{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T23:22:37Z","timestamp":1790810557239,"version":"4.1.0"},"publisher-location":"Cham","reference-count":75,"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":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-56617-7_9","type":"book-chapter","created":{"date-parts":[[2017,3,30]],"date-time":"2017-03-30T22:33:34Z","timestamp":1490913214000},"page":"247-277","source":"Crossref","is-referenced-by-count":58,"title":["Lattice-Based SNARGs and Their Application to More Efficient Obfuscation"],"prefix":"10.1007","author":[{"given":"Dan","family":"Boneh","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuval","family":"Ishai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amit","family":"Sahai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David J.","family":"Wu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2017,4,1]]},"reference":[{"key":"9_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-40041-4_1","volume-title":"Advances in Cryptology \u2013 CRYPTO 2013","author":"J Alperin-Sheriff","year":"2013","unstructured":"Alperin-Sheriff, J., Peikert, C.: Practical bootstrapping in quasilinear time. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 1\u201320. Springer, Heidelberg (2013). doi: 10.1007\/978-3-642-40041-4_1"},{"key":"9_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/978-3-662-44371-2_17","volume-title":"Advances in Cryptology \u2013 CRYPTO 2014","author":"J Alperin-Sheriff","year":"2014","unstructured":"Alperin-Sheriff, J., Peikert, C.: Faster bootstrapping with polynomial error. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 297\u2013314. Springer, Heidelberg (2014). doi: 10.1007\/978-3-662-44371-2_17"},{"key":"9_CR3","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: 10.1007\/978-3-662-47989-6_15"},{"key":"9_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1007\/978-3-319-56620-7_6","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2017, Part III","author":"P Ananth","year":"2017","unstructured":"Ananth, P., Sahai, A.: Projective arithmetic functional encryption and indistinguishability obfuscation from degree-5 multilinear maps. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017, Part III. LNCS, vol. 10212, pp. 152\u2013181. Springer, Heidelberg (2017)"},{"key":"9_CR5","doi-asserted-by":"crossref","unstructured":"Ananth, P.V., Gupta, D., Ishai, Y., Sahai, A.: Optimizing obfuscation: avoiding Barrington\u2019s theorem. In: ACM CCS (2014)","DOI":"10.1145\/2660267.2660342"},{"key":"9_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1007\/978-3-662-45608-8_9","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2014","author":"B Applebaum","year":"2014","unstructured":"Applebaum, B.: Bootstrapping obfuscators via fast pseudorandom functions. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8874, pp. 162\u2013172. Springer, Heidelberg (2014). doi: 10.1007\/978-3-662-45608-8_9"},{"key":"9_CR7","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: 10.1007\/978-3-662-46497-7_21"},{"key":"9_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1007\/978-3-642-03356-8_35","volume-title":"Advances in Cryptology - CRYPTO 2009","author":"B Applebaum","year":"2009","unstructured":"Applebaum, B., Cash, D., Peikert, C., Sahai, A.: Fast cryptographic primitives and circular-secure encryption based on hard learning problems. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 595\u2013618. Springer, Heidelberg (2009). doi: 10.1007\/978-3-642-03356-8_35"},{"key":"9_CR9","doi-asserted-by":"crossref","unstructured":"Arora, S., Lund, C., Motwani, R., Sudan, M., Szegedy, M.: Proof verification and the hardness of approximation problems. In: FOCS (1992)","DOI":"10.1109\/SFCS.1992.267823"},{"key":"9_CR10","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: 10.1007\/978-3-662-49896-5_27"},{"key":"9_CR11","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: 10.1007\/978-3-642-55220-5_13"},{"key":"9_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/3-540-44647-8_1","volume-title":"Advances in Cryptology \u2014 CRYPTO 2001","author":"B Barak","year":"2001","unstructured":"Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S., Yang, K.: On the (im)possibility of obfuscating programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1\u201318. Springer, Heidelberg (2001). doi: 10.1007\/3-540-44647-8_1"},{"key":"9_CR13","doi-asserted-by":"crossref","unstructured":"Barrington, D.A.M.: Bounded-width polynomial-size branching programs recognize exactly those languages in nc $${^1}$$ . In: STOC (1986)","DOI":"10.1145\/12130.12131"},{"key":"9_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1007\/978-3-540-28628-8_17","volume-title":"Advances in Cryptology \u2013 CRYPTO 2004","author":"M Bellare","year":"2004","unstructured":"Bellare, M., Palacio, A.: The knowledge-of-exponent assumptions and 3-round zero-knowledge protocols. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 273\u2013289. Springer, Heidelberg (2004). doi: 10.1007\/978-3-540-28628-8_17"},{"key":"9_CR15","doi-asserted-by":"crossref","unstructured":"Bitansky, N., Canetti, R., Chiesa, A., Tromer, E.: From extractable collision resistance to succinct non-interactive arguments of knowledge, and back again. In: ITCS (2012)","DOI":"10.1145\/2090236.2090263"},{"key":"9_CR16","doi-asserted-by":"crossref","unstructured":"Bitansky, N., Canetti, R., Paneth, O., Rosen, A.: On the existence of extractable one-way functions. In: STOC (2014)","DOI":"10.1145\/2591796.2591859"},{"key":"9_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/978-3-642-32009-5_16","volume-title":"Advances in Cryptology \u2013 CRYPTO 2012","author":"N Bitansky","year":"2012","unstructured":"Bitansky, N., Chiesa, A.: Succinct arguments from multi-prover interactive proofs and their efficiency benefits. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 255\u2013272. Springer, Heidelberg (2012). doi: 10.1007\/978-3-642-32009-5_16"},{"key":"9_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/978-3-642-36594-2_18","volume-title":"Theory of Cryptography","author":"N Bitansky","year":"2013","unstructured":"Bitansky, N., Chiesa, A., Ishai, Y., Paneth, O., Ostrovsky, R.: Succinct non-interactive arguments via linear interactive proofs. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 315\u2013333. Springer, Heidelberg (2013). doi: 10.1007\/978-3-642-36594-2_18"},{"key":"9_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"474","DOI":"10.1007\/978-3-662-49096-9_20","volume-title":"Theory of Cryptography","author":"N Bitansky","year":"2016","unstructured":"Bitansky, N., Paneth, O., Wichs, D.: Perfect structure on the edge of chaos. In: Kushilevitz, E., Malkin, T. (eds.) TCC 2016. LNCS, vol. 9562, pp. 474\u2013502. Springer, Heidelberg (2016). doi: 10.1007\/978-3-662-49096-9_20"},{"key":"9_CR20","doi-asserted-by":"crossref","unstructured":"Bitansky, N., Vaikuntanathan, V.: Indistinguishability obfuscation from functional encryption. In: FOCS (2015)","DOI":"10.1109\/FOCS.2015.20"},{"key":"9_CR21","doi-asserted-by":"crossref","unstructured":"Blum, A., Kalai, A., Wasserman, H.: Noise-tolerant learning, the parity problem, and the statistical query model. In: STOC (2000)","DOI":"10.1145\/335305.335355"},{"key":"9_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1007\/3-540-44647-8_13","volume-title":"Advances in Cryptology \u2014 CRYPTO 2001","author":"D Boneh","year":"2001","unstructured":"Boneh, D., Franklin, M.K.: Identity-based encryption from the weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213\u2013229. Springer, Heidelberg (2001). doi: 10.1007\/3-540-44647-8_13"},{"key":"9_CR23","doi-asserted-by":"crossref","unstructured":"Boneh, D., Segev, G., Waters, B.: Targeted malleability: homomorphic encryption for restricted computations. In: ITCS (2012)","DOI":"10.1145\/2090236.2090264"},{"issue":"1","key":"9_CR24","doi-asserted-by":"crossref","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(1), 71\u201390 (2003)","journal-title":"Contemp. Math."},{"key":"9_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"480","DOI":"10.1007\/978-3-662-44371-2_27","volume-title":"Advances in Cryptology \u2013 CRYPTO 2014","author":"D Boneh","year":"2014","unstructured":"Boneh, D., Zhandry, M.: Multiparty key exchange, efficient traitor tracing, and more from indistinguishability obfuscation. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014. LNCS, vol. 8616, pp. 480\u2013499. Springer, Heidelberg (2014). doi: 10.1007\/978-3-662-44371-2_27"},{"key":"9_CR26","doi-asserted-by":"crossref","unstructured":"Bos, J., Costello, C., Ducas, L., Mironov, I., Naehrig, M., Nikolaenko, V., Raghunathan, A., Stebila, D.: Frodo: take off the ring! practical, quantum-secure key exchange from LWE. IACR Cryptology ePrint Archive 2016 (2016)","DOI":"10.1145\/2976749.2978425"},{"key":"9_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"868","DOI":"10.1007\/978-3-642-32009-5_50","volume-title":"Advances in Cryptology \u2013 CRYPTO 2012","author":"Z Brakerski","year":"2012","unstructured":"Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical GapSVP. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 868\u2013886. Springer, Heidelberg (2012). doi: 10.1007\/978-3-642-32009-5_50"},{"key":"9_CR28","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. In: ITCS (2012)","DOI":"10.1145\/2090236.2090262"},{"key":"9_CR29","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., Langlois, A., Peikert, C., Regev, O., Stehl\u00e9, D.: Classical hardness of learning with errors. In: STOC (2013)","DOI":"10.1145\/2488608.2488680"},{"key":"9_CR30","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: 10.1007\/978-3-642-54242-8_1"},{"key":"9_CR31","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., Vaikuntanathan, V.: Efficient fully homomorphic encryption from (standard) LWE. In: FOCS (2011)","DOI":"10.1109\/FOCS.2011.12"},{"key":"9_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-25385-0_1","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2011","author":"Y Chen","year":"2011","unstructured":"Chen, Y., Nguyen, P.Q.: BKZ 2.0: better lattice security estimates. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 1\u201320. Springer, Heidelberg (2011). doi: 10.1007\/978-3-642-25385-0_1"},{"key":"9_CR33","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: 10.1007\/978-3-642-40041-4_26"},{"key":"9_CR34","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1007\/978-3-540-69407-6_21","volume-title":"Logic and Theory of Algorithms","author":"G Crescenzo","year":"2008","unstructured":"Crescenzo, G., Lipmaa, H.: Succinct NP proofs from an extractability assumption. In: Beckmann, A., Dimitracopoulos, C., L\u00f6we, B. (eds.) CiE 2008. LNCS, vol. 5028, pp. 175\u2013185. Springer, Heidelberg (2008). doi: 10.1007\/978-3-540-69407-6_21"},{"key":"9_CR35","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1007\/3-540-46766-1_36","volume-title":"Advances in Cryptology \u2014 CRYPTO 1991","author":"I Damg\u00e5rd","year":"1992","unstructured":"Damg\u00e5rd, I.: Towards practical public key systems secure against chosen ciphertext attacks. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 445\u2013456. Springer, Heidelberg (1992). doi: 10.1007\/3-540-46766-1_36"},{"key":"9_CR36","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1007\/978-3-642-28914-9_4","volume-title":"Theory of Cryptography","author":"I Damg\u00e5rd","year":"2012","unstructured":"Damg\u00e5rd, I., Faust, S., Hazay, C.: Secure two-party computation with low communication. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 54\u201374. Springer, Heidelberg (2012). doi: 10.1007\/978-3-642-28914-9_4"},{"key":"9_CR37","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1007\/978-3-662-46800-5_24","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2015","author":"L Ducas","year":"2015","unstructured":"Ducas, L., Micciancio, D.: FHEW: bootstrapping homomorphic encryption in less than a second. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 617\u2013640. Springer, Heidelberg (2015). doi: 10.1007\/978-3-662-46800-5_24"},{"key":"9_CR38","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1007\/3-540-47721-7_12","volume-title":"Advances in Cryptology \u2014 CRYPTO 1986","author":"A Fiat","year":"1987","unstructured":"Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186\u2013194. Springer, Heidelberg (1987). doi: 10.1007\/3-540-47721-7_12"},{"key":"9_CR39","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: 10.1007\/978-3-642-38348-9_1"},{"key":"9_CR40","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1007\/978-3-642-54242-8_4","volume-title":"Theory of Cryptography","author":"S Garg","year":"2014","unstructured":"Garg, S., Gentry, C., Halevi, S., Raykova, M.: Two-round secure MPC from indistinguishability obfuscation. In: Lindell, Y. (ed.) TCC 2014. LNCS, vol. 8349, pp. 74\u201394. Springer, Heidelberg (2014). doi: 10.1007\/978-3-642-54242-8_4"},{"key":"9_CR41","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 (2013)","DOI":"10.1109\/FOCS.2013.13"},{"key":"9_CR42","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"626","DOI":"10.1007\/978-3-642-38348-9_37","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2013","author":"R Gennaro","year":"2013","unstructured":"Gennaro, R., Gentry, C., Parno, B., Raykova, M.: Quadratic span programs and succinct NIZKs without PCPs. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 626\u2013645. Springer, Heidelberg (2013). doi: 10.1007\/978-3-642-38348-9_37"},{"key":"9_CR43","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: 10.1007\/978-3-662-46497-7_20"},{"key":"9_CR44","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1007\/978-3-642-29011-4_28","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2012","author":"C Gentry","year":"2012","unstructured":"Gentry, C., Halevi, S., Smart, N.P.: Fully homomorphic encryption with polylog overhead. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 465\u2013482. Springer, Heidelberg (2012). doi: 10.1007\/978-3-642-29011-4_28"},{"key":"9_CR45","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1007\/978-3-642-40041-4_5","volume-title":"Advances in Cryptology \u2013 CRYPTO 2013","author":"C Gentry","year":"2013","unstructured":"Gentry, C., Sahai, A., Waters, B.: Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013. LNCS, vol. 8042, pp. 75\u201392. Springer, Heidelberg (2013). doi: 10.1007\/978-3-642-40041-4_5"},{"key":"9_CR46","doi-asserted-by":"crossref","unstructured":"Gentry, C., Wichs, D.: Separating succinct non-interactive arguments from all falsifiable assumptions. In: STOC (2011)","DOI":"10.1145\/1993636.1993651"},{"key":"9_CR47","unstructured":"Goldwasser, S., Lin, H., Rubinstein, A.: Delegation of computation without rejection problem from designated verifier CS-proofs. IACR Cryptology ePrint Archive 2011 (2011)"},{"key":"9_CR48","doi-asserted-by":"crossref","unstructured":"Goldwasser, S., Micali, S.: Probabilistic encryption and how to play mental poker keeping secret all partial information. In: STOC (1982)","DOI":"10.1145\/800070.802212"},{"key":"9_CR49","doi-asserted-by":"crossref","unstructured":"Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof-systems (extended abstract). In: STOC (1985)","DOI":"10.1145\/22145.22178"},{"key":"9_CR50","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1007\/978-3-642-11799-2_19","volume-title":"Theory of Cryptography","author":"V Goyal","year":"2010","unstructured":"Goyal, V., Ishai, Y., Sahai, A., Venkatesan, R., Wadia, A.: Founding cryptography on tamper-proof hardware tokens. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 308\u2013326. Springer, Heidelberg (2010). doi: 10.1007\/978-3-642-11799-2_19"},{"key":"9_CR51","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/978-3-642-17373-8_19","volume-title":"Advances in Cryptology - ASIACRYPT 2010","author":"J Groth","year":"2010","unstructured":"Groth, J.: Short pairing-based non-interactive zero-knowledge arguments. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 321\u2013340. Springer, Heidelberg (2010). doi: 10.1007\/978-3-642-17373-8_19"},{"key":"9_CR52","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/10722028_23","volume-title":"Algorithmic Number Theory","author":"A Joux","year":"2000","unstructured":"Joux, A.: A one round protocol for tripartite Diffie\u2013Hellman. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 385\u2013393. Springer, Heidelberg (2000). doi: 10.1007\/10722028_23"},{"key":"9_CR53","doi-asserted-by":"crossref","unstructured":"Kilian, J.: A note on efficient zero-knowledge proofs and arguments (extended abstract). In: STOC (1992)","DOI":"10.1145\/129712.129782"},{"key":"9_CR54","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/978-3-662-47989-6_3","volume-title":"Advances in Cryptology \u2013 CRYPTO 2015","author":"P Kirchner","year":"2015","unstructured":"Kirchner, P., Fouque, P.-A.: An improved BKW algorithm for LWE with applications to cryptography and lattices. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 43\u201362. Springer, Heidelberg (2015). doi: 10.1007\/978-3-662-47989-6_3"},{"key":"9_CR55","doi-asserted-by":"crossref","unstructured":"Koppula, V., Lewko, A.B., Waters, B.: Indistinguishability obfuscation for turing machines with unbounded memory. In: STOC (2015)","DOI":"10.1145\/2746539.2746614"},{"key":"9_CR56","doi-asserted-by":"crossref","unstructured":"Lewi, K., Malozemoff, A.J., Apon, D., Carmer, B., Foltzer, A., Wagner, D., Archer, D.W., Boneh, D., Katz, J., Raykova, M.: 5Gen: a framework for prototyping applications using multilinear maps and matrix branching programs. In: ACM CCS (2016)","DOI":"10.1145\/2976749.2978314"},{"key":"9_CR57","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: 10.1007\/978-3-662-49890-3_2"},{"key":"9_CR58","doi-asserted-by":"crossref","unstructured":"Lin, H.: Indistinguishability obfuscation from DDH on 5-linear maps and locality-5 PRGs. IACR Cryptology ePrint Archive 2016 (2016)","DOI":"10.1007\/978-3-319-63688-7_20"},{"key":"9_CR59","doi-asserted-by":"crossref","unstructured":"Lin, R., Vaikuntanathan, V.: Indistinguishability obfuscation from DDH-like assumptions on constant-degree graded encodings. In: FOCS (2016)","DOI":"10.1109\/FOCS.2016.11"},{"key":"9_CR60","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1007\/978-3-642-19074-2_21","volume-title":"Topics in Cryptology \u2013 CT-RSA 2011","author":"R Lindner","year":"2011","unstructured":"Lindner, R., Peikert, C.: Better key sizes (and attacks) for LWE-based encryption. In: Kiayias, A. (ed.) CT-RSA 2011. LNCS, vol. 6558, pp. 319\u2013339. Springer, Heidelberg (2011). doi: 10.1007\/978-3-642-19074-2_21"},{"key":"9_CR61","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1007\/978-3-642-28914-9_10","volume-title":"Theory of Cryptography","author":"H Lipmaa","year":"2012","unstructured":"Lipmaa, H.: Progression-free sets and sublinear pairing-based non-interactive zero-knowledge arguments. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 169\u2013189. Springer, Heidelberg (2012). doi: 10.1007\/978-3-642-28914-9_10"},{"key":"9_CR62","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-13190-5_1","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"V Lyubashevsky","year":"2010","unstructured":"Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 1\u201323. Springer, Heidelberg (2010). doi: 10.1007\/978-3-642-13190-5_1"},{"issue":"4","key":"9_CR63","doi-asserted-by":"crossref","first-page":"1253","DOI":"10.1137\/S0097539795284959","volume":"30","author":"S Micali","year":"2000","unstructured":"Micali, S.: Computationally sound proofs. SIAM J. Comput. 30(4), 1253\u20131298 (2000)","journal-title":"SIAM J. Comput."},{"issue":"4","key":"9_CR64","first-page":"343","volume":"2","author":"T Mie","year":"2008","unstructured":"Mie, T.: Polylogarithmic two-round argument systems. J. Math. Cryptol. 2(4), 343\u2013363 (2008)","journal-title":"J. Math. Cryptol."},{"key":"9_CR65","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1007\/978-3-540-45146-4_6","volume-title":"Advances in Cryptology - CRYPTO 2003","author":"M Naor","year":"2003","unstructured":"Naor, M.: On cryptographic assumptions and challenges. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 96\u2013109. Springer, Heidelberg (2003). doi: 10.1007\/978-3-540-45146-4_6"},{"key":"9_CR66","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/3-540-48910-X_16","volume-title":"Advances in Cryptology \u2014 EUROCRYPT \u201999","author":"P Paillier","year":"1999","unstructured":"Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223\u2013238. Springer, Heidelberg (1999). doi: 10.1007\/3-540-48910-X_16"},{"key":"9_CR67","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"554","DOI":"10.1007\/978-3-540-85174-5_31","volume-title":"Advances in Cryptology \u2013 CRYPTO 2008","author":"C Peikert","year":"2008","unstructured":"Peikert, C., Vaikuntanathan, V., Waters, B.: A framework for efficient and composable oblivious transfer. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 554\u2013571. Springer, Heidelberg (2008). doi: 10.1007\/978-3-540-85174-5_31"},{"key":"9_CR68","doi-asserted-by":"crossref","unstructured":"Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC (2005)","DOI":"10.1145\/1060590.1060603"},{"key":"9_CR69","doi-asserted-by":"crossref","unstructured":"Sahai, A., Waters, B.: How to use indistinguishability obfuscation: deniable encryption, and more. In: STOC (2014)","DOI":"10.1145\/2591796.2591825"},{"key":"9_CR70","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/BF01581144","volume":"66","author":"C Schnorr","year":"1994","unstructured":"Schnorr, C., Euchner, M.: Lattice basis reduction: improved practical algorithms and solving subset sum problems. Math. Program. 66, 181\u2013199 (1994)","journal-title":"Math. Program."},{"issue":"4","key":"9_CR71","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1145\/322217.322225","volume":"27","author":"JT Schwartz","year":"1980","unstructured":"Schwartz, J.T.: Fast probabilistic algorithms for verification of polynomial identities. J. ACM 27(4), 701\u2013717 (1980)","journal-title":"J. ACM"},{"key":"9_CR72","unstructured":"Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: FOCS (1994)"},{"issue":"5","key":"9_CR73","doi-asserted-by":"crossref","first-page":"1474","DOI":"10.1137\/S0097539796298637","volume":"26","author":"DR Simon","year":"1997","unstructured":"Simon, D.R.: On the power of quantum computation. SIAM J. Comput. 26(5), 1474\u20131483 (1997)","journal-title":"SIAM J. Comput."},{"key":"9_CR74","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: 10.1007\/978-3-662-46803-6_15"},{"key":"9_CR75","doi-asserted-by":"crossref","unstructured":"Zippel, R.: Probabilistic algorithms for sparse polynomials. In: EUROSAM (1979)","DOI":"10.1007\/3-540-09519-5_73"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 EUROCRYPT 2017"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-56617-7_9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,20]],"date-time":"2019-09-20T08:02:09Z","timestamp":1568966529000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-56617-7_9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319566160","9783319566177"],"references-count":75,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-56617-7_9","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017]]}}}