{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T16:10:08Z","timestamp":1747930208528,"version":"3.41.0"},"publisher-location":"Cham","reference-count":21,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319171418"},{"type":"electronic","value":"9783319171425"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"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":[[2015]]},"DOI":"10.1007\/978-3-319-17142-5_8","type":"book-chapter","created":{"date-parts":[[2015,4,15]],"date-time":"2015-04-15T11:19:29Z","timestamp":1429096769000},"page":"75-86","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Some New Consequences of the Hypothesis That P Has Fixed Polynomial-Size Circuits"],"prefix":"10.1007","author":[{"given":"Ning","family":"Ding","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,4,16]]},"reference":[{"issue":"2","key":"8_CR1","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1145\/2160158.2160159","volume":"59","author":"B Barak","year":"2012","unstructured":"Barak, B., Goldreich, O., Impagliazzo, R., Rudich, S., Sahai, A., Vadhan, S.P., Yang, K.: On the (im)possibility of obfuscating programs. J. ACM 59(2), 6 (2012)","journal-title":"J. ACM"},{"issue":"2","key":"8_CR2","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1016\/j.jcss.2005.06.010","volume":"72","author":"B Barak","year":"2006","unstructured":"Barak, B., Lindell, Y., Vadhan, S.P.: Lower bounds for non-black-box zero knowledge. J. Comput. Syst. Sci. 72(2), 321\u2013391 (2006)","journal-title":"J. Comput. Syst. Sci."},{"key":"8_CR3","doi-asserted-by":"crossref","unstructured":"Buhrman, H., Fortnow, L., Thierauf, T.: Nonrelativizing separations. In: IEEE Conference on Computational Complexity, pp. 8\u201312. IEEE Computer Society (1998)","DOI":"10.1109\/CCC.1998.694585"},{"key":"8_CR4","doi-asserted-by":"crossref","unstructured":"Dwork, C., Naor, M.: Zaps and their applications. In: FOCS, pp. 283\u2013293. IEEE Computer Society (2000)","DOI":"10.1109\/SFCS.2000.892117"},{"key":"8_CR5","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. IEEE Computer Society (2013)","DOI":"10.1109\/FOCS.2013.13"},{"issue":"3","key":"8_CR6","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/s001459900010","volume":"9","author":"O Goldreich","year":"1996","unstructured":"Goldreich, O., Kahan, A.: How to construct constant-round zero-knowledge proof systems for np. J. Cryptol. 9(3), 167\u2013190 (1996)","journal-title":"J. Cryptol."},{"issue":"1","key":"8_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF00195207","volume":"7","author":"O Goldreich","year":"1994","unstructured":"Goldreich, O., Oren, Y.: Definitions and properties of zero-knowledge proof systems. J. Cryptol. 7(1), 1\u201332 (1994)","journal-title":"J. Cryptol."},{"issue":"1","key":"8_CR8","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1137\/0218012","volume":"18","author":"S Goldwasser","year":"1989","unstructured":"Goldwasser, S., Micali, S., Rackoff, C.: The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1), 186\u2013208 (1989)","journal-title":"SIAM J. Comput."},{"issue":"4","key":"8_CR9","doi-asserted-by":"publisher","first-page":"1364","DOI":"10.1137\/S0097539793244708","volume":"28","author":"J H\u00e5stad","year":"1999","unstructured":"H\u00e5stad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A pseudorandom generator from any one-way function. SIAM J. Comput. 28(4), 1364\u20131396 (1999)","journal-title":"SIAM J. Comput."},{"key":"8_CR10","doi-asserted-by":"crossref","unstructured":"Impagliazzo, R., Wigderson, A.: P = BPP if e requires exponential circuits: derandomizing the xor lemma. In: Leighton, F.T., Shor, P.W. (eds.) STOC, pp. 220\u2013229. ACM (1997)","DOI":"10.1145\/258533.258590"},{"key":"8_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1007\/3-540-45687-2_29","volume-title":"Mathematical Foundations of Computer Science 2002","author":"K Iwama","year":"2002","unstructured":"Iwama, K., Morizumi, H.: An explicit lower bound of 5$$n$$-$$o$$($$n$$) for boolean circuits. In: Diks, K., Rytter, W. (eds.) MFCS 2002. LNCS, vol. 2420, pp. 353\u2013364. Springer, Heidelberg (2002)"},{"issue":"1\u20133","key":"8_CR12","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1016\/S0019-9958(82)90382-5","volume":"55","author":"R Kannan","year":"1982","unstructured":"Kannan, R.: Circuit-size lower bounds and non-reducibility to sparse sets. Inf. Control 55(1\u20133), 40\u201356 (1982)","journal-title":"Inf. Control"},{"key":"8_CR13","doi-asserted-by":"crossref","unstructured":"Karp, R.M., Lipton, R.J.: Some connections between nonuniform and uniform complexity classes. In: Miller, R.E., Ginsburg, S., Burkhard, W.A., Lipton, R.J. (eds.) STOC, pp. 302\u2013309. ACM (1980)","DOI":"10.1145\/800141.804678"},{"key":"8_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/978-3-540-78524-8_5","volume-title":"Theory of Cryptography","author":"J Katz","year":"2008","unstructured":"Katz, J.: Which languages have 4-round zero-knowledge proofs? In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 73\u201388. Springer, Heidelberg (2008)"},{"key":"8_CR15","doi-asserted-by":"crossref","unstructured":"Koppula, V., Lewko, A.B., Waters, B.: Indistinguishability obfuscation for turing machines with unbounded memory. Cryptology ePrint Archive, Report 2014\/925 (2014). http:\/\/eprint.iacr.org\/","DOI":"10.1145\/2746539.2746614"},{"key":"8_CR16","doi-asserted-by":"crossref","unstructured":"Lipton, R.J.: Some consequences of our failure to prove non-linear lower bounds on explicit functions. In: Structure in Complexity Theory Conference, pp. 79\u201387. IEEE Computer Society (1994)","DOI":"10.1109\/SCT.1994.315815"},{"key":"8_CR17","doi-asserted-by":"crossref","unstructured":"Santhanam, R.: Circuit lower bounds for merlin-arthur classes. In: Johnson, D.S., Feige, U. (eds.) STOC, pp. 275\u2013283. ACM (2007)","DOI":"10.1145\/1250790.1250832"},{"key":"8_CR18","doi-asserted-by":"crossref","unstructured":"Shaltiel, R., Umans, C.: Simple extractors for all min-entropies and a new pseudo-random generator. In: FOCS, pp. 648\u2013657. IEEE Computer Society (2001)","DOI":"10.1109\/SFCS.2001.959941"},{"issue":"2","key":"8_CR19","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1016\/S0022-0000(03)00046-1","volume":"67","author":"C Umans","year":"2003","unstructured":"Umans, C.: Pseudo-random generators for all hardnesses. J. Comput. Syst. Sci. 67(2), 419\u2013440 (2003)","journal-title":"J. Comput. Syst. Sci."},{"key":"8_CR20","unstructured":"Vinodchandran, N.V.: A note on the circuit complexity.In: Electronic Colloquium on Computational Complexity (ECCC) (056) (2004)"},{"key":"8_CR21","doi-asserted-by":"crossref","unstructured":"Williams, R.: Improving exhaustive search implies superpolynomial lower bounds. In: Schulman, L.J. (ed.) STOC, pp. 231\u2013240. ACM (2010)","DOI":"10.1145\/1806689.1806723"}],"container-title":["Lecture Notes in Computer Science","Theory and Applications of Models of Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-17142-5_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,22]],"date-time":"2025-05-22T15:34:03Z","timestamp":1747928043000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-17142-5_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319171418","9783319171425"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-17142-5_8","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2015]]},"assertion":[{"value":"16 April 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}