{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T01:25:34Z","timestamp":1775265934540,"version":"3.50.1"},"publisher-location":"Cham","reference-count":34,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030038090","type":"print"},{"value":"9783030038106","type":"electronic"}],"license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018]]},"DOI":"10.1007\/978-3-030-03810-6_20","type":"book-chapter","created":{"date-parts":[[2018,11,7]],"date-time":"2018-11-07T16:30:29Z","timestamp":1541608229000},"page":"544-574","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["Return of GGH15: Provable Security Against Zeroizing Attacks"],"prefix":"10.1007","author":[{"given":"James","family":"Bartusek","sequence":"first","affiliation":[]},{"given":"Jiaxin","family":"Guan","sequence":"additional","affiliation":[]},{"given":"Fermi","family":"Ma","sequence":"additional","affiliation":[]},{"given":"Mark","family":"Zhandry","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,11,8]]},"reference":[{"key":"20_CR1","doi-asserted-by":"crossref","unstructured":"Bartusek, J., Guan, J., Ma, F., Zhandry, M.: Return of GGH15: Provable security against zeroizing attacks. Cryptology ePrint Archive, Report 2018\/511 (2018). https:\/\/eprint.iacr.org\/2018\/511","DOI":"10.1007\/978-3-030-03810-6_20"},{"key":"20_CR2","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1090\/conm\/324\/05731","volume":"324","author":"D Boneh","year":"2003","unstructured":"Boneh, D., Silverberg, A.: Applications of multilinear forms to cryptography. Contemp. Math. 324, 71\u201390 (2003)","journal-title":"Contemp. Math."},{"key":"20_CR3","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, pp. 40\u201349 (2013)","DOI":"10.1109\/FOCS.2013.13"},{"key":"20_CR4","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). https:\/\/doi.org\/10.1007\/978-3-642-38348-9_1"},{"key":"20_CR5","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). https:\/\/doi.org\/10.1007\/978-3-642-40041-4_26"},{"key":"20_CR6","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). https:\/\/doi.org\/10.1007\/978-3-662-46497-7_20"},{"key":"20_CR7","doi-asserted-by":"crossref","unstructured":"Regev, O.: On lattices, learning with errors, random linear codes, and cryptography, pp. 84\u201393 (2005)","DOI":"10.1145\/1060590.1060603"},{"key":"20_CR8","doi-asserted-by":"crossref","unstructured":"Wichs, D., Zirdelis, G.: Obfuscating compute-and-compare programs under LWE, pp. 600\u2013611 (2017)","DOI":"10.1109\/FOCS.2017.61"},{"key":"20_CR9","doi-asserted-by":"crossref","unstructured":"Goyal, R., Koppula, V., Waters, B.: Lockable obfuscation, pp. 612\u2013621 (2017)","DOI":"10.1109\/FOCS.2017.62"},{"key":"20_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1007\/978-3-319-96881-0_20","volume-title":"Advances in Cryptology \u2013 CRYPTO 2018","author":"Y Chen","year":"2018","unstructured":"Chen, Y., Vaikuntanathan, V., Wee, H.: GGH15 beyond permutation branching programs: proofs, attacks, and candidates. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 577\u2013607. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-96881-0_20"},{"key":"20_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"446","DOI":"10.1007\/978-3-319-56620-7_16","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2017","author":"R Canetti","year":"2017","unstructured":"Canetti, R., Chen, Y.: Constraint-hiding constrained PRFs for NC$$^1$$ from LWE. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10210, pp. 446\u2013476. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-56620-7_16"},{"key":"20_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"528","DOI":"10.1007\/978-3-319-56614-6_18","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2017","author":"R Goyal","year":"2017","unstructured":"Goyal, R., Koppula, V., Waters, B.: Separating semantic and circular security for symmetric-key bit encryption from the learning with errors assumption. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10211, pp. 528\u2013557. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-56614-6_18"},{"key":"20_CR13","doi-asserted-by":"crossref","unstructured":"Shor, P.W.: Algorithms for quantum computation: Discrete logarithms and factoring, pp. 124\u2013134 (1994)","DOI":"10.1109\/SFCS.1994.365700"},{"key":"20_CR14","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). https:\/\/doi.org\/10.1007\/978-3-662-53018-4_6"},{"key":"20_CR15","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). https:\/\/doi.org\/10.1007\/978-3-662-49896-5_20"},{"key":"20_CR16","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, pp. 893\u2013902 (2016)","DOI":"10.1137\/1.9781611974331.ch64"},{"key":"20_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/978-3-319-96878-0_6","volume-title":"Advances in Cryptology \u2013 CRYPTO 2018","author":"A Pellet-Mary","year":"2018","unstructured":"Pellet-Mary, A.: Quantum attacks against indistinguishablility obfuscators proved secure in the weak multilinear map model. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10993, pp. 153\u2013183. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-96878-0_6"},{"key":"20_CR18","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). https:\/\/doi.org\/10.1007\/978-3-662-46800-5_1"},{"key":"20_CR19","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). https:\/\/doi.org\/10.1007\/978-3-662-53008-5_21"},{"key":"20_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"278","DOI":"10.1007\/978-3-319-56617-7_10","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2017","author":"Y Chen","year":"2017","unstructured":"Chen, Y., Gentry, C., Halevi, S.: Cryptanalyses of candidate branching program obfuscators. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10212, pp. 278\u2013307. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-56617-7_10"},{"key":"20_CR21","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). https:\/\/doi.org\/10.1007\/978-3-662-53644-5_10"},{"key":"20_CR22","unstructured":"Ma, F., Zhandry, M.: New multilinear maps from CLT13 with provable security against zeroizing attacks. Cryptology ePrint Archive, Report 2017\/946 (2017). http:\/\/eprint.iacr.org\/2017\/946"},{"key":"20_CR23","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). https:\/\/doi.org\/10.1007\/978-3-642-55220-5_13"},{"key":"20_CR24","unstructured":"Halevi, S.: Graded encoding, variations on a scheme. Cryptology ePrint Archive, Report 2015\/866 (2015). http:\/\/eprint.iacr.org\/2015\/866"},{"key":"20_CR25","unstructured":"Miles, E., Sahai, A., Weiss, M.: Protecting obfuscation against arithmetic attacks. Cryptology ePrint Archive, Report 2014\/878 (2014). http:\/\/eprint.iacr.org\/2014\/878"},{"key":"20_CR26","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). https:\/\/doi.org\/10.1007\/978-3-662-49896-5_27"},{"key":"20_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1007\/978-3-662-46803-6_19","volume-title":"Advances in Cryptology - EUROCRYPT 2015","author":"D Boneh","year":"2015","unstructured":"Boneh, D., Lewi, K., Raykova, M., Sahai, A., Zhandry, M., Zimmerman, J.: Semantically secure order-revealing encryption: multi-input functional encryption without obfuscation. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 563\u2013594. Springer, Heidelberg (2015). https:\/\/doi.org\/10.1007\/978-3-662-46803-6_19"},{"key":"20_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1007\/978-3-030-03810-6_19","volume-title":"Theory of Cryptography","author":"F Ma","year":"2018","unstructured":"Ma, F., Zhandry, M.: The mmap strikes back: Obfuscation and new multilinear maps immune to CLT13 zeroizing attacks. In: Beimel, A., Dziembowski, S. (eds.) TCC 2018. LNCS, vol. 11240, pp. 513\u2013543. Springer, Cham (2018)"},{"key":"20_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1007\/978-3-642-40041-4_23","volume-title":"Advances in Cryptology \u2013 CRYPTO 2013","author":"D Boneh","year":"2013","unstructured":"Boneh, D., Lewi, K., Montgomery, H., Raghunathan, A.: Key homomorphic PRFs and their applications. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 410\u2013428. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-40041-4_23"},{"key":"20_CR30","doi-asserted-by":"crossref","unstructured":"Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing, pp. 197\u2013206. ACM (2008)","DOI":"10.1145\/1374376.1374407"},{"key":"20_CR31","doi-asserted-by":"crossref","unstructured":"Garg, S., Miles, E., Mukherjee, P., Sahai, A., Srinivasan, A., Zhandry, M.: Secure obfuscation in a weak multilinear map model. Cryptology ePrint Archive, Report 2016\/817 (2016). http:\/\/eprint.iacr.org\/2016\/817","DOI":"10.1007\/978-3-662-53644-5_10"},{"key":"20_CR32","doi-asserted-by":"crossref","unstructured":"Barrington, D.A.M.: Bounded-width polynomial-size branching programs recognize exactly those languages in $$\\text{NC}^1$$, pp. 1\u20135 (1986)","DOI":"10.1145\/12130.12131"},{"issue":"4","key":"20_CR33","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1007\/BF01457454","volume":"261","author":"AK Lenstra","year":"1982","unstructured":"Lenstra, A.K., Lenstra, H.W., Lov\u00e1sz, L.: Factoring polynomials with rational coefficients. Mathematische Annalen 261(4), 515\u2013534 (1982)","journal-title":"Mathematische Annalen"},{"issue":"5","key":"20_CR34","doi-asserted-by":"publisher","first-page":"1639","DOI":"10.1109\/18.259647","volume":"39","author":"AJ Menezes","year":"1993","unstructured":"Menezes, A.J., Okamoto, T., Vanstone, S.A.: Reducing elliptic curve logarithms to logarithms in a finite field. IEEE Trans. Inf. Theory 39(5), 1639\u20131646 (1993)","journal-title":"IEEE Trans. Inf. Theory"}],"container-title":["Lecture Notes in Computer Science","Theory of Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-03810-6_20","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T00:20:57Z","timestamp":1775262057000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-03810-6_20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"ISBN":["9783030038090","9783030038106"],"references-count":34,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-03810-6_20","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018]]},"assertion":[{"value":"8 November 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"TCC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Theory of Cryptography Conference","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Panaji","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"India","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2018","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 November 2018","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 November 2018","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"tcc2018","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/tcc.iacr.org\/2018\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}