{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T00:27:02Z","timestamp":1769300822884,"version":"3.49.0"},"publisher-location":"Cham","reference-count":74,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030778828","type":"print"},{"value":"9783030778835","type":"electronic"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-77883-5_4","type":"book-chapter","created":{"date-parts":[[2021,6,15]],"date-time":"2021-06-15T23:06:10Z","timestamp":1623798370000},"page":"97-126","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":30,"title":["Indistinguishability Obfuscation from Simple-to-State Hard Problems: New Assumptions, New Techniques, and Simplification"],"prefix":"10.1007","author":[{"given":"Romain","family":"Gay","sequence":"first","affiliation":[]},{"given":"Aayush","family":"Jain","sequence":"additional","affiliation":[]},{"given":"Huijia","family":"Lin","sequence":"additional","affiliation":[]},{"given":"Amit","family":"Sahai","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,6,16]]},"reference":[{"key":"4_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"733","DOI":"10.1007\/978-3-662-46447-2_33","volume-title":"Public-Key Cryptography \u2013 PKC 2015","author":"M Abdalla","year":"2015","unstructured":"Abdalla, M., Bourse, F., De Caro, A., Pointcheval, D.: Simple functional encryption schemes for inner products. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 733\u2013751. Springer, Heidelberg (2015). https:\/\/doi.org\/10.1007\/978-3-662-46447-2_33"},{"key":"4_CR2","doi-asserted-by":"crossref","unstructured":"Abdalla, M., Catalano, D., Gay, R., Ursu, B.: Inner-product functional encryption with fine-grained access control. Cryptology ePrint Archive, Report 2020\/577 (2020). https:\/\/eprint.iacr.org\/2020\/577","DOI":"10.1007\/978-3-030-64840-4_16"},{"key":"4_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1007\/978-3-030-17653-2_7","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2019","author":"S Agrawal","year":"2019","unstructured":"Agrawal, S.: Indistinguishability obfuscation without multilinear maps: new methods for bootstrapping and instantiation. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019, Part I. LNCS, vol. 11476, pp. 191\u2013225. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-17653-2_7"},{"key":"4_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/978-3-662-53015-3_12","volume-title":"Advances in Cryptology \u2013 CRYPTO 2016","author":"S Agrawal","year":"2016","unstructured":"Agrawal, S., Libert, B., Stehl\u00e9, D.: Fully secure functional encryption for inner products, from standard assumptions. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016, Part III. LNCS, vol. 9816, pp. 333\u2013362. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53015-3_12"},{"key":"4_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1007\/978-3-030-45721-1_5","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2020","author":"S Agrawal","year":"2020","unstructured":"Agrawal, S., Pellet-Mary, A.: Indistinguishability obfuscation without maps: attacks and fixes for noisy linear FE. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020, Part I. LNCS, vol. 12105, pp. 110\u2013140. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-45721-1_5"},{"key":"4_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1007\/978-3-319-70500-2_7","volume-title":"Theory of Cryptography","author":"S Agrawal","year":"2017","unstructured":"Agrawal, S., Rosen, A.: Functional encryption for bounded collusions, revisited. In: Kalai, Y., Reyzin, L. (eds.) TCC 2017, Part I. LNCS, vol. 10677, pp. 173\u2013205. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-70500-2_7"},{"issue":"2","key":"4_CR7","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1145\/2815111.2815158","volume":"49","author":"MR Albrecht","year":"2015","unstructured":"Albrecht, M.R., Cid, C., Faug\u00e8re, J.-C., Fitzpatrick, R., Perret, L.: Algebraic algorithms for LWE problems. ACM Commun. Comput. Algebra 49(2), 62 (2015)","journal-title":"ACM Commun. Comput. Algebra"},{"key":"4_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1007\/978-3-662-48000-7_32","volume-title":"Advances in Cryptology \u2013 CRYPTO 2015","author":"P Ananth","year":"2015","unstructured":"Ananth, P., Brakerski, Z., Segev, G., Vaikuntanathan, V.: From selective to adaptive security in functional encryption. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015, Part II. LNCS, vol. 9216, pp. 657\u2013677. Springer, Heidelberg (2015). https:\/\/doi.org\/10.1007\/978-3-662-48000-7_32"},{"key":"4_CR9","doi-asserted-by":"crossref","unstructured":"Ananth, P., Gupta, D., Ishai, Y., Sahai, A.: Optimizing obfuscation: avoiding Barrington\u2019s theorem. In: ACM CCS, pp. 646\u2013658 (2014)","DOI":"10.1145\/2660267.2660342"},{"key":"4_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"284","DOI":"10.1007\/978-3-030-26954-8_10","volume-title":"Advances in Cryptology \u2013 CRYPTO 2019","author":"P Ananth","year":"2019","unstructured":"Ananth, P., Jain, A., Lin, H., Matt, C., Sahai, A.: Indistinguishability obfuscation without multilinear maps: new paradigms via low degree weak pseudorandomness and security amplification. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019, Part III. LNCS, vol. 11694, pp. 284\u2013332. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-26954-8_10"},{"key":"4_CR11","doi-asserted-by":"crossref","unstructured":"Ananth, P., Jain, A., Sahai, A.: Indistinguishability obfuscation without multilinear maps: IO from LWE, bilinear maps, and weak pseudorandomness. IACR Cryptology ePrint Archive 2018:615 (2018)","DOI":"10.1007\/978-3-030-26954-8_10"},{"key":"4_CR12","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, Part I. LNCS, vol. 9215, pp. 308\u2013326. Springer, Heidelberg (2015). https:\/\/doi.org\/10.1007\/978-3-662-47989-6_15"},{"key":"4_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1007\/978-3-319-56620-7_6","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2017","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 I. LNCS, vol. 10210, pp. 152\u2013181. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-56620-7_6"},{"key":"4_CR14","doi-asserted-by":"crossref","unstructured":"Applebaum, B.: Pseudorandom generators with long stretch and low locality from random local one-way functions. In: Karloff, H.J., Pitassi, T. (eds.) 44th ACM STOC, pp. 805\u2013816. ACM Press, May 2012","DOI":"10.1145\/2213977.2214050"},{"key":"4_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1007\/978-3-642-28914-9_34","volume-title":"Theory of Cryptography","author":"B Applebaum","year":"2012","unstructured":"Applebaum, B., Bogdanov, A., Rosen, A.: A dichotomy for local small-bias generators. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 600\u2013617. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-28914-9_34"},{"key":"4_CR16","doi-asserted-by":"crossref","unstructured":"Applebaum, B., Lovett, S.: Algebraic attacks against random local functions and their countermeasures. In: Wichs, D., Mansour, Y. (eds.) 48th ACM STOC, pp. 1087\u20131100. ACM Press, June 2016","DOI":"10.1145\/2897518.2897554"},{"key":"4_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1007\/978-3-642-22006-7_34","volume-title":"Automata, Languages and Programming","author":"S Arora","year":"2011","unstructured":"Arora, S., Ge, R.: New algorithms for learning in presence of errors. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part I. LNCS, vol. 6755, pp. 403\u2013415. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-22006-7_34"},{"key":"4_CR18","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":"4_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/978-3-319-63688-7_3","volume-title":"Advances in Cryptology \u2013 CRYPTO 2017","author":"CEZ Baltico","year":"2017","unstructured":"Baltico, C.E.Z., Catalano, D., Fiore, D., Gay, R.: Practical functional encryption for quadratic functions with applications to predicate encryption. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017, Part I. LNCS, vol. 10401, pp. 67\u201398. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-63688-7_3"},{"key":"4_CR20","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":"4_CR21","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., et al.: On the (im)possibility of obfuscating programs. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 1\u201318. Springer, Heidelberg (2001). https:\/\/doi.org\/10.1007\/3-540-44647-8_1"},{"key":"4_CR22","unstructured":"Bartusek, J., Ishai, Y., Jain, A., Ma, F., Sahai, A., Zhandry, M.: Affine determinant programs: a framework for obfuscation and witness encryption. In: Vidick, T. (ed.) 11th Innovations in Theoretical Computer Science Conference, ITCS 2020, Seattle, Washington, USA, 12\u201314 January 2020. LIPIcs, vol. 151, pp. 82:1\u201382:39. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2020)"},{"key":"4_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1007\/978-3-662-53644-5_15","volume-title":"Theory of Cryptography","author":"N Bitansky","year":"2016","unstructured":"Bitansky, N., Nishimaki, R., Passel\u00e8gue, A., Wichs, D.: From cryptomania to obfustopia through secret-key functional encryption. In: Hirt, M., Smith, A. (eds.) TCC 2016, Part II. LNCS, vol. 9986, pp. 391\u2013418. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53644-5_15"},{"key":"4_CR24","doi-asserted-by":"crossref","unstructured":"Bitansky, N., Paneth, O., Rosen, A.: On the cryptographic hardness of finding a Nash equilibrium. In: Guruswami, V. (ed.) 56th FOCS, pp. 1480\u20131498. IEEE Computer Society Press, October 2015","DOI":"10.1109\/FOCS.2015.94"},{"key":"4_CR25","doi-asserted-by":"crossref","unstructured":"Bitansky, N., Vaikuntanathan, V.: Indistinguishability obfuscation from functional encryption. In: Guruswami, V. (ed.) 56th FOCS, pp. 171\u2013190. IEEE Computer Society Press, October 2015","DOI":"10.1109\/FOCS.2015.20"},{"issue":"1","key":"4_CR26","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/s00037-011-0034-0","volume":"21","author":"A Bogdanov","year":"2012","unstructured":"Bogdanov, A., Qiao, Y.: On the security of Goldreich\u2019s one-way function. Comput. Complex. 21(1), 83\u2013127 (2012)","journal-title":"Comput. Complex."},{"key":"4_CR27","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.: Identity-based encryption from the Weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213\u2013229. Springer, Heidelberg (2001). https:\/\/doi.org\/10.1007\/3-540-44647-8_13"},{"key":"4_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/978-3-642-19571-6_16","volume-title":"Theory of Cryptography","author":"D Boneh","year":"2011","unstructured":"Boneh, D., Sahai, A., Waters, B.: Functional encryption: definitions and challenges. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 253\u2013273. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-19571-6_16"},{"key":"4_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/978-3-030-45721-1_4","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2020","author":"Z Brakerski","year":"2020","unstructured":"Brakerski, Z., D\u00f6ttling, N., Garg, S., Malavolta, G.: Candidate iO from homomorphic encryption schemes. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12105, pp. 79\u2013109. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-45721-1_4"},{"key":"4_CR30","doi-asserted-by":"crossref","unstructured":"Brakerski, Z., Gentry, C., Vaikuntanathan, V.: (Leveled) fully homomorphic encryption without bootstrapping. In: Innovations in Theoretical Computer Science 2012, Cambridge, MA, USA, 8\u201310 January 2012, pp. 309\u2013325 (2012)","DOI":"10.1145\/2090236.2090262"},{"key":"4_CR31","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). https:\/\/doi.org\/10.1007\/978-3-642-54242-8_1"},{"key":"4_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1007\/978-3-642-22792-9_29","volume-title":"Advances in Cryptology \u2013 CRYPTO 2011","author":"Z Brakerski","year":"2011","unstructured":"Brakerski, Z., Vaikuntanathan, V.: Fully homomorphic encryption from ring-LWE and security for key dependent messages. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 505\u2013524. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-22792-9_29"},{"key":"4_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1007\/978-3-662-44371-2_11","volume-title":"Advances in Cryptology \u2013 CRYPTO 2014","author":"C Brzuska","year":"2014","unstructured":"Brzuska, C., Farshim, P., Mittelbach, A.: Indistinguishability obfuscation and UCEs: the case of computationally unpredictable sources. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part I. LNCS, vol. 8616, pp. 188\u2013205. Springer, Heidelberg (2014). https:\/\/doi.org\/10.1007\/978-3-662-44371-2_11"},{"key":"4_CR34","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1007\/978-3-319-31517-1_2","volume-title":"Progress in Cryptology \u2013 AFRICACRYPT 2016","author":"J Buchmann","year":"2016","unstructured":"Buchmann, J., G\u00f6pfert, F., Player, R., Wunderer, T.: On the hardness of LWE with binary error: revisiting the hybrid lattice-reduction and meet-in-the-middle attack. In: Pointcheval, D., Nitaj, A., Rachidi, T. (eds.) AFRICACRYPT 2016. LNCS, vol. 9646, pp. 24\u201343. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-31517-1_2"},{"key":"4_CR35","unstructured":"Caho, S., Tibouchi, M., Abe, M.: Sample-time trade-off for the Arora-Ge attack on binary LWE. In: Symposium on Cryptography and Information Theory (2019)"},{"key":"4_CR36","unstructured":"Sun, C., Tibouchi, M., Abe, M.: Revisiting the hardness of binary error LWE. Cryptology ePrint Archive, Report 2020\/666 (2020). https:\/\/eprint.iacr.org\/2020\/666"},{"key":"4_CR37","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, Part II. LNCS, vol. 10992, pp. 577\u2013607. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-96881-0_20"},{"key":"4_CR38","doi-asserted-by":"crossref","unstructured":"Cohen, A., Holmgren, J., Nishimaki, R., Vaikuntanathan, V., Wichs, D.: Watermarking cryptographic capabilities. In: STOC (2016)","DOI":"10.1145\/2897518.2897651"},{"key":"4_CR39","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1007\/978-3-030-03329-3_4","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2018","author":"G Couteau","year":"2018","unstructured":"Couteau, G., Dupin, A., M\u00e9aux, P., Rossi, M., Rotella, Y.: On the concrete security of Goldreich\u2019s pseudorandom generator. In: Peyrin, T., Galbraith, S. (eds.) ASIACRYPT 2018, Part II. LNCS, vol. 11273, pp. 96\u2013124. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-030-03329-3_4"},{"key":"4_CR40","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: 54th FOCS, pp. 40\u201349. IEEE Computer Society Press, October 2013","DOI":"10.1109\/FOCS.2013.13"},{"key":"4_CR41","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, Part II. LNCS, vol. 9986, pp. 241\u2013268. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53644-5_10"},{"key":"4_CR42","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1007\/978-3-662-53008-5_20","volume-title":"Advances in Cryptology \u2013 CRYPTO 2016","author":"S Garg","year":"2016","unstructured":"Garg, S., Pandey, O., Srinivasan, A.: Revisiting the cryptographic hardness of finding a Nash equilibrium. In: Robshaw, M., Katz, J. (eds.) CRYPTO 2016, Part II. LNCS, vol. 9815, pp. 579\u2013604. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53008-5_20"},{"key":"4_CR43","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/978-3-030-45374-9_4","volume-title":"Public-Key Cryptography \u2013 PKC 2020","author":"R Gay","year":"2020","unstructured":"Gay, R.: A new paradigm for public-key functional encryption for degree-2 polynomials. In: Kiayias, A., Kohlweiss, M., Wallden, P., Zikas, V. (eds.) PKC 2020, Part I. LNCS, vol. 12110, pp. 95\u2013120. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-45374-9_4"},{"key":"4_CR44","doi-asserted-by":"crossref","unstructured":"Gay, R., Jain, A., Lin, H., Sahai, A.: Indistinguishability obfuscation from simple-to-state hard problems: new assumptions, new techniques, and simplification. IACR Cryptology ePrint Archive 2020:764 (2020)","DOI":"10.1007\/978-3-030-77883-5_4"},{"key":"4_CR45","unstructured":"Gentry, C., Jutla, C.S., Kane, D.: Obfuscation using tensor products. In: Electronic Colloquium on Computational Complexity (ECCC), vol. 25, p. 149 (2018)"},{"key":"4_CR46","doi-asserted-by":"crossref","unstructured":"Gentry, C., Lewko, A.B., Sahai, A., Waters, B.: Indistinguishability obfuscation from the multilinear subgroup elimination assumption. IACR Cryptology ePrint Archive 2014:309 (2014)","DOI":"10.1109\/FOCS.2015.19"},{"key":"4_CR47","unstructured":"Goldreich, O.: Candidate one-way functions based on expander graphs. In: Electronic Colloquium on Computational Complexity (ECCC), vol. 7, no. 90 (2000)"},{"key":"4_CR48","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"578","DOI":"10.1007\/978-3-642-55220-5_32","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2014","author":"S Goldwasser","year":"2014","unstructured":"Goldwasser, S., et al.: Multi-input functional encryption. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 578\u2013602. Springer, Heidelberg (2014). https:\/\/doi.org\/10.1007\/978-3-642-55220-5_32"},{"key":"4_CR49","doi-asserted-by":"crossref","unstructured":"Goldwasser, S., Kalai, Y.T., Popa, R.A., Vaikuntanathan, V., Zeldovich, N.: Reusable garbled circuits and succinct functional encryption. In: Boneh, D., Roughgarden, T., Feigenbaum, J. (eds.) 45th ACM STOC, pp. 555\u2013564. ACM Press, June 2013","DOI":"10.1145\/2488608.2488678"},{"key":"4_CR50","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/978-3-540-85174-5_3","volume-title":"Advances in Cryptology \u2013 CRYPTO 2008","author":"S Goldwasser","year":"2008","unstructured":"Goldwasser, S., Kalai, Y.T., Rothblum, G.N.: One-time programs. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 39\u201356. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-85174-5_3"},{"key":"4_CR51","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1007\/978-3-642-32009-5_11","volume-title":"Advances in Cryptology \u2013 CRYPTO 2012","author":"S Gorbunov","year":"2012","unstructured":"Gorbunov, S., Vaikuntanathan, V., Wee, H.: Functional encryption with bounded collusions via multi-party computation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 162\u2013179. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-32009-5_11"},{"key":"4_CR52","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1007\/978-3-662-48000-7_25","volume-title":"Advances in Cryptology \u2013 CRYPTO 2015","author":"S Gorbunov","year":"2015","unstructured":"Gorbunov, S., Vaikuntanathan, V., Wee, H.: Predicate encryption for circuits from LWE. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015, Part II. LNCS, vol. 9216, pp. 503\u2013523. Springer, Heidelberg (2015). https:\/\/doi.org\/10.1007\/978-3-662-48000-7_25"},{"key":"4_CR53","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"715","DOI":"10.1007\/978-3-662-53890-6_24","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2016","author":"D Hofheinz","year":"2016","unstructured":"Hofheinz, D., Jager, T., Khurana, D., Sahai, A., Waters, B., Zhandry, M.: How to generate and use universal samplers. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016, Part II. LNCS, vol. 10032, pp. 715\u2013744. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-53890-6_24"},{"key":"4_CR54","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"494","DOI":"10.1007\/978-3-642-40041-4_27","volume-title":"Advances in Cryptology \u2013 CRYPTO 2013","author":"S Hohenberger","year":"2013","unstructured":"Hohenberger, S., Sahai, A., Waters, B.: Full domain hash from (leveled) multilinear maps and identity-based aggregate signatures. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 494\u2013512. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-40041-4_27"},{"key":"4_CR55","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/978-3-030-17653-2_9","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2019","author":"A Jain","year":"2019","unstructured":"Jain, A., Lin, H., Matt, C., Sahai, A.: How to leverage hardness of constant-degree expanding polynomials over $$\\mathbb{R}$$ to build $$i\\cal{O}$$. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019, Part I. LNCS, vol. 11476, pp. 251\u2013281. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-17653-2_9"},{"key":"4_CR56","unstructured":"Jain, A., Lin, H., Sahai, A.: Indistinguishability obfuscation from well-founded assumptions. Cryptology ePrint Archive, Report 2020\/1003 (2020). https:\/\/eprint.iacr.org\/2020\/1003"},{"key":"4_CR57","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). https:\/\/doi.org\/10.1007\/10722028_23"},{"key":"4_CR58","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":"4_CR59","doi-asserted-by":"crossref","unstructured":"Kothari, P.K., Mori, R., O\u2019Donnell, R., Witmer, D.: Sum of squares lower bounds for refuting any CSP. In: Hatami, H., McKenzie, P., King, V. (eds.) 49th ACM STOC, pp. 132\u2013145. ACM Press, June 2017","DOI":"10.1145\/3055399.3055485"},{"key":"4_CR60","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, Part I. LNCS, vol. 9665, pp. 28\u201357. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-49890-3_2"},{"key":"4_CR61","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"599","DOI":"10.1007\/978-3-319-63688-7_20","volume-title":"Advances in Cryptology \u2013 CRYPTO 2017","author":"H Lin","year":"2017","unstructured":"Lin, H.: Indistinguishability obfuscation from SXDH on 5-linear maps and locality-5 PRGs. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017, Part I. LNCS, vol. 10401, pp. 599\u2013629. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-63688-7_20"},{"key":"4_CR62","unstructured":"Lin, H., Matt, C.: Pseudo flawed-smudging generators and their application to indistinguishability obfuscation. IACR Cryptology ePrint Archive 2018:646 (2018)"},{"key":"4_CR63","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"630","DOI":"10.1007\/978-3-319-63688-7_21","volume-title":"Advances in Cryptology \u2013 CRYPTO 2017","author":"H Lin","year":"2017","unstructured":"Lin, H., Tessaro, S.: Indistinguishability obfuscation from trilinear maps and block-wise local PRGs. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017, Part I. LNCS, vol. 10401, pp. 630\u2013660. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-63688-7_21"},{"key":"4_CR64","doi-asserted-by":"crossref","unstructured":"Lin, H., Vaikuntanathan, V.: Indistinguishability obfuscation from DDH-like assumptions on constant-degree graded encodings. In: Dinur, I. (ed.) 57th FOCS, pp. 11\u201320. IEEE Computer Society Press, October 2016","DOI":"10.1109\/FOCS.2016.11"},{"key":"4_CR65","unstructured":"Lombardi, A., Vaikuntanathan, V.: Minimizing the complexity of Goldreich\u2019s pseudorandom generator. IACR Cryptology ePrint Archive 2017:277 (2017)"},{"key":"4_CR66","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/978-3-642-40041-4_2","volume-title":"Advances in Cryptology \u2013 CRYPTO 2013","author":"D Micciancio","year":"2013","unstructured":"Micciancio, D., Peikert, C.: Hardness of SIS and LWE with small parameters. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 21\u201339. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-40041-4_2"},{"key":"4_CR67","unstructured":"Mossel, E., Shpilka, A., Trevisan, L.: On e-biased generators in NC0. In: 44th FOCS, pp. 136\u2013145. IEEE Computer Society Press, October 2003"},{"key":"4_CR68","doi-asserted-by":"crossref","unstructured":"O\u2019Donnell, R., Witmer, D.: Goldreich\u2019s PRG: evidence for near-optimal polynomial stretch. In: IEEE 29th Conference on Computational Complexity, CCC 2014, Vancouver, BC, Canada, 11\u201313 June 2014, pp. 1\u201312. IEEE Computer Society (2014)","DOI":"10.1109\/CCC.2014.9"},{"key":"4_CR69","unstructured":"O\u2019Neill, A.: Definitional issues in functional encryption. IACR Cryptology ePrint Archive 2010:556 (2010)"},{"key":"4_CR70","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, Part I. LNCS, vol. 8616, pp. 500\u2013517. Springer, Heidelberg (2014). https:\/\/doi.org\/10.1007\/978-3-662-44371-2_28"},{"key":"4_CR71","doi-asserted-by":"crossref","unstructured":"Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: STOC, pp. 84\u201393 (2005)","DOI":"10.1145\/1060590.1060603"},{"key":"4_CR72","doi-asserted-by":"crossref","unstructured":"Sahai, A., Seyalioglu, H.: Worry-free encryption: functional encryption with public keys. In: Al-Shaer, E., Keromytis, A.D., Shmatikov, V. (eds.) Proceedings of the 17th ACM Conference on Computer and Communications Security, ACM CCS 2010, pp. 463\u2013472. ACM (2010)","DOI":"10.1145\/1866307.1866359"},{"key":"4_CR73","doi-asserted-by":"crossref","unstructured":"Sahai, A., Waters, B.: How to use indistinguishability obfuscation: deniable encryption, and more. In: Shmoys, D.B. (ed.) STOC, pp. 475\u2013484. ACM (2014)","DOI":"10.1145\/2591796.2591825"},{"key":"4_CR74","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). https:\/\/doi.org\/10.1007\/11426639_27"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 EUROCRYPT 2021"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-77883-5_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,1]],"date-time":"2024-09-01T21:53:28Z","timestamp":1725227608000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-77883-5_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030778828","9783030778835"],"references-count":74,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-77883-5_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"16 June 2021","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":"Zagreb","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Croatia","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 October 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21 October 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"40","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"eurocrypt2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/eurocrypt.iacr.org\/2021\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"HotCRP","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"400","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"78","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"20% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"at least 3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"21","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}