{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T13:28:16Z","timestamp":1778160496536,"version":"3.51.4"},"publisher-location":"Berlin, Heidelberg","reference-count":24,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783662493861","type":"print"},{"value":"9783662493878","type":"electronic"}],"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"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-662-49387-8_14","type":"book-chapter","created":{"date-parts":[[2016,2,17]],"date-time":"2016-02-17T14:25:41Z","timestamp":1455719141000},"page":"359-385","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Reducing Depth in Constrained PRFs: From Bit-Fixing to $$\\mathbf {NC}^{1}$$"],"prefix":"10.1007","author":[{"given":"Nishanth","family":"Chandran","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Srinivasan","family":"Raghuraman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dhinakaran","family":"Vinayagamurthy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,2,18]]},"reference":[{"key":"14_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/978-3-662-46497-7_2","volume-title":"Theory of Cryptography","author":"A Banerjee","year":"2015","unstructured":"Banerjee, A., Fuchsbauer, G., Peikert, C., Pietrzak, K., Stevens, S.: Key-homomorphic constrained pseudorandom functions. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 31\u201360. Springer, Heidelberg (2015)"},{"key":"14_CR2","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1007\/978-3-642-54631-0_29","volume-title":"Public-Key Cryptography \u2013 PKC 2014","author":"Elette Boyle","year":"2014","unstructured":"Boyle, E., Goldwasser, S., Ivan, I.: Functional signatures and pseudorandom functions. In: Public Key Cryptography, pp. 501\u2013519 (2014)"},{"key":"14_CR3","series-title":"Lecture Notes in Computer Science","first-page":"1","volume-title":"Theory of Cryptography","author":"Z Brakerski","year":"2015","unstructured":"Brakerski, Z., Vaikuntanathan, V.: Constrained key-homomorphic PRFs from standard lattice assumptions. Or: how to secretly embed a circuit in your PRF. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 1\u201330. Springer, Heidelberg (2015)"},{"key":"14_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"280","DOI":"10.1007\/978-3-642-42045-0_15","volume-title":"Advances in Cryptology - ASIACRYPT 2013","author":"D Boneh","year":"2013","unstructured":"Boneh, D., Waters, B.: Constrained pseudorandom functions and their applications. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 280\u2013300. Springer, Heidelberg (2013)"},{"key":"14_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/978-3-662-46800-5_1","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2015","author":"JH Cheon","year":"2015","unstructured":"Cheon, J.H., Han, K., Lee, C., Ryu, H., Stehl\u00e9, D.: Cryptanalysis of the multilinear map over the integers. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015, Part I. LNCS, vol. 9056, pp. 3\u201312. Springer, Heidelberg (2015)"},{"key":"14_CR6","unstructured":"Cheon, J.H., Lee, C., Ryu, H.: Cryptanalysis of the new CLT multilinear maps. Cryptology ePrint Archive, Report 2015\/934 (2015)"},{"key":"14_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"476","DOI":"10.1007\/978-3-642-40041-4_26","volume-title":"Advances in Cryptology \u2013 CRYPTO 2013","author":"J-S Coron","year":"2013","unstructured":"Coron, J.-S., Lepoint, T., Tibouchi, M.: Practical multilinear maps over the integers. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 476\u2013493. Springer, Heidelberg (2013)"},{"key":"14_CR8","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/978-3-662-47989-6_13","volume-title":"Advances in Cryptology \u2013 CRYPTO 2015","author":"J-S Coron","year":"2015","unstructured":"Coron, J.-S., Lepoint, T., Tibouchi, M.: New multilinear maps over the integers. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015, Part I. LNCS, vol. 9215, pp. 267\u2013286. Springer, Heidelberg (2015)"},{"key":"14_CR9","unstructured":"Chandran, N., Raghuraman, S., Vinayagamurthy, D.: Constrained pseudorandom functions: verifiable and delegatable. IACR Cryptology ePrint Archive, 2014:522 (2014)"},{"key":"14_CR10","doi-asserted-by":"crossref","unstructured":"Chandran, N., Raghuraman, S., Vinayagamurthy, D.: Reducing depth in constrained PRFs: from bit-fixing to \n                      \n                        \n                      \n                      \n$$\\rm NC^{1}$$\n\n                    . IACR Cryptology ePrint Archive, 2015:829 (2015)","DOI":"10.1007\/978-3-662-49387-8_14"},{"key":"14_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1007\/978-3-662-45608-8_5","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2014","author":"G Fuchsbauer","year":"2014","unstructured":"Fuchsbauer, G., Konstantinov, M., Pietrzak, K., Rao, V.: Adaptive security of constrained PRFs. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014, Part II. LNCS, vol. 8874, pp. 82\u2013101. Springer, Heidelberg (2014)"},{"key":"14_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/978-3-319-10879-7_7","volume-title":"Security and Cryptography for Networks","author":"G Fuchsbauer","year":"2014","unstructured":"Fuchsbauer, G.: Constrained verifiable random functions. In: Abdalla, M., De Prisco, R. (eds.) SCN 2014. LNCS, vol. 8642, pp. 95\u2013114. Springer, Heidelberg (2014)"},{"key":"14_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-38348-9_1","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2013","author":"S Garg","year":"2013","unstructured":"Garg, S., Gentry, C., Halevi, S.: Candidate multilinear maps from ideal lattices. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 1\u201317. Springer, Heidelberg (2013)"},{"key":"14_CR14","unstructured":"Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: 54th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2013, 26\u201329 October, 2013, Berkeley, CA, USA, pp. 40\u201349 (2013)"},{"key":"14_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1007\/978-3-642-40084-1_27","volume-title":"Advances in Cryptology \u2013 CRYPTO 2013","author":"S Garg","year":"2013","unstructured":"Garg, S., Gentry, C., Halevi, S., Sahai, A., Waters, B.: Attribute-based encryption for circuits from multilinear maps. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 479\u2013499. Springer, Heidelberg (2013)"},{"key":"14_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"498","DOI":"10.1007\/978-3-662-46497-7_20","volume-title":"Theory of Cryptography","author":"C Gentry","year":"2015","unstructured":"Gentry, C., Gorbunov, S., Halevi, S.: Graph-induced multilinear maps from lattices. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015, Part II. LNCS, vol. 9015, pp. 498\u2013527. Springer, Heidelberg (2015)"},{"issue":"4","key":"14_CR17","doi-asserted-by":"publisher","first-page":"792","DOI":"10.1145\/6490.6503","volume":"33","author":"O Goldreich","year":"1986","unstructured":"Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions. J. ACM 33(4), 792\u2013807 (1986)","journal-title":"J. ACM"},{"key":"14_CR18","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 Conference on Computer and Communications Security, pp. 89\u201398 (2006)","DOI":"10.1145\/1180405.1180418"},{"key":"14_CR19","doi-asserted-by":"crossref","unstructured":"Gorbunov, S., Vaikuntanathan, V., Wee, H.: Attribute-based encryption for circuits. In: STOC, pp. 545\u2013554 (2013)","DOI":"10.1145\/2488608.2488677"},{"key":"14_CR20","unstructured":"Hu, Y., Jia, H.: Cryptanalysis of GGH map. IACR Cryptology ePrint Archive, 2015:301 (2015)"},{"key":"14_CR21","unstructured":"Hofheinz, D., Kamath, A., Koppula, V., Waters, B.: Adaptively secure constrained pseudorandom functions. IACR Cryptology ePrint Archive, 2014:720 (2014)"},{"key":"14_CR22","unstructured":"Kiayias, A., Papadopoulos, S., Triandopoulos, N., Zacharias, T.: Delegatable pseudorandom functions and applications. In: ACM SIGSAC Conference on Computer and Communications Security, CCS 2013, Berlin, Germany, 4\u20138 November, 2013, pp. 669\u2013684 (2013)"},{"key":"14_CR23","unstructured":"Minaud, B., Fouque, P.-A.: Cryptanalysis of the new multilinear map over the integers. Cryptology ePrint Archive, Report 2015\/941 (2015)"},{"key":"14_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","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. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 457\u2013473. Springer, Heidelberg (2005)"}],"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\/978-3-662-49387-8_14","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,18]],"date-time":"2020-02-18T11:20:50Z","timestamp":1582024850000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-49387-8_14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783662493861","9783662493878"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-49387-8_14","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016]]},"assertion":[{"value":"18 February 2016","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}