{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T15:31:15Z","timestamp":1777390275163,"version":"3.51.4"},"publisher-location":"Cham","reference-count":39,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319566160","type":"print"},{"value":"9783319566177","type":"electronic"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","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":[[2017]]},"DOI":"10.1007\/978-3-319-56617-7_10","type":"book-chapter","created":{"date-parts":[[2017,3,30]],"date-time":"2017-03-30T22:33:34Z","timestamp":1490913214000},"page":"278-307","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["Cryptanalyses of Candidate Branching Program Obfuscators"],"prefix":"10.1007","author":[{"given":"Yilei","family":"Chen","sequence":"first","affiliation":[]},{"given":"Craig","family":"Gentry","sequence":"additional","affiliation":[]},{"given":"Shai","family":"Halevi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,4,1]]},"reference":[{"key":"10_CR1","doi-asserted-by":"publisher","unstructured":"Ajtai, M.: Generating hard instances of the short basis problem. In: Wiedermann, J., Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 1\u20139. Springer, Heidelberg (1999). doi:\n                      10.1007\/3-540-48523-6_1","DOI":"10.1007\/3-540-48523-6_1"},{"key":"10_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/978-3-662-53018-4_6","volume-title":"Advances in Cryptology \u2013 CRYPTO 2016","author":"M Albrecht","year":"2016","unstructured":"Albrecht, M., Bai, S., Ducas, L.: A subfield lattice attack on overstretched NTRU assumptions. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9814, pp. 153\u2013178. Springer, Heidelberg (2016). doi:\n                      10.1007\/978-3-662-53018-4_6"},{"key":"10_CR3","doi-asserted-by":"crossref","unstructured":"Ananth, P., Gupta, D., Ishai, Y., Sahai, A.: Optimizing obfuscation: avoiding Barrington\u2019s theorem. In: Proceedings of the ACM SIGSAC Conference on Computer and Communications Security, pp. 646\u2013658. ACM (2014)","DOI":"10.1145\/2660267.2660342"},{"key":"10_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1007\/978-3-662-47989-6_15","volume-title":"Advances in Cryptology \u2013 CRYPTO 2015","author":"P Ananth","year":"2015","unstructured":"Ananth, P., Jain, A.: Indistinguishability obfuscation from compact functional encryption. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 308\u2013326. Springer, Heidelberg (2015). doi:\n                      10.1007\/978-3-662-47989-6_15"},{"key":"10_CR5","unstructured":"Apon, D., D\u00f6ttling, N., Garg, S., Mukherjee, P.: Cryptanalysis of indistinguishability obfuscations of circuits over GGH13. Cryptology ePrint Archive, report 2016\/1003 (2016)"},{"key":"10_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"528","DOI":"10.1007\/978-3-662-46497-7_21","volume-title":"Theory of Cryptography","author":"B Applebaum","year":"2015","unstructured":"Applebaum, B., Brakerski, Z.: Obfuscating circuits via composite-order graded encoding. In: Dodis, Y., Nielsen, J.B. (eds.) TCC 2015. LNCS, vol. 9015, pp. 528\u2013556. Springer, Heidelberg (2015). doi:\n                      10.1007\/978-3-662-46497-7_21"},{"key":"10_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"764","DOI":"10.1007\/978-3-662-49896-5_27","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2016","author":"S Badrinarayanan","year":"2016","unstructured":"Badrinarayanan, S., Miles, E., Sahai, A., Zhandry, M.: Post-zeroizing obfuscation: new mathematical tools, and the case of evasive circuits. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 764\u2013791. Springer, Heidelberg (2016). doi:\n                      10.1007\/978-3-662-49896-5_27"},{"key":"10_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/978-3-642-55220-5_13","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2014","author":"B Barak","year":"2014","unstructured":"Barak, B., Garg, S., Kalai, Y.T., Paneth, O., Sahai, A.: Protecting obfuscation against algebraic attacks. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 221\u2013238. Springer, Heidelberg (2014). doi:\n                      10.1007\/978-3-642-55220-5_13"},{"issue":"A","key":"10_CR9","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1112\/S1461157014000345","volume":"17","author":"J-F Biasse","year":"2014","unstructured":"Biasse, J.-F., Fieker, C.: Subexponential class group, unit group computation in large degree number fields. LMS J. Comput. Math. 17(A), 385\u2013403 (2014)","journal-title":"LMS J. Comput. Math."},{"key":"10_CR10","doi-asserted-by":"crossref","unstructured":"Biasse, J.F., Song, F.: Efficient quantum algorithms for computing class groups and solving the principal ideal problem in arbitrary degree number fields. In: Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 893\u2013902. SIAM (2016)","DOI":"10.1137\/1.9781611974331.ch64"},{"key":"10_CR11","doi-asserted-by":"crossref","unstructured":"Bitansky, N., Vaikuntanathan, V.: Indistinguishability obfuscation from functional encryption. In: FOCS, pp. 171\u2013190. IEEE Computer Society (2015)","DOI":"10.1109\/FOCS.2015.20"},{"key":"10_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-54242-8_1","volume-title":"Theory of Cryptography","author":"Z Brakerski","year":"2014","unstructured":"Brakerski, Z., Rothblum, G.N.: Virtual black-box obfuscation for all circuits via generic graded encoding. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 1\u201325. Springer, Heidelberg (2014). doi:\n                      10.1007\/978-3-642-54242-8_1"},{"key":"10_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","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. LNCS, vol. 9056, pp. 3\u201312. Springer, Heidelberg (2015). doi:\n                      10.1007\/978-3-662-46800-5_1"},{"key":"10_CR14","doi-asserted-by":"crossref","unstructured":"Cheon, J.H., Jeong, J., Lee, C.: An algorithm for CSPR problems and cryptanalysis of the GGH multilinear map without an encoding of zero. To be appear at ANTS (2016)","DOI":"10.1112\/S1461157016000371"},{"issue":"4","key":"10_CR15","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/s001459900030","volume":"10","author":"D Coppersmith","year":"1997","unstructured":"Coppersmith, D.: Small solutions to polynomial equations, and low exponent RSA vulnerabilities. J. Cryptol. 10(4), 233\u2013260 (1997)","journal-title":"J. Cryptol."},{"key":"10_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/978-3-662-47989-6_12","volume-title":"Advances in Cryptology \u2013 CRYPTO 2015","author":"J-S Coron","year":"2015","unstructured":"Coron, J.-S., et al.: Zeroizing without low-level zeroes: new MMAP attacks and their limitations. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 247\u2013266. Springer, Heidelberg (2015). doi:\n                      10.1007\/978-3-662-47989-6_12"},{"key":"10_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1007\/978-3-662-53008-5_21","volume-title":"Advances in Cryptology \u2013 CRYPTO 2016","author":"J-S Coron","year":"2016","unstructured":"Coron, J.-S., Lee, M.S., Lepoint, T., Tibouchi, M.: Cryptanalysis of GGH15 multilinear maps. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9815, pp. 607\u2013628. Springer, Heidelberg (2016). doi:\n                      10.1007\/978-3-662-53008-5_21"},{"key":"10_CR18","doi-asserted-by":"crossref","unstructured":"Coron, J.-S., Lee, M.S., Lepoint, T., Tibouchi, M.: Zeroizing attacks on indistinguishability obfuscation over CLT13. To be appear at PKC 2017. Cryptology ePrint Archive, report 2016\/1011 (2016)","DOI":"10.1007\/978-3-662-54365-8_3"},{"key":"10_CR19","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. LNCS, vol. 8042, pp. 476\u2013493. Springer, Heidelberg (2013). doi:\n                      10.1007\/978-3-642-40041-4_26"},{"key":"10_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"559","DOI":"10.1007\/978-3-662-49896-5_20","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2016","author":"R Cramer","year":"2016","unstructured":"Cramer, R., Ducas, L., Peikert, C., Regev, O.: Recovering short generators of principal ideals in cyclotomic rings. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9666, pp. 559\u2013585. Springer, Heidelberg (2016). doi:\n                      10.1007\/978-3-662-49896-5_20"},{"key":"10_CR21","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). doi:\n                      10.1007\/978-3-642-38348-9_1"},{"key":"10_CR22","doi-asserted-by":"crossref","unstructured":"Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Candidate indistinguishability obfuscation and functional encryption for all circuits. In: FOCS, pp. 40\u201349 (2013)","DOI":"10.1109\/FOCS.2013.13"},{"key":"10_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"480","DOI":"10.1007\/978-3-662-49099-0_18","volume-title":"Theory of Cryptography","author":"S Garg","year":"2016","unstructured":"Garg, S., Gentry, C., Halevi, S., Zhandry, M.: Functional encryption without obfuscation. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9563, pp. 480\u2013511. Springer, Heidelberg (2016). doi:\n                      10.1007\/978-3-662-49099-0_18"},{"key":"10_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/978-3-662-53644-5_10","volume-title":"Theory of Cryptography","author":"S Garg","year":"2016","unstructured":"Garg, S., Miles, E., Mukherjee, P., Sahai, A., Srinivasan, A., Zhandry, M.: Secure obfuscation in a weak multilinear map model. In: Hirt, M., Smith, A. (eds.) TCC 2016. LNCS, vol. 9986, pp. 241\u2013268. Springer, Heidelberg (2016). doi:\n                      10.1007\/978-3-662-53644-5_10"},{"key":"10_CR25","unstructured":"Garg, S., Mukherjee, P., Srinivasan, A.: Obfuscation without the vulnerabilities of multilinear maps. Technical report (2016)"},{"key":"10_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","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. LNCS, vol. 9015, pp. 498\u2013527. Springer, Heidelberg (2015). doi:\n                      10.1007\/978-3-662-46497-7_20"},{"key":"10_CR27","doi-asserted-by":"crossref","unstructured":"Garg, S., Gentry, C., Halevi, S., Raykova, M., Sahai, A., Waters, B.: Indistinguishability obfuscation from the multilinear subgroup elimination assumption. In: IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS), pp. 151\u2013170. IEEE (2015)","DOI":"10.1109\/FOCS.2015.19"},{"key":"10_CR28","doi-asserted-by":"crossref","unstructured":"Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: STOC, pp. 197\u2013206 (2008)","DOI":"10.1145\/1374376.1374407"},{"key":"10_CR29","unstructured":"Halevi, S.: Graded encoding, variations on a scheme. Cryptology ePrint Archive, report 2015\/866 (2015)"},{"key":"10_CR30","doi-asserted-by":"crossref","unstructured":"Lenstra, A.K., Lenstra, H.W., Manasse, M.S., Pollard, J.M.: The number field sieve. In: STOC, pp. 564\u2013572. ACM (1990)","DOI":"10.1145\/100216.100295"},{"key":"10_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1007\/978-3-662-49890-3_2","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2016","author":"H Lin","year":"2016","unstructured":"Lin, H.: Indistinguishability obfuscation from constant-degree graded encoding schemes. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9665, pp. 28\u201357. Springer, Heidelberg (2016). doi:\n                      10.1007\/978-3-662-49890-3_2"},{"key":"10_CR32","doi-asserted-by":"crossref","unstructured":"Lin, H., Vaikuntanathan, V.: Indistinguishability obfuscation from DDH-like assumptions on constant-degree graded encodings. In: FOCS, pp. 11\u201320. IEEE Computer Society (2016)","DOI":"10.1109\/FOCS.2016.11"},{"key":"10_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1007\/978-3-642-29011-4_41","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2012","author":"D Micciancio","year":"2012","unstructured":"Micciancio, D., Peikert, C.: Trapdoors for lattices: simpler, tighter, faster, smaller. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 700\u2013718. Springer, Heidelberg (2012). doi:\n                      10.1007\/978-3-642-29011-4_41"},{"key":"10_CR34","unstructured":"Miles, E., Sahai, A., Weiss, M.: Protecting obfuscation against arithmetic attacks. IACR Cryptology ePrint Archive 2014:878 (2014)"},{"key":"10_CR35","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"629","DOI":"10.1007\/978-3-662-53008-5_22","volume-title":"Advances in Cryptology \u2013 CRYPTO 2016","author":"E Miles","year":"2016","unstructured":"Miles, E., Sahai, A., Zhandry, M.: Annihilation attacks for multilinear maps: cryptanalysis of indistinguishability obfuscation over GGH13. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016. LNCS, vol. 9815, pp. 629\u2013658. Springer, Heidelberg (2016). doi:\n                      10.1007\/978-3-662-53008-5_22"},{"key":"10_CR36","first-page":"588","volume":"2016","author":"E Miles","year":"2016","unstructured":"Miles, E., Sahai, A., Zhandry, M.: Secure obfuscation in a weak multilinear map model: a simple construction secure against all known attacks. IACR Cryptology ePrint Archive 2016, 588 (2016)","journal-title":"IACR Cryptology ePrint Archive"},{"key":"10_CR37","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"500","DOI":"10.1007\/978-3-662-44371-2_28","volume-title":"Advances in Cryptology \u2013 CRYPTO 2014","author":"R Pass","year":"2014","unstructured":"Pass, R., Seth, K., Telang, S.: Indistinguishability obfuscation from semantically-secure multilinear encodings. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 500\u2013517. Springer, Heidelberg (2014). doi:\n                      10.1007\/978-3-662-44371-2_28"},{"issue":"2","key":"10_CR38","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1137\/S0036144598347011","volume":"41","author":"PW Shor","year":"1999","unstructured":"Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303\u2013332 (1999)","journal-title":"SIAM Rev."},{"key":"10_CR39","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1007\/978-3-662-46803-6_15","volume-title":"Advances in Cryptology - EUROCRYPT 2015","author":"J Zimmerman","year":"2015","unstructured":"Zimmerman, J.: How to obfuscate programs directly. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 439\u2013467. Springer, Heidelberg (2015). doi:\n                      10.1007\/978-3-662-46803-6_15"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 EUROCRYPT 2017"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-56617-7_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T01:51:07Z","timestamp":1558317067000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-56617-7_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319566160","9783319566177"],"references-count":39,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-56617-7_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017]]},"assertion":[{"value":"1 April 2017","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"EUROCRYPT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Annual International Conference on the Theory and Applications of Cryptographic Techniques","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Paris","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"France","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2017","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"30 April 2017","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"4 May 2017","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"36","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"eurocrypt2017","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/eurocrypt2017.di.ens.fr\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}