{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T23:25:14Z","timestamp":1769297114906,"version":"3.49.0"},"publisher-location":"Berlin, Heidelberg","reference-count":33,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540345466","type":"print"},{"value":"9783540345473","type":"electronic"}],"license":[{"start":{"date-parts":[[2006,1,1]],"date-time":"2006-01-01T00:00:00Z","timestamp":1136073600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006]]},"DOI":"10.1007\/11761679_21","type":"book-chapter","created":{"date-parts":[[2006,7,4]],"date-time":"2006-07-04T14:11:19Z","timestamp":1152022279000},"page":"339-358","source":"Crossref","is-referenced-by-count":242,"title":["Perfect Non-interactive Zero Knowledge for NP"],"prefix":"10.1007","author":[{"given":"Jens","family":"Groth","sequence":"first","affiliation":[]},{"given":"Rafail","family":"Ostrovsky","sequence":"additional","affiliation":[]},{"given":"Amit","family":"Sahai","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"21_CR1","doi-asserted-by":"crossref","unstructured":"Aiello, W., H\u00e5stad, J.: Perfect zero-knowledge languages can be recognized in two rounds. In: Proceedings of FOCS 1987, pp. 439\u2013448 (1987)","DOI":"10.1109\/SFCS.1987.47"},{"issue":"6","key":"21_CR2","doi-asserted-by":"publisher","first-page":"1084","DOI":"10.1137\/0220068","volume":"20","author":"M. Blum","year":"1991","unstructured":"Blum, M., De Santis, A., Micali, S., Persiano, G.: Noninteractive zero-knowledge. SIAM Jornal of Computation\u00a020(6), 1084\u20131118 (1991)","journal-title":"SIAM Jornal of Computation"},{"key":"21_CR3","doi-asserted-by":"crossref","unstructured":"Blum, M., Feldman, P., Micali, S.: Non-interactive zero-knowledge and its applications. In: Proceedings of STOC 1988, pp. 103\u2013112 (1988)","DOI":"10.1145\/62212.62222"},{"key":"21_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","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)"},{"issue":"2","key":"21_CR5","first-page":"156","volume":"37","author":"G. Brassard","year":"1988","unstructured":"Brassard, G., Chaum, D., Cr\u00e8peau, C.: Minimum disclosure proofs of knowledge. JCSS\u00a037(2), 156\u2013189 (1988)","journal-title":"JCSS"},{"key":"21_CR6","doi-asserted-by":"crossref","unstructured":"Brassard, G., Cr\u00e8peau, C.: Non-transitive transfer of confidence: A perfect zero-knowledge interactive protocol for sat and beyond. In: Proceedings of FOCS 1986, pp. 188\u2013195 (1986)","DOI":"10.1109\/SFCS.1986.33"},{"key":"21_CR7","unstructured":"Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: Proceedings of FOCS 2001, pp. 136\u2013145 (2001), Full paper available at: http:\/\/eprint.iacr.org\/2000\/067"},{"key":"21_CR8","unstructured":"Canetti, R., Lindell, Y., Ostrovsky, R., Sahai, A.: Universally composable two-party and multi-party secure computation. In: Proceedings of STOC 2002, pp. 494\u2013503 (2002), Full paper available at: http:\/\/eprint.iacr.org\/2002\/140"},{"key":"21_CR9","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":"21_CR10","doi-asserted-by":"crossref","unstructured":"Damg\u00e5rd, I., Groth, J.: Non-interactive and reusable non-malleable commitment schemes. In: Proceedings of STOC 2003, pp. 426\u2013437 (2003)","DOI":"10.1145\/780542.780605"},{"key":"21_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"566","DOI":"10.1007\/3-540-44647-8_33","volume-title":"Advances in Cryptology - CRYPTO 2001","author":"A. Santis De","year":"2001","unstructured":"De Santis, A., Di Crescenzo, G., Ostrovsky, R., Persiano, G., Sahai, A.: Robust non-interactive zero knowledge. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol.\u00a02139, pp. 566\u2013598. Springer, Heidelberg (2001)"},{"key":"21_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/3-540-48523-6_24","volume-title":"Automata, Languages and Programming","author":"A. Santis De","year":"1999","unstructured":"De Santis, A., Di Crescenzo, G., Persiano, G.: Non-interactive zero-knowledge: A low-randomness characterization of np. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol.\u00a01644, pp. 271\u2013280. Springer, Heidelberg (1999)"},{"key":"21_CR13","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. Santis De","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)"},{"key":"21_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"784","DOI":"10.1007\/BFb0055102","volume-title":"Automata, Languages and Programming","author":"A. Santis De","year":"1998","unstructured":"De Santis, A., Di Crescenzo, G., Persiano, G., Yung, M.: Image density is complete for non-interactive-szk. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol.\u00a01443, pp. 784\u2013795. Springer, Heidelberg (1998)"},{"key":"21_CR15","doi-asserted-by":"crossref","unstructured":"Di Crescenzo, G., Ishai, Y., Ostrovsky, R.: Non-interactive and non-malleable commitment. In: Proceedings of STOC 1998, pp. 141\u2013150 (1998)","DOI":"10.1145\/276698.276722"},{"key":"21_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1007\/3-540-44987-6_4","volume-title":"Advances in Cryptology - EUROCRYPT 2001","author":"G. Crescenzo Di","year":"2001","unstructured":"Di Crescenzo, G., Katz, J., Ostrovsky, R., Smith, A.: Efficient and non-interactive non-malleable commitment. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol.\u00a02045, pp. 40\u201359. Springer, Heidelberg (2001)"},{"issue":"2","key":"21_CR17","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 J. of Computing\u00a030(2), 391\u2013437 (2000), Earlier version at STOC 1991","journal-title":"SIAM J. of Computing"},{"issue":"1","key":"21_CR18","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 J. Comput.\u00a029(1), 1\u201328 (1999), Earlier version entitled Multiple Non-Interactive Zero Knowledge Proofs Based on a Single Random String appeared at FOCS 1990","journal-title":"SIAM J. Comput."},{"key":"21_CR19","doi-asserted-by":"crossref","unstructured":"Fortnow, L.: The complexity of perfect zero-knowledge. In: Proceedings of STOC 1987, pp. 204\u2013209 (1987)","DOI":"10.1145\/28395.28418"},{"key":"21_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/3-540-39200-9_11","volume-title":"Advances in Cryptology \u2013 EUROCRPYT 2003","author":"J.A. Garay","year":"2003","unstructured":"Garay, J.A., MacKenzie, P.D., Yang, K.: Strengthening zero-knowledge protocols using signatures. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol.\u00a02656, pp. 177\u2013194. Springer, Heidelberg (2003), Full paper available at: http:\/\/eprint.iacr.org\/2003\/037"},{"key":"21_CR21","doi-asserted-by":"crossref","unstructured":"Goldreich, O., Levin, L.A.: A hard-core predicate for all one-way functions. In: proceedings of STOC 1989, pp. 25\u201332 (1989)","DOI":"10.1145\/73007.73010"},{"key":"21_CR22","doi-asserted-by":"publisher","first-page":"1116","DOI":"10.1137\/S0097539795280524","volume":"27","author":"O. Goldreich","year":"1998","unstructured":"Goldreich, O., Ostrovsky, R., Petrank, E.: Computational complexity and knowledge complexity. SIAM J. Comput.\u00a027, 1116\u20131141 (1998)","journal-title":"SIAM J. Comput."},{"key":"21_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"467","DOI":"10.1007\/3-540-48405-1_30","volume-title":"Advances in Cryptology - CRYPTO \u201999","author":"O. Goldreich","year":"1999","unstructured":"Goldreich, O., Sahai, A., Vadhan, S.P.: Can statistical zero knowledge be made non-interactive? or on the relationship of szk and niszk. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol.\u00a01666, pp. 467\u2013484. Springer, Heidelberg (1999)"},{"key":"21_CR24","unstructured":"Groth, J.: Honest verifier zero-knowledge arguments applied. Dissertation Series DS-04-3, BRICS, PhD thesis. xii+119\u00a0pp (2004)"},{"key":"21_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1007\/978-3-540-30576-7_4","volume-title":"Theory of Cryptography","author":"J. Groth","year":"2005","unstructured":"Groth, J.: Cryptography in subgroups of \u2124 n *. In: Kilian, J. (ed.) TCC 2005. LNCS, vol.\u00a03378, pp. 50\u201365. Springer, Heidelberg (2005)"},{"key":"21_CR26","unstructured":"Groth, J., Ostrovsky, R., Sahai, A.: Perfect non-interactive zero-knowledge for np. ECCC Report TR05-097 (2005), http:\/\/eccc.uni-trier.de\/eccc-reports\/2005\/TR05-097\/index.html"},{"issue":"1","key":"21_CR27","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":"21_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1007\/978-3-540-24676-3_23","volume-title":"Advances in Cryptology - EUROCRYPT 2004","author":"P.D. MacKenzie","year":"2004","unstructured":"MacKenzie, P.D., Yang, K.: On simulation-sound trapdoor commitments. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol.\u00a03027, pp. 382\u2013400. Springer, Heidelberg (2004), Full paper available at: http:\/\/eprint.iacr.org\/2003\/252"},{"key":"21_CR29","doi-asserted-by":"crossref","unstructured":"Ostrovsky, R.: One-way functions, hard on average problems, and statistical zero-knowledge proofs. In: Proceedings of Structure in Complexity Theory Conference, pp. 133\u2013138 (1991)","DOI":"10.1109\/SCT.1991.160253"},{"key":"21_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1007\/978-3-540-45146-4_19","volume-title":"Advances in Cryptology - CRYPTO 2003","author":"R. Pass","year":"2003","unstructured":"Pass, R.: On deniability in the common reference string and random oracle model. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol.\u00a02729, pp. 316\u2013337. Springer, Heidelberg (2003)"},{"key":"21_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"118","DOI":"10.1007\/11535218_8","volume-title":"Advances in Cryptology \u2013 CRYPTO 2005","author":"R. Pass","year":"2005","unstructured":"Pass, R., Shelat, A.: Characterizing non-interactive zero-knowledge in the public and secret parameter models. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol.\u00a03621, pp. 118\u2013134. Springer, Heidelberg (2005)"},{"key":"21_CR32","doi-asserted-by":"crossref","unstructured":"Sahai, A.: Non-malleable non-interactive zero-knowledge and adaptive chosen-ciphertext security. In: Proceedings of FOCS 2001, pp. 543\u2013553 (2001)","DOI":"10.1109\/SFFCS.1999.814628"},{"issue":"2","key":"21_CR33","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1145\/636865.636868","volume":"50","author":"A. Sahai","year":"2003","unstructured":"Sahai, A., Vadhan, S.P.: A complete problem for statistical zero knowledge. J. ACM\u00a050(2), 196\u2013249 (2003)","journal-title":"J. ACM"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology - EUROCRYPT 2006"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11761679_21","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,9]],"date-time":"2025-01-09T18:52:57Z","timestamp":1736448777000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11761679_21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006]]},"ISBN":["9783540345466","9783540345473"],"references-count":33,"URL":"https:\/\/doi.org\/10.1007\/11761679_21","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006]]}}}