{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T13:34:22Z","timestamp":1789133662004,"version":"build-2803163510"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2013,5,25]],"date-time":"2013-05-25T00:00:00Z","timestamp":1369440000000},"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":["J Cryptol"],"published-print":{"date-parts":[[2014,7]]},"DOI":"10.1007\/s00145-013-9153-x","type":"journal-article","created":{"date-parts":[[2013,5,24]],"date-time":"2013-05-24T14:27:01Z","timestamp":1369405621000},"page":"544-593","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Verifiable Random Functions: Relations to Identity-Based Key Encapsulation and New Constructions"],"prefix":"10.1007","volume":"27","author":[{"given":"Michel","family":"Abdalla","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dario","family":"Catalano","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dario","family":"Fiore","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2013,5,25]]},"reference":[{"key":"9153_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"554","DOI":"10.1007\/978-3-642-01001-9_32","volume-title":"Advances in Cryptology\u2014EUROCRYPT 2009","author":"M. Abdalla","year":"2009","unstructured":"M. Abdalla, D. Catalano, D. Fiore, Verifiable random functions from identity-based key encapsulation, in Advances in Cryptology\u2014EUROCRYPT 2009, Cologne, Germany, April 26\u201330, ed. by A. Joux. Lecture Notes in Computer Science, vol.\u00a05479 (Springer, Berlin, 2009), pp. 554\u2013571"},{"key":"9153_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-22792-9_1","volume-title":"Advances in Cryptology\u2014CRYPTO 2011","author":"B. Barak","year":"2011","unstructured":"B. Barak, Y. Dodis, H. Krawczyk, O. Pereira, K. Pietrzak, F.-X. Standaert, Y. Yu, Leftover hash lemma, revisited, in Advances in Cryptology\u2014CRYPTO 2011, Santa Barbara, CA, USA, August. Lecture Notes in Computer Science (Springer, Berlin, 2011), pp. 1\u201320"},{"issue":"2","key":"9153_CR3","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1007\/s00145-007-9000-z","volume":"21","author":"K. Bentahar","year":"2008","unstructured":"K. Bentahar, P. Farshim, J. Malone-Lee, N.P. Smart, Generic constructions of identity-based and certificateless KEMs. J. Cryptol.\n                  21(2), 178\u2013199 (2008)","journal-title":"J. Cryptol."},{"key":"9153_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\u2014EUROCRYPT 2004","author":"D. Boneh","year":"2004","unstructured":"D. Boneh, X. Boyen, Efficient selective-ID secure identity based encryption without random oracles, in Advances in Cryptology\u2014EUROCRYPT 2004, Interlaken, Switzerland, May 2\u20136, ed. by C. Cachin, J. Camenisch. Lecture Notes in Computer Science, vol.\u00a03027 (Springer, Berlin, 2004), pp. 223\u2013238"},{"key":"9153_CR5","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\u2014CRYPTO 2004","author":"D. Boneh","year":"2004","unstructured":"D. Boneh, X. Boyen, Secure identity based encryption without random oracles, in Advances in Cryptology\u2014CRYPTO 2004, Santa Barbara, CA, USA, August 15\u201319, ed. by M. Franklin. Lecture Notes in Computer Science, vol.\u00a03152 (Springer, Berlin, 2004), pp. 443\u2013459"},{"key":"9153_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1007\/978-3-540-24676-3_4","volume-title":"Advances in Cryptology\u2014EUROCRYPT 2004","author":"D. Boneh","year":"2004","unstructured":"D. Boneh, X. Boyen, Short signatures without random oracles, in Advances in Cryptology\u2014EUROCRYPT 2004, Interlaken, Switzerland, May 2\u20136, ed. by C. Cachin, J. Camenisch. Lecture Notes in Computer Science, vol.\u00a03027 (Springer, Berlin, 2004), pp. 56\u201373"},{"key":"9153_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\u2014CRYPTO 2001","author":"D. Boneh","year":"2001","unstructured":"D. Boneh, M.K. Franklin, Identity-based encryption from the Weil pairing, in Advances in Cryptology\u2014CRYPTO 2001, Santa Barbara, CA, USA, August 19\u201323, ed. by J. Kilian. Lecture Notes in Computer Science, vol.\u00a02139 (Springer, Berlin, 2001), pp. 213\u2013229"},{"key":"9153_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/978-3-540-28628-8_3","volume-title":"Advances in Cryptology\u2014CRYPTO 2004","author":"D. Boneh","year":"2004","unstructured":"D. Boneh, X. Boyen, H. Shacham, Short group signatures, in Advances in Cryptology\u2014CRYPTO 2004, Santa Barbara, CA, USA, August 15\u201319, ed. by M. Franklin. Lecture Notes in Computer Science, vol.\u00a03152 (Springer, Berlin, 2004), pp. 41\u201355"},{"key":"9153_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"440","DOI":"10.1007\/11426639_26","volume-title":"Advances in Cryptology\u2014EUROCRYPT 2005","author":"D. Boneh","year":"2005","unstructured":"D. Boneh, X. Boyen, E.-J. Goh, Hierarchical identity based encryption with constant size ciphertext, in Advances in Cryptology\u2014EUROCRYPT 2005, Aarhus, Denmark, May 22\u201326, ed. by R. Cramer. Lecture Notes in Computer Science, vol.\u00a03494 (Springer, Berlin, 2005), pp. 440\u2013456"},{"key":"9153_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1007\/11535218_16","volume-title":"Advances in Cryptology\u2014CRYPTO 2005","author":"D. Boneh","year":"2005","unstructured":"D. Boneh, C. Gentry, B. Waters, Collusion resistant broadcast encryption with short ciphertexts and private keys, in Advances in Cryptology\u2014CRYPTO 2005, Santa Barbara, CA, USA, August 14\u201318, ed. by V. Shoup. Lecture Notes in Computer Science, vol.\u00a03621 (Springer, Berlin, 2005), pp. 258\u2013275"},{"key":"9153_CR11","first-page":"4","volume-title":"ACM CCS 10: The 17th Conference on Computer and Communications Security","author":"D. Boneh","year":"2010","unstructured":"D. Boneh, H.W. Montgomery, A. Raghunathan, Algebraic pseudorandom functions with improved efficiency from the augmented cascade, in ACM CCS 10: The 17th Conference on Computer and Communications Security, Chicago, Illinois, USA, October\u00a04\u20138, ed. by E. Al-Shaer, A.D. Keromytis, V. Shmatikov (ACM Press, New York, 2010), pp. 4\u20138"},{"key":"9153_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1007\/978-3-642-00457-5_33","volume-title":"TCC 2009: The 6th Theory of Cryptography Conference","author":"Z. Brakerski","year":"2009","unstructured":"Z. Brakerski, S. Goldwasser, G.N. Rothblum, V. Vaikuntanathan, Weak verifiable random functions, in TCC 2009: The 6th Theory of Cryptography Conference, March 15\u201317, ed. by R. Omer. Lecture Notes in Computer Science, vol.\u00a05444 (Springer, Berlin, 2009), pp. 558\u2013576"},{"key":"9153_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/3-540-39200-9_16","volume-title":"Advances in Cryptology\u2014EUROCRYPT 2003","author":"R. Canetti","year":"2003","unstructured":"R. Canetti, S. Halevi, J. Katz, A forward-secure public-key encryption scheme, in Advances in Cryptology\u2014EUROCRYPT 2003, Warsaw, Poland, May\u00a04\u20138, ed. by E. Biham. Lecture Notes in Computer Science, vol.\u00a02656 (Springer, Berlin, 2003), pp. 255\u2013271"},{"key":"9153_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1007\/978-3-642-13190-5_27","volume-title":"Advances in Cryptology\u2014EUROCRYPT 2010","author":"D. Cash","year":"2010","unstructured":"D. Cash, D. Hofheinz, E. Kiltz, C. Peikert, Bonsai trees, or how to delegate a lattice basis, in Advances in Cryptology\u2014EUROCRYPT 2010, French Riviera, May 30\u2013June 3, ed. by H. Gilbert. Lecture Notes in Computer Science, vol.\u00a06110 (Springer, Berlin, 2010), pp. 523\u2013552"},{"key":"9153_CR15","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1007\/s00145-011-9105-2","volume":"25","author":"D. Cash","year":"2012","unstructured":"D. Cash, D. Hofheinz, E. Kiltz, C. Peikert, Bonsai trees, or how to delegate a lattice basis. J. Cryptol.\n                  25, 601\u2013639 (2012)","journal-title":"J. Cryptol."},{"key":"9153_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/978-3-540-74143-5_17","volume-title":"Advances in Cryptology\u2014CRYPTO 2007","author":"M. Chase","year":"2007","unstructured":"M. Chase, A. Lysyanskaya, Simulatable VRFs with applications to multi-theorem NIZK, in Advances in Cryptology\u2014CRYPTO 2007, Santa Barbara, CA, USA, August 19\u201323, ed. by A. Menezes. Lecture Notes in Computer Science, vol.\u00a04622 (Springer, Berlin, 2007), pp. 303\u2013322"},{"key":"9153_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/11761679_1","volume-title":"Advances in Cryptology\u2014EUROCRYPT 2006","author":"J.H. Cheon","year":"2006","unstructured":"J.H. Cheon, Security analysis of the strong Diffie\u2013Hellman problem, in Advances in Cryptology\u2014EUROCRYPT 2006, St. Petersburg, Russia, May\u00a028\u2013June\u00a01, ed. by S. Vaudenay. Lecture Notes in Computer Science, vol.\u00a04004 (Springer, Berlin, 2006), pp. 1\u201311"},{"key":"9153_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1007\/978-3-540-76900-2_31","volume-title":"Advances in Cryptology\u2014ASIACRYPT 2007","author":"R. Cramer","year":"2007","unstructured":"R. Cramer, G. Hanaoka, D. Hofheinz, H. Imai, E. Kiltz, R. Pass, A. Shelat, V. Vaikuntanathan, Bounded CCA2-secure encryption, in Advances in Cryptology\u2014ASIACRYPT 2007, Kuching, Malaysia, December\u00a02\u20136, ed. by K. Kurosawa. Lecture Notes in Computer Science, vol.\u00a04833 (Springer, Berlin, 2007), pp. 502\u2013518"},{"issue":"6","key":"9153_CR19","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1109\/TIT.1976.1055638","volume":"22","author":"W. Diffie","year":"1976","unstructured":"W. Diffie, M.E. Hellman, New directions in cryptography. IEEE Trans. Inf. Theory\n                  22(6), 644\u2013654 (1976)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"9153_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/3-540-36288-6_1","volume-title":"PKC 2003: The 6th International Workshop on Theory and Practice in Public Key Cryptography","author":"Y. Dodis","year":"2003","unstructured":"Y. Dodis, Efficient construction of (distributed) verifiable random functions, in PKC 2003: The 6th International Workshop on Theory and Practice in Public Key Cryptography, Miami, USA, January\u00a06\u20138, ed. by Y. Desmedt. Lecture Notes in Computer Science, vol.\u00a02567 (Springer, Berlin, 2003), pp. 1\u201317"},{"key":"9153_CR21","unstructured":"Y. Dodis, P. Puniya, Verifiable random permutations. Cryptology ePrint Archive, Report 2006\/078, 2006. \n                    http:\/\/eprint.iacr.org\/"},{"key":"9153_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1007\/978-3-540-30580-4_28","volume-title":"PKC 2005: the 8th International Workshop on Theory and Practice in Public Key Cryptography, Les Diablerets","author":"Y. Dodis","year":"2005","unstructured":"Y. Dodis, A. Yampolskiy, A verifiable random function with short proofs and keys, in PKC 2005: the 8th International Workshop on Theory and Practice in Public Key Cryptography, Les Diablerets, Les Diablerets, Switzerland, January\u00a023\u201326, ed. by S. Vaudenay. Lecture Notes in Computer Science, vol.\u00a03386 (Springer, Berlin, 2005), pp. 416\u2013431"},{"key":"9153_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/3-540-46035-7_5","volume-title":"Advances in Cryptology\u2014EUROCRYPT 2002","author":"Y. Dodis","year":"2002","unstructured":"Y. Dodis, J. Katz, S. Xu, M. Yung, Key-insulated public key cryptosystems, in Advances in Cryptology\u2014EUROCRYPT 2002, Amsterdam, The Netherlands, April\u00a028\u2013May\u00a02, ed. by L.R. Knudsen. Lecture Notes in Computer Science, vol.\u00a02332 (Springer, Berlin, 2002), pp. 65\u201382"},{"key":"9153_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1007\/3-540-39568-7_2","volume-title":"Advances in Cryptology\u2014CRYPTO\u201984","author":"T. ElGamal","year":"1985","unstructured":"T. ElGamal, A public key cryptosystem and a signature scheme based on discrete logarithms, in Advances in Cryptology\u2014CRYPTO\u201984, Santa Barbara, CA, USA, August 19\u201323, ed. by G.R. Blakley, D. Chaum. Lecture Notes in Computer Science, vol.\u00a0196 (Springer, Berlin, 1985), pp. 10\u201318"},{"key":"9153_CR25","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/BF02772959","volume":"51","author":"P. Erd\u00f6s","year":"1985","unstructured":"P. Erd\u00f6s, P. Frankel, Z. Furedi, Families of finite sets in which no set is covered by the union of r others. Isr. J. Math.\n                  51, 79\u201389 (1985)","journal-title":"Isr. J. Math."},{"key":"9153_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"636","DOI":"10.1007\/978-3-642-28914-9_36","volume-title":"TCC 2012: The 9th Theory of Cryptography Conference","author":"D. Fiore","year":"2012","unstructured":"D. Fiore, D. Schr\u00f6der, Uniqueness is a different story: impossibility of verifiable random functions from trapdoor permutations, in TCC 2012: The 9th Theory of Cryptography Conference, Taormina, Sicily, Italy, March 19\u201321, ed. by R. Cramer. Lecture Notes in Computer Science, vol.\u00a07194 (Springer, Berlin, 2012), pp. 636\u2013653"},{"key":"9153_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1007\/11761679_27","volume-title":"Advances in Cryptology\u2014EUROCRYPT 2006","author":"C. Gentry","year":"2006","unstructured":"C. Gentry, Practical identity-based encryption without random oracles, in Advances in Cryptology\u2014EUROCRYPT 2006, St. Petersburg, Russia, May 28\u2013June 1, ed. by S. Vaudenay. Lecture Notes in Computer Science, vol.\u00a04004 (Springer, Berlin, 2006), pp. 445\u2013464"},{"key":"9153_CR28","first-page":"25","volume-title":"21st ACM STOC Annual ACM Symposium on Theory of Computing","author":"O. Goldreich","year":"1989","unstructured":"O. Goldreich, L.A. Levin, A hard-core predicate for all one-way functions, in 21st ACM STOC Annual ACM Symposium on Theory of Computing, Seattle, Washington, USA, May\u00a015\u201317 (ACM Press, New York, 1989), pp. 25\u201332"},{"key":"9153_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1007\/3-540-48071-4_16","volume-title":"Advances in Cryptology\u2014CRYPTO\u201992","author":"S. Goldwasser","year":"1993","unstructured":"S. Goldwasser, R. Ostrovsky, Invariant signatures and non-interactive zero-knowledge proofs are equivalent (extended abstract), in Advances in Cryptology\u2014CRYPTO\u201992, Santa Barbara, CA, USA, August 16\u201320, ed. by E.F. Brickell. Lecture Notes in Computer Science, vol.\u00a0740 (Springer, Berlin, 1993), pp. 228\u2013245"},{"issue":"4","key":"9153_CR30","doi-asserted-by":"publisher","first-page":"1364","DOI":"10.1137\/S0097539793244708","volume":"28","author":"J. H\u00e5stad","year":"1999","unstructured":"J. H\u00e5stad, R. Impagliazzo, L.A. Levin, M. Luby, A pseudorandom generator from any one-way function. SIAM J. Comput.\n                  28(4), 1364\u20131396 (1999)","journal-title":"SIAM J. Comput."},{"key":"9153_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/978-3-540-24660-2_6","volume-title":"Topics in Cryptology\u2014CT-RSA 2004","author":"S.-H. Heng","year":"2004","unstructured":"S.-H. Heng, K. Kurosawa, k-resilient identity-based encryption in the standard model, in Topics in Cryptology\u2014CT-RSA 2004, San Francisco, CA, USA, February\u00a023\u201327, ed. by T. Okamoto. Lecture Notes in Computer Science, vol.\u00a02964 (Springer, Berlin, 2004), pp. 67\u201380"},{"key":"9153_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/978-3-642-01001-9_19","volume-title":"Advances in Cryptology\u2014EUROCRYPT 2009","author":"S. Hohenberger","year":"2009","unstructured":"S. Hohenberger, B. Waters, Realizing hash-and-sign signatures under standard assumptions, in Advances in Cryptology\u2014EUROCRYPT 2009, Cologne, Germany, April\u00a026\u201330, ed. by A. Joux. Lecture Notes in Computer Science, vol.\u00a05479 (Springer, Berlin, 2009), pp. 333\u2013350"},{"key":"9153_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"656","DOI":"10.1007\/978-3-642-13190-5_33","volume-title":"Advances in Cryptology\u2014EUROCRYPT 2010","author":"S. Hohenberger","year":"2010","unstructured":"S. Hohenberger, B. Waters, Constructing verifiable random functions with large input spaces, in Advances in Cryptology\u2014EUROCRYPT 2010, French Riviera, May 30\u2013June 3, ed. by H. Gilbert. Lecture Notes in Computer Science, vol.\u00a06110 (Springer, Berlin, 2010), pp. 656\u2013672"},{"key":"9153_CR34","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"590","DOI":"10.1007\/978-3-540-24676-3_35","volume-title":"Advances in Cryptology\u2014EUROCRYPT 2004","author":"S. Jarecki","year":"2004","unstructured":"S. Jarecki, V. Shmatikov, Handcuffing big brother: an abuse-resilient transaction escrow scheme, in Advances in Cryptology\u2014EUROCRYPT 2004, Interlaken, Switzerland, May 2\u20136, ed. by C. Cachin, J. Camenisch. Lecture Notes in Computer Science, vol.\u00a03027 (Springer, Berlin, 2004), pp. 590\u2013608"},{"key":"9153_CR35","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1007\/3-540-48405-1_38","volume-title":"Advances in Cryptology\u2014CRYPTO\u201999","author":"R. Kumar","year":"1999","unstructured":"R. Kumar, S. Rajagopalan, A. Sahai, Coding constructions for blacklisting problems without computational assumptions, in Advances in Cryptology\u2014CRYPTO\u201999, Santa Barbara, CA, USA, August 15\u201319, ed. by M.J. Wiener. Lecture Notes in Computer Science, vol.\u00a01666 (Springer, Berlin, 1999), pp. 609\u2013623"},{"key":"9153_CR36","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1007\/11593447_10","volume-title":"Advances in Cryptology\u2014ASIACRYPT 2005","author":"M. Liskov","year":"2005","unstructured":"M. Liskov, Updatable zero-knowledge databases, in Advances in Cryptology\u2014ASIACRYPT 2005, Chennai, India, December 4\u20138, ed. by B.K. Roy. Lecture Notes in Computer Science, vol.\u00a03788 (Springer, Berlin, 2005), pp. 174\u2013198"},{"key":"9153_CR37","doi-asserted-by":"crossref","unstructured":"M. Luby, C. Rackoff, How to construct pseudorandom permutations from pseudorandom functions. SIAM J. Comput.\n                  17(2) (1988)","DOI":"10.1137\/0217022"},{"key":"9153_CR38","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1007\/3-540-45708-9_38","volume-title":"Advances in Cryptology\u2014CRYPTO 2002","author":"A. Lysyanskaya","year":"2002","unstructured":"A. Lysyanskaya, Unique signatures and verifiable random functions from the DH-DDH separation, in Advances in Cryptology\u2014CRYPTO 2002, Santa Barbara, CA, USA, August 18\u201322, ed. by M. Yung. Lecture Notes in Computer Science, vol.\u00a02442 (Springer, Berlin, 2002), pp. 597\u2013612"},{"key":"9153_CR39","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"542","DOI":"10.1007\/3-540-44647-8_32","volume-title":"Advances in Cryptology\u2014CRYPTO 2001","author":"S. Micali","year":"2001","unstructured":"S. Micali, L. Reyzin, Soundness in the public-key model, in Advances in Cryptology\u2014CRYPTO 2001, Santa Barbara, CA, USA, August 19\u201323, ed. by J. Kilian. Lecture Notes in Computer Science, vol.\u00a02139 (Springer, Berlin, 2001), pp. 542\u2013565"},{"key":"9153_CR40","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/3-540-45760-7_11","volume-title":"Topics in Cryptology\u2014CT-RSA 2002","author":"S. Micali","year":"2002","unstructured":"S. Micali, R.L. Rivest, Micropayments revisited, in Topics in Cryptology\u2014CT-RSA 2002, San Jose, CA, USA, February\u00a018\u201322, ed. by B. Preneel. Lecture Notes in Computer Science, vol.\u00a02271 (Springer, Berlin, 2002), pp. 149\u2013163"},{"key":"9153_CR41","first-page":"120","volume-title":"40th Annual Symposium on Foundations of Computer Science","author":"S. Micali","year":"1999","unstructured":"S. Micali, M.O. Rabin, S.P. Vadhan, Verifiable random functions, in 40th Annual Symposium on Foundations of Computer Science, New York, New York, USA, October\u00a017\u201319 (IEEE Computer Society Press, Los Alamitos, 1999), pp. 120\u2013130"},{"key":"9153_CR42","doi-asserted-by":"publisher","first-page":"458","DOI":"10.1109\/SFCS.1997.646134","volume-title":"38th Annual Symposium on Foundations of Computer Science","author":"M. Naor","year":"1997","unstructured":"M. Naor, O. Reingold, Number-theoretic constructions of efficient pseudo-random functions, in 38th Annual Symposium on Foundations of Computer Science, Miami Beach, Florida, October 19\u201322 (IEEE Computer Society Press, Los Alamitos, 1997), pp. 458\u2013467"},{"key":"9153_CR43","volume-title":"2003 Symposium on Cryptography and Information Security\u2014SCIS\u20192003","author":"R. Sakai","year":"2003","unstructured":"R. Sakai, M. Kasahara, Id based cryptosystems with pairing on elliptic curve, in 2003 Symposium on Cryptography and Information Security\u2014SCIS\u20192003, Hamamatsu, Japan (2003). \n                    http:\/\/eprint.iacr.org\/2003\/054"},{"key":"9153_CR44","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\u2014CRYPTO\u201984","author":"A. Shamir","year":"1985","unstructured":"A. Shamir, Identity-based cryptosystems and signature schemes, in Advances in Cryptology\u2014CRYPTO\u201984, Santa Barbara, CA, USA, August 19\u201323, ed. by G.R. Blakley, D. Chaum. Lecture Notes in Computer Science, vol.\u00a0196 (Springer, Berlin, 1985), pp. 47\u201353"},{"key":"9153_CR45","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139165464","volume-title":"A Computational Introduction to Number Theory and Algebra","author":"V. Shoup","year":"2005","unstructured":"V. Shoup, A Computational Introduction to Number Theory and Algebra (Cambridge University Press, Cambridge, 2005)"},{"key":"9153_CR46","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1007\/11426639_7","volume-title":"Advances in Cryptology\u2014EUROCRYPT 2005","author":"B.R. Waters","year":"2005","unstructured":"B.R. Waters, Efficient identity-based encryption without random oracles, in Advances in Cryptology\u2014EUROCRYPT 2005, Aarhus, Denmark, May\u00a022\u201326, ed. by R. Cramer. Lecture Notes in Computer Science, vol.\u00a03494 (Springer, Berlin, 2005), pp. 114\u2013127"}],"container-title":["Journal of Cryptology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00145-013-9153-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00145-013-9153-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00145-013-9153-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00145-013-9153-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,8]],"date-time":"2020-04-08T08:11:34Z","timestamp":1586333494000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00145-013-9153-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,5,25]]},"references-count":46,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2014,7]]}},"alternative-id":["9153"],"URL":"https:\/\/doi.org\/10.1007\/s00145-013-9153-x","relation":{},"ISSN":["0933-2790","1432-1378"],"issn-type":[{"value":"0933-2790","type":"print"},{"value":"1432-1378","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,5,25]]},"assertion":[{"value":"4 January 2010","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 May 2013","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}