3-662-49384-7_6","type":"book-chapter","created":{"date-parts":[[2016,2,20]],"date-time":"2016-02-20T00:24:21Z","timestamp":1455927861000},"page":"133-163","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["Extended Nested Dual System Groups, Revisited"],"prefix":"10.1007","author":[{"given":"Junqing","family":"Gong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaolei","family":"Dong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhenfu","family":"Cao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaohua","family":"Tang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,2,18]]},"reference":[{"key":"6_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1007\/978-3-642-34961-4_3","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2012","author":"M Abe","year":"2012","unstructured":"Abe, M., Chase, M., David, B., Kohlweiss, M., Nishimaki, R., Ohkubo, M.: Constant-size structure-preserving signatures: generic constructions and simple assumptions. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 4\u201324. Springer, Heidelberg (2012)"},{"key":"6_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/978-3-662-49099-0_10","volume-title":"Theory of Cryptography","author":"S Agrawal","year":"2016","unstructured":"Agrawal, S., Chase, M.: A study of pair encodings: predicate encryption in prime order groups. In: Kushilevitz, E., et al. (eds.) TCC 2016-A. LNCS, vol. 9563, pp. 259\u2013288. Springer, Heidelberg (2016)"},{"key":"6_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1007\/978-3-642-13190-5_28","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"S Agrawal","year":"2010","unstructured":"Agrawal, S., Boneh, D., Boyen, X.: Efficient lattice (H)IBE in the standard model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 553\u2013572. Springer, Heidelberg (2010)"},{"key":"6_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1007\/978-3-642-14623-7_6","volume-title":"Advances in Cryptology \u2013 CRYPTO 2010","author":"S Agrawal","year":"2010","unstructured":"Agrawal, S., Boneh, D., Boyen, X.: Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical IBE. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 98\u2013115. Springer, Heidelberg (2010)"},{"key":"6_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1007\/978-3-642-55220-5_31","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2014","author":"N Attrapadung","year":"2014","unstructured":"Attrapadung, N.: Dual system encryption via doubly selective security: framework, fully secure functional encryption for regular languages, and more. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 557\u2013577. Springer, Heidelberg (2014)"},{"key":"6_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1007\/978-3-662-48797-6_22","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2015","author":"N Attrapadung","year":"2015","unstructured":"Attrapadung, N., Hanaoka, G., Yamada, S.: A framework for identity-based encryption with almost tight security. In: Iwata, T., et al. (eds.) ASIACRYPT 2015. LNCS, vol. 9452, pp. 521\u2013548. Springer, Heidelberg (2015)"},{"key":"6_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1007\/978-3-319-16715-2_5","volume-title":"Topics in Cryptology \u2014 CT-RSA 2015","author":"N Attrapadung","year":"2015","unstructured":"Attrapadung, N., Yamada, S.: Duality in ABE: converting attribute based encryption for dual predicate and dual policy via computational encodings. In: Nyberg, K. (ed.) CT-RSA 2015. LNCS, vol. 9048, pp. 87\u2013105. Springer, Heidelberg (2015)"},{"key":"6_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/978-3-642-19571-6_15","volume-title":"Theory of Cryptography","author":"M Bellare","year":"2011","unstructured":"Bellare, M., Waters, B., Yilek, S.: Identity-based encryption secure against selective opening attack. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 235\u2013252. Springer, Heidelberg (2011)"},{"key":"6_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"408","DOI":"10.1007\/978-3-662-44371-2_23","volume-title":"Advances in Cryptology \u2013 CRYPTO 2014","author":"O Blazy","year":"2014","unstructured":"Blazy, O., Kiltz, E., Pan, J.: (Hierarchical) Identity-based encryption from affine message authentication. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part\u00a0I. LNCS, vol. 8616, pp. 408\u2013425. Springer, Heidelberg (2014)"},{"key":"6_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","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":"6_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1007\/978-3-540-28628-8_27","volume-title":"Advances in Cryptology \u2013 CRYPTO 2004","author":"D Boneh","year":"2004","unstructured":"Boneh, D., Boyen, X.: Secure identity based encryption without random oracles. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 443\u2013459. Springer, Heidelberg (2004)"},{"key":"6_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","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, p. 213. Springer, Heidelberg (2001)"},{"key":"6_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1007\/978-3-662-46803-6_20","volume-title":"Advances in Cryptology - EUROCRYPT 2015","author":"J Chen","year":"2015","unstructured":"Chen, J., Gay, R., Wee, H.: Improved dual system ABE in prime-order groups via predicate encodings. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 595\u2013624. Springer, Heidelberg (2015)"},{"key":"6_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1007\/978-3-642-36334-4_8","volume-title":"Pairing-Based Cryptography \u2013 Pairing 2012","author":"J Chen","year":"2013","unstructured":"Chen, J., Lim, H.W., Ling, S., Wang, H., Wee, H.: Shorter IBE and signatures via asymmetric pairings. In: Abdalla, M., Lange, T. (eds.) Pairing 2012. LNCS, vol. 7708, pp. 122\u2013140. Springer, Heidelberg (2013)"},{"key":"6_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1007\/978-3-642-40084-1_25","volume-title":"Advances in Cryptology \u2013 CRYPTO 2013","author":"J Chen","year":"2013","unstructured":"Chen, J., Wee, H.: Fully, (Almost) tightly secure IBE and dual system groups. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 435\u2013460. Springer, Heidelberg (2013)"},{"key":"6_CR16","first-page":"265","volume":"2014","author":"J Chen","year":"2014","unstructured":"Chen, J., Wee, H.: Dual system groups and its applications - compact HIBE and more. IACR Crypt. ePrint Arch. 2014, 265 (2014)","journal-title":"IACR Crypt. ePrint Arch."},{"key":"6_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"360","DOI":"10.1007\/3-540-45325-3_32","volume-title":"Cryptography and Coding","author":"C Cocks","year":"2001","unstructured":"Cocks, C.: An identity based encryption scheme based on quadratic residues. In: Honary, B. (ed.) Cryptography and Coding 2001. LNCS, vol. 2260, p. 360. Springer, Heidelberg (2001)"},{"key":"6_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1007\/11761679_27","volume-title":"Advances in Cryptology - EUROCRYPT 2006","author":"C Gentry","year":"2006","unstructured":"Gentry, C.: Practical identity-based encryption without random oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 445\u2013464. Springer, Heidelberg (2006)"},{"key":"6_CR19","doi-asserted-by":"crossref","unstructured":"Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pp. 197\u2013206 (2008)","DOI":"10.1145\/1374376.1374407"},{"issue":"3","key":"6_CR20","doi-asserted-by":"publisher","first-page":"525","DOI":"10.1007\/s10623-015-0117-z","volume":"80","author":"Junqing Gong","year":"2015","unstructured":"Gong, J., Cao, Z., Tang, S., Chen, J.: Extended dual system group and shorter unbounded hierarchical identity based encryption. Des. Codes Crypt. (2015). doi:10.1007\/s10623-015-0117-z","journal-title":"Designs, Codes and Cryptography"},{"key":"6_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"799","DOI":"10.1007\/978-3-662-46447-2_36","volume-title":"Public-Key Cryptography \u2013 PKC 2015","author":"D Hofheinz","year":"2015","unstructured":"Hofheinz, D., Koch, J., Striecks, C.: Identity-based encryption with (almost) tight security in the multi-instance, multi-ciphertext setting. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 799\u2013822. Springer, Heidelberg (2015)"},{"key":"6_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-42033-7_1","volume-title":"Advances in Cryptology - ASIACRYPT 2013","author":"CS Jutla","year":"2013","unstructured":"Jutla, C.S., Roy, A.: Shorter quasi-adaptive NIZK proofs for linear subspaces. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part I. LNCS, vol. 8269, pp. 1\u201320. Springer, Heidelberg (2013)"},{"key":"6_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1007\/978-3-662-44381-1_17","volume-title":"Advances in Cryptology \u2013 CRYPTO 2014","author":"CS Jutla","year":"2014","unstructured":"Jutla, C.S., Roy, A.: Switching lemma for bilinear tests and constant-size NIZK proofs for linear subspaces. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 295\u2013312. Springer, Heidelberg (2014)"},{"key":"6_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1007\/978-3-642-20465-4_30","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2011","author":"A Lewko","year":"2011","unstructured":"Lewko, A., Waters, B.: Unbounded HIBE and attribute-based encryption. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 547\u2013567. Springer, Heidelberg (2011)"},{"key":"6_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1007\/978-3-642-29011-4_20","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2012","author":"A Lewko","year":"2012","unstructured":"Lewko, A.: Tools for simulating features of composite order bilinear groups in the prime order setting. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 318\u2013335. Springer, Heidelberg (2012)"},{"key":"6_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1007\/978-3-642-13190-5_4","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"A Lewko","year":"2010","unstructured":"Lewko, A., Okamoto, T., Sahai, A., Takashima, K., Waters, B.: Fully secure functional encryption: attribute-based encryption and (hierarchical) inner product encryption. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 62\u201391. Springer, Heidelberg (2010)"},{"key":"6_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1007\/978-3-642-32009-5_12","volume-title":"Advances in Cryptology \u2013 CRYPTO 2012","author":"A Lewko","year":"2012","unstructured":"Lewko, A., Waters, B.: New proof methods for attribute-based encryption: achieving full security through selective techniques. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 180\u2013198. Springer, Heidelberg (2012)"},{"issue":"2","key":"6_CR28","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1145\/972639.972643","volume":"51","author":"M Naor","year":"2004","unstructured":"Naor, M., Reingold, O.: Number-theoretic constructions of efficient pseudo-random functions. J. ACM 51(2), 231\u2013262 (2004)","journal-title":"J. ACM"},{"key":"6_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/978-3-540-85538-5_4","volume-title":"Pairing-Based Cryptography \u2013 Pairing 2008","author":"T Okamoto","year":"2008","unstructured":"Okamoto, T., Takashima, K.: Homomorphic encryption and signatures from vector decomposition. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol. 5209, pp. 57\u201374. Springer, Heidelberg (2008)"},{"key":"6_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1007\/978-3-642-10366-7_13","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2009","author":"T Okamoto","year":"2009","unstructured":"Okamoto, T., Takashima, K.: Hierarchical predicate encryption for inner-products. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 214\u2013231. Springer, Heidelberg (2009)"},{"key":"6_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1007\/978-3-642-34961-4_22","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2012","author":"T Okamoto","year":"2012","unstructured":"Okamoto, T., Takashima, K.: Fully secure unbounded inner-product and attribute-based encryption. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 349\u2013366. Springer, Heidelberg (2012)"},{"key":"6_CR32","first-page":"298","volume":"2012","author":"SC Ramanna","year":"2012","unstructured":"Ramanna, S.C., Chatterjee, S., Sarkar, P.: Variants of waters\u2019 dual system primitives using asymmetric pairings - (extended abstract). Pub. Key Crypt. - PKC 2012, 298\u2013315 (2012)","journal-title":"Pub. Key Crypt. - PKC"},{"key":"6_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/3-540-39568-7_5","volume-title":"Advances in Cryptology","author":"A Shamir","year":"1985","unstructured":"Shamir, A.: Identity-based cryptosystems and signature schemes. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 47\u201353. Springer, Heidelberg (1985)"},{"key":"6_CR34","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1007\/3-540-69053-0_18","volume-title":"Advances in Cryptology - EUROCRYPT \u201997","author":"V Shoup","year":"1997","unstructured":"Shoup, V.: Lower bounds for discrete logarithms and related problems. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 256\u2013266. Springer, Heidelberg (1997)"},{"key":"6_CR35","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1007\/11426639_7","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2005","author":"B Waters","year":"2005","unstructured":"Waters, B.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114\u2013127. Springer, Heidelberg (2005)"},{"key":"6_CR36","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"619","DOI":"10.1007\/978-3-642-03356-8_36","volume-title":"Advances in Cryptology - CRYPTO 2009","author":"B Waters","year":"2009","unstructured":"Waters, B.: Dual system encryption: realizing fully secure IBE and HIBE under simple assumptions. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 619\u2013636. Springer, Heidelberg (2009)"},{"key":"6_CR37","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"616","DOI":"10.1007\/978-3-642-54242-8_26","volume-title":"Theory of Cryptography","author":"H Wee","year":"2014","unstructured":"Wee, H.: Dual system encryption via predicate encodings. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 616\u2013637. Springer, Heidelberg (2014)"}],"container-title":["Lecture Notes in Computer Science","Public-Key Cryptography \u2013 PKC 2016"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-49384-7_6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,4]],"date-time":"2021-02-04T14:34:05Z","timestamp":1612449245000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-49384-7_6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783662493830","9783662493847"],"references-count":37,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-49384-7_6","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2016]]},"assertion":[{"value":"18 February 2016","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}