{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T15:49:20Z","timestamp":1774021760332,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":36,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540789666","type":"print"},{"value":"9783540789673","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/978-3-540-78967-3_24","type":"book-chapter","created":{"date-parts":[[2008,4,4]],"date-time":"2008-04-04T00:11:30Z","timestamp":1207267890000},"page":"415-432","source":"Crossref","is-referenced-by-count":641,"title":["Efficient Non-interactive Proof Systems for Bilinear Groups"],"prefix":"10.1007","author":[{"given":"Jens","family":"Groth","sequence":"first","affiliation":[]},{"given":"Amit","family":"Sahai","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"24_CR1","unstructured":"Ballard, L., Green, M. de Medeiros, B., Monrose, F.: Correlation-resistant storage via keyword-searchable encryption. Cryptology ePrint Archive, Report 2005\/417 (2005), \n                  \n                    http:\/\/eprint.iacr.org\/2005\/417"},{"key":"24_CR2","unstructured":"Barreto, P.: The pairing-based crypto lounge (2006), \n                  \n                    http:\/\/paginas.terra.com.br\/informatica\/paulobarreto\/pblounge.html"},{"key":"24_CR3","unstructured":"Belenkiy, M., Chase, M., Kohlweiss, M., Lysyanskaya, A.: Non-interactive anonymous credentials. In: PACS 2000. LNCS (2008), \n                  \n                    http:\/\/eprint.iacr.org\/2007\/384"},{"key":"24_CR4","doi-asserted-by":"crossref","unstructured":"Blum, M., Feldman, P., Micali, S.: Non-interactive zero-knowledge and its applications. In: STOC, pp. 103\u2013112 (1988)","DOI":"10.1145\/62212.62222"},{"key":"24_CR5","unstructured":"Boneh, D.: Personal communication (2006)"},{"key":"24_CR6","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.\u00a03027, pp. 223\u2013238. Springer, Heidelberg (2004)"},{"key":"24_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","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.\u00a03152, pp. 443\u2013459. Springer, Heidelberg (2004)"},{"key":"24_CR8","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. (ed.) CRYPTO 2004. LNCS, vol.\u00a03152, pp. 41\u201355. Springer, Heidelberg (2004)"},{"key":"24_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1007\/978-3-540-24676-3_30","volume-title":"Advances in Cryptology - EUROCRYPT 2004","author":"D. Boneh","year":"2004","unstructured":"Boneh, D., Di Crescenzo, G., Ostrovsky, R., Persiano, G.: Public key encryption with keyword search. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol.\u00a03027, pp. 506\u2013522. Springer, Heidelberg (2004)"},{"issue":"3","key":"24_CR10","doi-asserted-by":"publisher","first-page":"586","DOI":"10.1137\/S0097539701398521","volume":"32","author":"D. Boneh","year":"2003","unstructured":"Boneh, D., Franklin, M.K.: Identity-based encryption from the Weil pairing. SIAM Journal of Computing\u00a032(3), 586\u2013615 (2003)","journal-title":"SIAM Journal of Computing"},{"key":"24_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/978-3-540-30576-7_18","volume-title":"Theory of Cryptography","author":"D. Boneh","year":"2005","unstructured":"Boneh, D., Goh, E.-J., Nissim, K.: Evaluating 2-DNF formulas on ciphertexts. In: Kilian, J. (ed.) TCC 2005. LNCS, vol.\u00a03378, pp. 325\u2013341. Springer, Heidelberg (2005)"},{"key":"24_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1007\/11761679_34","volume-title":"Advances in Cryptology - EUROCRYPT 2006","author":"D. Boneh","year":"2006","unstructured":"Boneh, D., Sahai, A., Waters, B.: Fully collusion resistant traitor tracing with short ciphertexts and private keys. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol.\u00a04004, pp. 573\u2013592. Springer, Heidelberg (2006)"},{"key":"24_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"427","DOI":"10.1007\/11761679_26","volume-title":"Advances in Cryptology - EUROCRYPT 2006","author":"X. Boyen","year":"2006","unstructured":"Boyen, X., Waters, B.: Compact group signatures without random oracles. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol.\u00a04004, pp. 427\u2013444. Springer, Heidelberg (2006)"},{"key":"24_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-540-71677-8_1","volume-title":"Public Key Cryptography \u2013 PKC 2007","author":"X. Boyen","year":"2007","unstructured":"Boyen, X., Waters, B.: Full-domain subgroup hiding and constant-size group signatures. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol.\u00a04450, pp. 1\u201315. Springer, Heidelberg (2007), \n                  \n                    http:\/\/www.cs.stanford.edu\/~xb\/pkc07\/"},{"key":"24_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1007\/978-3-540-73420-8_38","volume-title":"Automata, Languages and Programming","author":"N. Chandran","year":"2007","unstructured":"Chandran, N., Groth, J., Sahai, A.: Ring signatures of sub-linear size without random oracles. In: Arge, L., Cachin, C., Jurdzi\u0144ski, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol.\u00a04596, pp. 423\u2013434. Springer, Heidelberg (2007)"},{"key":"24_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/3-540-47555-9_28","volume-title":"Advances in Cryptology - EUROCRYPT \u201992","author":"I. Damg\u00e5rd","year":"1993","unstructured":"Damg\u00e5rd, I.: Non-interactive circuit based proofs and non-interactive perfect zero-knowledge with proprocessing. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol.\u00a0658, pp. 341\u2013355. Springer, Heidelberg (1993)"},{"key":"24_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1007\/3-540-45726-7_15","volume-title":"Randomization and Approximation Techniques in Computer Science","author":"A. De Santis","year":"2002","unstructured":"De Santis, A., Di Crescenzo, G., Persiano, G.: Randomness-optimal characterization of two NP proof systems. In: Rolim, J.D.P., Vadhan, S.P. (eds.) RANDOM 2002. LNCS, vol.\u00a02483, pp. 179\u2013193. Springer, Heidelberg (2002)"},{"issue":"2","key":"24_CR18","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1137\/S0097539795291562","volume":"30","author":"D. Dolev","year":"2000","unstructured":"Dolev, D., Dwork, C., Naor, M.: Non-malleable cryptography. SIAM Journal of Computing\u00a030(2), 391\u2013437 (2000)","journal-title":"SIAM Journal of Computing"},{"issue":"1","key":"24_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/S0097539792230010","volume":"29","author":"U. Feige","year":"1999","unstructured":"Feige, U., Lapidot, D., Shamir, A.: Multiple non-interactive zero knowledge proofs under general assumptions. SIAM Journal of Computing\u00a029(1), 1\u201328 (1999)","journal-title":"SIAM Journal of Computing"},{"key":"24_CR20","first-page":"201","volume":"7","author":"S.D. Galbraith","year":"2004","unstructured":"Galbraith, S.D., Rotger, V.: Easy decision Diffie-Hellman groups. London Mathematical Society Journal of Computation and Mathematics\u00a07, 201\u2013218 (2004)","journal-title":"London Mathematical Society Journal of Computation and Mathematics"},{"issue":"1","key":"24_CR21","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1137\/0218012","volume":"18","author":"S. Goldwasser","year":"1989","unstructured":"Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proofs. SIAM Journal of Computing\u00a018(1), 186\u2013208 (1989)","journal-title":"SIAM Journal of Computing"},{"key":"24_CR22","doi-asserted-by":"crossref","unstructured":"Goyal, V., Pandey, O., Sahai, A., Waters, B.: Attribute-based encryption for fine-grained access control of encrypted data. In: ACM CCS, pp. 89\u201398 (2006)","DOI":"10.1145\/1180405.1180418"},{"key":"24_CR23","series-title":"Lecture Notes in Artificial Intelligence","first-page":"444","volume-title":"Managing Knowledge in a World of Networks","author":"J. Groth","year":"2006","unstructured":"Groth, J.: Simulation-sound NIZK proofs for a practical language and constant size group signatures. In: Staab, S., Sv\u00e1tek, V. (eds.) EKAW 2006. LNCS (LNAI), vol.\u00a04248, pp. 444\u2013459. Springer, Heidelberg (2006), \n                  \n                    http:\/\/www.brics.dk\/~jg\/NIZKGroupSignFull.pdf"},{"key":"24_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1007\/978-3-540-76900-2_10","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2007","author":"J. Groth","year":"2007","unstructured":"Groth, J.: Fully anonymous group signatures without random oracles. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol.\u00a04833, pp. 164\u2013180. Springer, Heidelberg (2007), \n                  \n                    http:\/\/www.brics.dk\/~jg\/CertiSignFull.pdf"},{"key":"24_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/978-3-540-76900-2_4","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2007","author":"J. Groth","year":"2007","unstructured":"Groth, J., Lu, S.: A non-interactive shuffle with pairing based verifiability. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol.\u00a04833, pp. 51\u201367. Springer, Heidelberg (2007)"},{"key":"24_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/11818175_6","volume-title":"Advances in Cryptology - CRYPTO 2006","author":"J. Groth","year":"2006","unstructured":"Groth, J., Ostrovsky, R., Sahai, A.: Non-interactive zaps and new techniques for NIZK. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol.\u00a04117, pp. 97\u2013111. Springer, Heidelberg (2006)"},{"key":"24_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","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.\u00a04004, pp. 339\u2013358. Springer, Heidelberg (2006)"},{"key":"24_CR28","unstructured":"Groth, J. Sahai, A.: Efficient non-interactive proof systems for bilinear groups. Cryptology ePrint Archive, Report 2007\/155 (2007), \n                  \n                    http:\/\/eprint.iacr.org\/2007\/155"},{"issue":"1","key":"24_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s001459900032","volume":"11","author":"J. Kilian","year":"1998","unstructured":"Kilian, J., Petrank, E.: An efficient noninteractive zero-knowledge proof system for NP with general assumptions. Journal of Cryptology\u00a011(1), 1\u201327 (1998)","journal-title":"Journal of Cryptology"},{"key":"24_CR30","doi-asserted-by":"crossref","unstructured":"Micali, S.: Simple and fast optimistic protocols for fair electronic exchange. In: PODC, pp. 12\u201319 (2003)","DOI":"10.1145\/872035.872038"},{"key":"24_CR31","series-title":"London Mathematical Society Lecture Note Series","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1017\/CBO9780511546570.012","volume-title":"Advances in Elliptic Curve Cryptography","author":"K.G. Paterson","year":"2005","unstructured":"Paterson, K.G.: Cryptography from pairings. In: Blake, I.F., Seroussi, G., Smart, N.P. (eds.) Advances in Elliptic Curve Cryptography. London Mathematical Society Lecture Note Series, vol.\u00a0317, pp. 215\u2013251. Cambridge University Press, Cambridge (2005)"},{"key":"24_CR32","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.J.F. (ed.) EUROCRYPT 2005. LNCS, vol.\u00a03494, pp. 457\u2013473. Springer, Heidelberg (2005)"},{"key":"24_CR33","unstructured":"Scott, M.: Authenticated ID-based key exchange and remote log-in with simple token and PIN number. Cryptology ePrint Archive, Report 2002\/164 (2002), \n                  \n                    http:\/\/eprint.iacr.org\/2002\/164"},{"issue":"4","key":"24_CR34","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1007\/s00145-004-0313-x","volume":"17","author":"E.R. Verheul","year":"2004","unstructured":"Verheul, E.R.: Evidence that XTR is more secure than supersingular elliptic curve cryptosystems. Journal of Cryptology\u00a017(4), 277\u2013296 (2004)","journal-title":"Journal of Cryptology"},{"key":"24_CR35","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","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.J.F. (ed.) EUROCRYPT 2005. LNCS, vol.\u00a03494, pp. 114\u2013127. Springer, Heidelberg (2005)"},{"key":"24_CR36","unstructured":"Waters, B.: New techniques for slightly 2-homomorphic encryption, Manuscript (2006)"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 EUROCRYPT 2008"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-78967-3_24.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T07:05:48Z","timestamp":1619507148000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-78967-3_24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540789666","9783540789673"],"references-count":36,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-78967-3_24","relation":{},"subject":[]}}