{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,26]],"date-time":"2026-01-26T19:46:29Z","timestamp":1769456789663,"version":"3.49.0"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2015,11,23]],"date-time":"2015-11-23T00:00:00Z","timestamp":1448236800000},"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":[[2017,1]]},"DOI":"10.1007\/s00145-015-9221-5","type":"journal-article","created":{"date-parts":[[2015,11,23]],"date-time":"2015-11-23T18:38:08Z","timestamp":1448303888000},"page":"289-320","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Obfuscating Conjunctions"],"prefix":"10.1007","volume":"30","author":[{"given":"Zvika","family":"Brakerski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guy N.","family":"Rothblum","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,11,23]]},"reference":[{"key":"9221_CR1","doi-asserted-by":"crossref","unstructured":"B. Applebaum, Z. Brakerski, Obfuscating circuits via composite-order graded encoding, in Y. Dodis, J. B. Nielsen, editors, Theory of Cryptography\u201412th Theory of Cryptography Conference, TCC 2015, Warsaw, Poland, March 23\u201325, 2015, Proceedings, Part II. Lecture Notes in Computer Science, vol. 9015 (Springer, 2015), pp. 528\u2013556","DOI":"10.1007\/978-3-662-46497-7_21"},{"key":"9221_CR2","doi-asserted-by":"crossref","unstructured":"B. Adida, D. Wikstr\u00f6m, How to shuffle in public, in Vadhan [34], pp. 555\u2013574","DOI":"10.1007\/978-3-540-70936-7_30"},{"key":"9221_CR3","doi-asserted-by":"crossref","unstructured":"B. Barak, N. Bitansky, R. Canetti, Y. T. Kalai, O. Paneth, A. Sahai, Obfuscation for evasive functions, in Y. Lindell, editor, Theory of Cryptography\u201411th Theory of Cryptography Conference, TCC 2014, San Diego, CA, USA, February 24\u201326, 2014. Proceedings. Lecture Notes in Computer Science, vol. 8349 (Springer, 2014), pp. 26\u201351","DOI":"10.1007\/978-3-642-54242-8_2"},{"key":"9221_CR4","unstructured":"N. Bitansky, R. Canetti, On strong simulation and composable point obfuscation, in CRYPTO (2010), pp. 520\u2013537"},{"key":"9221_CR5","doi-asserted-by":"crossref","unstructured":"A. Boldyreva, S. Fehr, A. O\u2019Neill, On notions of security for deterministic encryption, and efficient constructions without random oracles, in D. Wagner, editor, CRYPTO. Lecture Notes in Computer Science, vol. 5157 (Springer, 2008), pp. 335\u2013359","DOI":"10.1007\/978-3-540-85174-5_19"},{"key":"9221_CR6","doi-asserted-by":"crossref","unstructured":"B. Barak, O. Goldreich, R. Impagliazzo, S. Rudich, A. Sahai, S. P. Vadhan, K. Yang, On the (im)possibility of obfuscating programs. J. ACM, 59(2), 6 (2012). Preliminary version in CRYPTO 2001","DOI":"10.1145\/2160158.2160159"},{"key":"9221_CR7","unstructured":"Z. Brakerski, G. N. Rothblum, Black-box obfuscation for d-cnfs, in Innovations in Theoretical Computer Science, ITCS\u201914, Princeton, NJ, USA, January 12\u201314, 2014 (2014), pp. 235\u2013250"},{"key":"9221_CR8","unstructured":"Z. Brakerski, G. N. Rothblum, Virtual black-box obfuscation for all circuits via generic graded encoding, in Theory of Cryptography\u201411th Theory of Cryptography Conference, TCC 2014, San Diego, CA, USA, February 24\u201326, 2014. Proceedings (2014), pp. 1\u201325"},{"key":"9221_CR9","first-page":"80","volume":"2002","author":"D Boneh","year":"2002","unstructured":"D. Boneh, A. Silverberg, Applications of multilinear forms to cryptography. IACR Crypt. ePrint Arch. 2002, 80 (2002)","journal-title":"IACR Crypt. ePrint Arch."},{"key":"9221_CR10","unstructured":"R. Canetti, Towards realizing random oracles: Hash functions that hide all partial information. in CRYPTO (1997), pp. 455\u2013469"},{"key":"9221_CR11","unstructured":"R. Canetti, R. R. Dakdouk, Obfuscating point functions with multibit output, in EUROCRYPT (2008), pp. 489\u2013508"},{"key":"9221_CR12","first-page":"596","volume":"2015","author":"J-S Coron","year":"2015","unstructured":"J.-S. Coron, C. Gentry, S. Halevi, T. Lepoint, H. K. Maji, E. Miles, M. Raykova, A. Sahai, M. Tibouchi, Zeroizing without low-level zeroes: new MMAP attacks and their limitations. IACR Crypt. ePrint Arch. 2015, 596 (2015)","journal-title":"IACR Crypt. ePrint Arch."},{"key":"9221_CR13","doi-asserted-by":"crossref","unstructured":"J. H. Cheon, K. Han, C. Lee, H. Ryu, D. Stehl\u00e9, Cryptanalysis of the multilinear map over the integers, in E. Oswald, M. Fischlin, editors, Advances in Cryptology\u2014EUROCRYPT 2015\u201434th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Sofia, Bulgaria, April 26\u201330, 2015, Proceedings, Part I. Lecture Notes in Computer Science, vol. 9056 (Springer, 2015), pp. 3\u201312","DOI":"10.1007\/978-3-662-46800-5_1"},{"key":"9221_CR14","doi-asserted-by":"crossref","unstructured":"J.-S. Coron, T. Lepoint, M. Tibouchi, Practical multilinear maps over the integers, in R. Canetti, J. A. Garay, editors, Advances in Cryptology\u2014CRYPTO 2013\u201433rd Annual Cryptology Conference, Santa Barbara, CA, USA, August 18\u201322, 2013. Proceedings, Part I. Lecture Notes in Computer Science, vol. 8042 (Springer, 2013), pp. 476\u2013493","DOI":"10.1007\/978-3-642-40041-4_26"},{"key":"9221_CR15","first-page":"162","volume":"2015","author":"J-S Coron","year":"2015","unstructured":"J.-S. Coron, T. Lepoint, M. Tibouchi, New multilinear maps over the integers. IACR Crypt. ePrint Arch. 2015, 162 (2015)","journal-title":"IACR Crypt. ePrint Arch."},{"key":"9221_CR16","unstructured":"R. Canetti, D. Micciancio, O. Reingold, Perfectly one-way probabilistic hash functions (preliminary version), in STOC (1998), pp. 131\u2013140"},{"key":"9221_CR17","unstructured":"R. Canetti, G. N. Rothblum, M. Varia. Obfuscation of hyperplane membership, in TCC (2010), pp. 72\u201389"},{"key":"9221_CR18","unstructured":"Y. Dodis, R. Ostrovsky, L. Reyzin, A. Smith, Fuzzy extractors: How to generate strong keys from biometrics and other noisy data. SIAM J. Comput. 38(1), 97\u2013139 (2008). Preliminary version in Eurocrypt 2004"},{"key":"9221_CR19","doi-asserted-by":"crossref","unstructured":"Y. Dodis, A. Smith, Correcting errors without leaking partial information, in Gabow and Fagin [20], pp. 654\u2013663","DOI":"10.1145\/1060590.1060688"},{"key":"9221_CR20","unstructured":"H. N. Gabow, R. Fagin, editors. Proceedings of the 37th Annual ACM Symposium on Theory of Computing, Baltimore, MD, USA, May 22\u201324, 2005. ACM (2005)"},{"key":"9221_CR21","doi-asserted-by":"crossref","unstructured":"S. Garg, C. Gentry, S. Halevi, Candidate multilinear maps from ideal lattices, in T. Johansson, P. Q. Nguyen, editors, EUROCRYPT. Lecture Notes in Computer Science, vol. 7881 (Springer, 2013) pp. 1\u201317. See also Cryptology ePrint Archive, Report 2012\/610","DOI":"10.1007\/978-3-642-38348-9_1"},{"key":"9221_CR22","unstructured":"S. Garg, C. Gentry, S. Halevi, M. Raykova, A. Sahai, B. Waters, 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 IEEE Computer Society (2013) pp. 40\u201349"},{"key":"9221_CR23","unstructured":"S. Goldwasser, Y. T. Kalai, On the impossibility of obfuscation with auxiliary input, in FOCS (2005) pp. 553\u2013562"},{"key":"9221_CR24","doi-asserted-by":"crossref","unstructured":"S. Goldwasser, G. N. Rothblum, On best-possible obfuscation, in Vadhan [34], pp. 194\u2013213","DOI":"10.1007\/978-3-540-70936-7_11"},{"key":"9221_CR25","unstructured":"Y. Hu, H. Jia, Cryptanalysis of ggh map. Crypt. ePrint Arch. Report 2015\/301 (2015). http:\/\/eprint.iacr.org\/"},{"issue":"1","key":"9221_CR26","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/s00145-009-9046-1","volume":"23","author":"D Hofheinz","year":"2010","unstructured":"D. Hofheinz, J. Malone-Lee, M. Stam, Obfuscation for cryptographic purposes. J. Cryptol. 23(1), 121\u2013168 (2010)","journal-title":"J. Cryptol."},{"issue":"4","key":"9221_CR27","doi-asserted-by":"publisher","first-page":"694","DOI":"10.1007\/s00145-010-9077-7","volume":"24","author":"S Hohenberger","year":"2011","unstructured":"S. Hohenberger, G. N. Rothblum, A. Shelat, V. Vaikuntanathan. Securely obfuscating re-encryption. J. Cryptol. 24(4), 694\u2013719 (2011)","journal-title":"J. Cryptol."},{"key":"9221_CR28","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/3897.001.0001","volume-title":"An Introduction to Computational Learning Theory","author":"MJ Kearns","year":"1994","unstructured":"M. J. Kearns, U. V. Vazirani, An Introduction to Computational Learning Theory (MIT Press, Cambridge, MA, USA, 1994)"},{"key":"9221_CR29","unstructured":"B. Lynn, M. Prabhakaran, A. Sahai, Positive results and techniques for obfuscation, in EUROCRYPT (2004), pp. 20\u201339"},{"key":"9221_CR30","unstructured":"U. M. Maurer, Abstract models of computation in cryptography, in IMA International Conference (2005), pp. 1\u201312"},{"key":"9221_CR31","unstructured":"R. Rothblum, On the circular security of bit-encryption, in TCC (2013), pp. 579\u2013598"},{"key":"9221_CR32","unstructured":"R. Renner, S. Wolf, Smooth renyi entropy and applications, in IEEE International Symposium on Information Theory, IEEE International Symposium on Information Theory (2004), p. 233"},{"key":"9221_CR33","unstructured":"V. Shoup, Lower bounds for discrete logarithms and related problems, in EUROCRYPT (1997), pp. 256\u2013266"},{"key":"9221_CR34","doi-asserted-by":"crossref","unstructured":"S. P. Vadhan, editor. Theory of Cryptography, 4th Theory of Cryptography Conference, TCC 2007, Amsterdam, The Netherlands, February 21\u201324, 2007, Proceedings. Lecture Notes in Computer Science, vol. 4392 (Springer, 2007)","DOI":"10.1007\/978-3-540-70936-7"},{"key":"9221_CR35","unstructured":"H. Wee, On obfuscating point functions, in Gabow and Fagin [20], pp. 523\u2013532"}],"container-title":["Journal of Cryptology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00145-015-9221-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00145-015-9221-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00145-015-9221-5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00145-015-9221-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,31]],"date-time":"2025-05-31T13:46:31Z","timestamp":1748699191000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00145-015-9221-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,23]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["9221"],"URL":"https:\/\/doi.org\/10.1007\/s00145-015-9221-5","relation":{},"ISSN":["0933-2790","1432-1378"],"issn-type":[{"value":"0933-2790","type":"print"},{"value":"1432-1378","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,23]]},"assertion":[{"value":"15 August 2013","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 November 2015","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"}]}}