{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,7]],"date-time":"2025-12-07T13:05:09Z","timestamp":1765112709708,"version":"build-2065373602"},"publisher-location":"Berlin, Heidelberg","reference-count":38,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642173721"},{"type":"electronic","value":"9783642173738"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2010]]},"DOI":"10.1007\/978-3-642-17373-8_31","type":"book-chapter","created":{"date-parts":[[2010,12,2]],"date-time":"2010-12-02T15:22:55Z","timestamp":1291303375000},"page":"539-556","source":"Crossref","is-referenced-by-count":17,"title":["The Semi-Generic Group Model and Applications to Pairing-Based Cryptography"],"prefix":"10.1007","author":[{"given":"Tibor","family":"Jager","sequence":"first","affiliation":[]},{"given":"Andy","family":"Rupp","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"31_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1007\/978-3-642-01001-9_2","volume-title":"Advances in Cryptology \u2014 EUROCRYPT 2009","author":"D. Aggarwal","year":"2010","unstructured":"Aggarwal, D., Maurer, U.: Breaking RSA generically is equivalent to factoring. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol.\u00a05479, pp. 36\u201353. Springer, Heidelberg (2010)"},{"key":"31_CR2","doi-asserted-by":"crossref","unstructured":"Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: ACM Conference on Computer and Communications Security, pp. 62\u201373 (1993)","DOI":"10.1145\/168588.168596"},{"key":"31_CR3","unstructured":"Boneh, D.: Number-theoretic assumptions. Invited Talk at TCC\u2019s Special Session on Assumptions for Cryptography (2007)"},{"key":"31_CR4","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. (eds.) EUROCRYPT 2004. LNCS, vol.\u00a03027, pp. 223\u2013238. Springer, Heidelberg (2004)"},{"key":"31_CR5","doi-asserted-by":"crossref","unstructured":"Boneh, D., Boyen, X., Goh, E.: Hierarchical identity based encryption with constant size ciphertext (full paper). Cryptology ePrint Archive, Report 2005\/015 (2005), http:\/\/eprint.iacr.org\/","DOI":"10.1007\/11426639_26"},{"key":"31_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/978-3-540-28628-8_3","volume-title":"Advances in Cryptology \u2013 CRYPTO 2004","author":"D. Boneh","year":"2004","unstructured":"Boneh, D., Boyen, X., Shacham, H.: Short group signatures. In: Franklin, M.K. (ed.) CRYPTO 2004. LNCS, vol.\u00a03152, pp. 41\u201355. Springer, Heidelberg (2004)"},{"key":"31_CR7","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.K.: Identity-based encryption from the Weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol.\u00a02139, pp. 213\u2013229. Springer, Heidelberg (2001)"},{"key":"31_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1007\/3-540-39200-9_26","volume-title":"Advances in Cryptology \u2013 EUROCRPYT 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.\u00a02656, pp. 416\u2013432. Springer, Heidelberg (2003)"},{"key":"31_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1007\/3-540-45682-1_30","volume-title":"Advances in Cryptology - 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.\u00a02248, pp. 514\u2013532. Springer, Heidelberg (2001)"},{"issue":"4","key":"31_CR10","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/s00145-004-0314-9","volume":"17","author":"D. Boneh","year":"2004","unstructured":"Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. J. Cryptology\u00a017(4), 297\u2013319 (2004)","journal-title":"J. Cryptology"},{"key":"31_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/978-3-540-85538-5_3","volume-title":"Pairing-Based Cryptography \u2013 Pairing 2008","author":"X. Boyen","year":"2008","unstructured":"Boyen, X.: The Uber-Assumption family. In: Galbraith, S.D., Paterson, K.G. (eds.) Pairing 2008. LNCS, vol.\u00a05209, pp. 39\u201356. Springer, Heidelberg (2008)"},{"key":"31_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"482","DOI":"10.1007\/978-3-540-74143-5_27","volume-title":"Advances in Cryptology - CRYPTO 2007","author":"E. Bresson","year":"2007","unstructured":"Bresson, E., Lakhnech, Y., Mazar\u00e9, L., Warinschi, B.: A generalization of DDH with applications to protocol analysis and computational soundness. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol.\u00a04622, pp. 482\u2013499. Springer, Heidelberg (2007)"},{"issue":"1","key":"31_CR13","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/s10623-003-6154-z","volume":"35","author":"D.R.L. Brown","year":"2005","unstructured":"Brown, D.R.L.: Generic groups, collision resistance, and ECDSA. Des. Codes Cryptography\u00a035(1), 119\u2013152 (2005)","journal-title":"Des. Codes Cryptography"},{"key":"31_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/11761679_1","volume-title":"Advances in Cryptology - EUROCRYPT 2006","author":"J. Cheon","year":"2006","unstructured":"Cheon, J.: Security analysis of the Strong Diffie-Hellman problem. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol.\u00a04004, pp. 1\u201311. Springer, Heidelberg (2006)"},{"key":"31_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1007\/3-540-36178-2_6","volume-title":"Advances in Cryptology - ASIACRYPT 2002","author":"A.W. Dent","year":"2002","unstructured":"Dent, A.W.: Adapting the weaknesses of the random oracle model to the generic group model. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol.\u00a02501, pp. 100\u2013109. Springer, Heidelberg (2002)"},{"key":"31_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"458","DOI":"10.1007\/3-540-44448-3_35","volume-title":"Advances in Cryptology - ASIACRYPT 2000","author":"M. Fischlin","year":"2000","unstructured":"Fischlin, M.: A note on security proofs in the generic model. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol.\u00a01976, pp. 458\u2013469. Springer, Heidelberg (2000)"},{"issue":"16","key":"31_CR17","doi-asserted-by":"publisher","first-page":"3113","DOI":"10.1016\/j.dam.2007.12.010","volume":"156","author":"S.D. Galbraith","year":"2008","unstructured":"Galbraith, S.D., Paterson, K.G., Smart, N.P.: Pairings for cryptographers. Discrete Applied Mathematics\u00a0156(16), 3113\u20133121 (2008)","journal-title":"Discrete Applied Mathematics"},{"key":"31_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/978-3-540-85174-5_2","volume-title":"Advances in Cryptology \u2013 CRYPTO 2008","author":"D. Hofheinz","year":"2008","unstructured":"Hofheinz, D., Kiltz, E.: Programmable hash functions and their applications. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol.\u00a05157, pp. 21\u201338. Springer, Heidelberg (2008)"},{"key":"31_CR19","unstructured":"Hohenberger, S.: The cryptographic impact of groups with infeasible inversion. Master\u2019s thesis, Massachusetts Institute of Technology (2003)"},{"key":"31_CR20","doi-asserted-by":"crossref","unstructured":"Jager, T., Rupp, A.: The semi-generic group model and applications to pairing-based cryptography (full paper) (2010), http:\/\/www.nds.rub.de\/chair\/publications\/","DOI":"10.1007\/978-3-642-17373-8_31"},{"key":"31_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1007\/978-3-642-10366-7_24","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2009","author":"T. Jager","year":"2009","unstructured":"Jager, T., Schwenk, J.: On the analysis of cryptographic assumptions in the generic ring model. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol.\u00a05912, pp. 399\u2013416. Springer, Heidelberg (2009)"},{"key":"31_CR22","doi-asserted-by":"crossref","unstructured":"Jao, D., Yoshida, K.: Boneh-Boyen signatures and the Strong Diffie-Hellman problem. Cryptology ePrint Archive, Report 2009\/221 (2009), http:\/\/eprint.iacr.org\/","DOI":"10.1007\/978-3-642-03298-1_1"},{"key":"31_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/10722028_23","volume-title":"Algorithmic Number Theory","author":"A. Joux","year":"2000","unstructured":"Joux, A.: A one round protocol for tripartite Diffie-Hellman. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol.\u00a01838, pp. 385\u2013394. Springer, Heidelberg (2000)"},{"issue":"4","key":"31_CR24","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1007\/s00145-004-0312-y","volume":"17","author":"A. Joux","year":"2004","unstructured":"Joux, A.: A one round protocol for tripartite Diffie-Hellman. J. Cryptology\u00a017(4), 263\u2013276 (2004)","journal-title":"J. Cryptology"},{"key":"31_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1007\/978-3-540-78967-3_9","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2008","author":"J. Katz","year":"2008","unstructured":"Katz, J., Sahai, A., Waters, B.: Predicate encryption supporting disjunctions, polynomial equations, and inner products. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol.\u00a04965, pp. 146\u2013162. Springer, Heidelberg (2008)"},{"key":"31_CR26","doi-asserted-by":"publisher","first-page":"13","DOI":"10.3934\/amc.2007.1.13","volume":"1","author":"N. Koblitz","year":"2007","unstructured":"Koblitz, N., Menezes, A.: Another look at generic groups. Advances in Mathematics of Communications\u00a01, 13\u201328 (2007)","journal-title":"Advances in Mathematics of Communications"},{"key":"31_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/11935230_16","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2006","author":"G. Leander","year":"2006","unstructured":"Leander, G., Rupp, A.: On the equivalence of RSA and factoring regarding generic ring algorithms. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol.\u00a04284, pp. 241\u2013251. Springer, Heidelberg (2006)"},{"key":"31_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/11586821_1","volume-title":"Cryptography and Coding","author":"U. Maurer","year":"2005","unstructured":"Maurer, U.: Abstract models of computation in cryptography. In: Smart, N.P. (ed.) Cryptography and Coding 2005. LNCS, vol.\u00a03796, pp. 1\u201312. Springer, Heidelberg (2005)"},{"issue":"5","key":"31_CR29","doi-asserted-by":"publisher","first-page":"1639","DOI":"10.1109\/18.259647","volume":"39","author":"A. Menezes","year":"1993","unstructured":"Menezes, A., Okamoto, T., Vanstone, S.: Reducing elliptic curve logarithms to logarithms in a finite field. IEEE Transactions on Information Theory\u00a039(5), 1639\u20131646 (1993)","journal-title":"IEEE Transactions on Information Theory"},{"key":"31_CR30","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1109\/TIT.1978.1055817","volume":"24","author":"S.C. Pohlig","year":"1978","unstructured":"Pohlig, S.C., Hellman, M.E.: An improved algorithm for computing logarithms over GF(p) and its cryptographic significance. IEEE Transactions on Information Theory\u00a024, 106\u2013110 (1978)","journal-title":"IEEE Transactions on Information Theory"},{"key":"31_CR31","first-page":"918","volume":"32","author":"J.M. Pollard","year":"1978","unstructured":"Pollard, J.M.: Monte Carlo methods for index computation mod p. Mathematics of Computation\u00a032, 918\u2013924 (1978)","journal-title":"Mathematics of Computation"},{"key":"31_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1007\/978-3-540-24638-1_28","volume-title":"Theory of Cryptography","author":"R.L. Rivest","year":"2004","unstructured":"Rivest, R.L.: On the notion of pseudo-free groups. In: Naor, M. (ed.) TCC 2004. LNCS, vol.\u00a02951, pp. 505\u2013521. Springer, Heidelberg (2004)"},{"key":"31_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1007\/978-3-540-89255-7_30","volume-title":"Advances in Cryptology - ASIACRYPT 2008","author":"A. Rupp","year":"2008","unstructured":"Rupp, A., Leander, G., Bangerter, E., Dent, A.W., Sadeghi, A.: Sufficient conditions for intractability over black-box groups: Generic lower bounds for generalized DL and DH problems. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol.\u00a05350, pp. 489\u2013505. Springer, Heidelberg (2008)"},{"key":"31_CR34","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","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.\u00a01233, pp. 256\u2013266. Springer, Heidelberg (1997)"},{"key":"31_CR35","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/3-540-45325-3_8","volume-title":"Cryptography and Coding","author":"N.P. Smart","year":"2001","unstructured":"Smart, N.P.: The exact security of ECIES in the generic group model. In: Honary, B. (ed.) Cryptography and Coding 2001. LNCS, vol.\u00a02260, pp. 73\u201384. Springer, Heidelberg (2001)"},{"key":"31_CR36","volume-title":"Modern Computer Algebra","author":"J. zur Gathen von","year":"2003","unstructured":"von zur Gathen, J., Gerhard, J.: Modern Computer Algebra, 2nd edn. Cambridge University Press, Cambridge (2003)","edition":"2"},{"key":"31_CR37","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.\u00a03494, pp. 114\u2013127. Springer, Heidelberg (2005)"},{"key":"31_CR38","unstructured":"Wolf, S.: Information-theoretically and computationally secure key agreement in cryptography. PhD thesis, ETH Zurich, ETH dissertation No. 13138 (1999)"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology - ASIACRYPT 2010"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-17373-8_31.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,24]],"date-time":"2020-11-24T02:52:54Z","timestamp":1606186374000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-17373-8_31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010]]},"ISBN":["9783642173721","9783642173738"],"references-count":38,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-17373-8_31","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2010]]}}}