{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,6]],"date-time":"2026-11-06T04:12:36Z","timestamp":1793938356486,"version":"4.8.0"},"publisher-location":"Berlin, Heidelberg","reference-count":31,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783662530078","type":"print"},{"value":"9783662530085","type":"electronic"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-662-53008-5_16","type":"book-chapter","created":{"date-parts":[[2016,7,20]],"date-time":"2016-07-20T06:10:14Z","timestamp":1468995014000},"page":"459-488","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["On the Communication Required for Unconditionally Secure Multiplication"],"prefix":"10.1007","author":[{"given":"Ivan","family":"Damg\u00e5rd","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jesper Buus","family":"Nielsen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Antigoni","family":"Polychroniadou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Raskin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2016,7,21]]},"reference":[{"key":"16_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1007\/3-540-38424-3_5","volume-title":"Advances in Cryptology - CRYPTO 1990","author":"D Beaver","year":"1991","unstructured":"Beaver, D., Feigenbaum, J., Kilian, J., Rogaway, P.: Security with low communication overhead. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 62\u201376. Springer, Heidelberg (1991)"},{"key":"16_CR2","doi-asserted-by":"crossref","unstructured":"Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation (extended abstract). In: 20th Annual ACM Symposium on Theory of Computing, pp. 1\u201310. ACM Press, May 1988","DOI":"10.1145\/62212.62213"},{"key":"16_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1007\/11535218_24","volume-title":"Advances in Cryptology \u2013 CRYPTO 2005","author":"O Barkol","year":"2005","unstructured":"Barkol, O., Ishai, Y.: Secure computation of constant-depth circuits with applications to database search problems. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 395\u2013411. Springer, Heidelberg (2005)"},{"key":"16_CR4","doi-asserted-by":"crossref","unstructured":"Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, STOC 1988, pp. 1\u201310. ACM, New York (1988)","DOI":"10.1145\/62212.62213"},{"key":"16_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"663","DOI":"10.1007\/978-3-642-32009-5_39","volume-title":"Advances in Cryptology \u2013 CRYPTO 2012","author":"E Ben-Sasson","year":"2012","unstructured":"Ben-Sasson, E., Fehr, S., Ostrovsky, R.: Near-linear unconditionally-secure multiparty computation with a dishonest minority. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 663\u2013680. Springer, Heidelberg (2012)"},{"issue":"2","key":"16_CR6","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/s000370050025","volume":"8","author":"C Blundo","year":"1999","unstructured":"Blundo, C., De Santis, A., Persiano, G., Vaccaro, U.: Randomness complexity of private computation. Comput. Complex. 8(2), 145\u2013168 (1999)","journal-title":"Comput. Complex."},{"key":"16_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1007\/978-3-540-78524-8_13","volume-title":"Theory of Cryptography","author":"Z Beerliov\u00e1-Trub\u00edniov\u00e1","year":"2008","unstructured":"Beerliov\u00e1-Trub\u00edniov\u00e1, Z., Hirt, M.: Perfectly-Secure MPC with linear communication complexity. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 213\u2013230. Springer, Heidelberg (2008)"},{"key":"16_CR8","doi-asserted-by":"crossref","unstructured":"Chaum, D., Cr\u00e9peau, C., Damg\u00e5rd, I.: Multiparty unconditionally secure protocols (extended abstract). In: 20th Annual ACM Symposium on Theory of Computing, pp. 11\u201319. ACM Press, May 1988","DOI":"10.1145\/62212.62214"},{"key":"16_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"272","DOI":"10.1007\/3-540-45708-9_18","volume-title":"Advances in Cryptology - CRYPTO 2002","author":"R Cramer","year":"2002","unstructured":"Cramer, R., Fehr, S.: Optimal black-box secret sharing over arbitrary abelian groups. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 272\u2013287. Springer, Heidelberg (2002)"},{"issue":"4","key":"16_CR10","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1016\/0020-0190(93)90120-X","volume":"45","author":"B Chor","year":"1993","unstructured":"Chor, B., Kushilevitz, E.: A communication-privacy tradeoff for modular addition. Inf. Process. Lett. 45(4), 205\u2013210 (1993)","journal-title":"Inf. Process. Lett."},{"key":"16_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1007\/978-3-540-85174-5_14","volume-title":"Advances in Cryptology \u2013 CRYPTO 2008","author":"I Damg\u00e5rd","year":"2008","unstructured":"Damg\u00e5rd, I., Ishai, Y., Kr\u00f8igaard, M., Nielsen, J.B., Smith, A.: Scalable multiparty computation with nearly optimal work and resilience. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 241\u2013261. Springer, Heidelberg (2008)"},{"key":"16_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"445","DOI":"10.1007\/978-3-642-13190-5_23","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"I Damg\u00e5rd","year":"2010","unstructured":"Damg\u00e5rd, I., Ishai, Y., Kr\u00f8igaard, M.: Perfectly secure multiparty computation and the computational overhead of cryptography. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 445\u2013465. Springer, Heidelberg (2010)"},{"key":"16_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"572","DOI":"10.1007\/978-3-540-74143-5_32","volume-title":"Advances in Cryptology - CRYPTO 2007","author":"I Damg\u00e5rd","year":"2007","unstructured":"Damg\u00e5rd, I., Nielsen, J.B.: Scalable and unconditionally secure multiparty computation. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 572\u2013590. Springer, Heidelberg (2007)"},{"key":"16_CR14","unstructured":"Damg\u00e5rd, I., Nielsen, J.B., Ostovsky, R., Rosen, A.:Unconditionally secure computation with reduced interaction. Cryptology ePrint Archive, Report 2015\/630 (2015). http:\/\/eprint.iacr.org\/"},{"key":"16_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/978-3-662-44381-1_12","volume-title":"Advances in Cryptology \u2013 CRYPTO 2014","author":"D Data","year":"2014","unstructured":"Data, D., Prabhakaran, M.M., Prabhakaran, V.M.: On the communication complexity of secure computation. In: Garay, J.A., Gennaro, R. (eds.) CRYPTO 2014, Part II. LNCS, vol. 8617, pp. 199\u2013216. Springer, Heidelberg (2014)"},{"key":"16_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1007\/978-3-642-32009-5_38","volume-title":"Advances in Cryptology \u2013 CRYPTO 2012","author":"I Damg\u00e5rd","year":"2012","unstructured":"Damg\u00e5rd, I., Pastro, V., Smart, N., Zakarias, S.: Multiparty computation from somewhat homomorphic encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 643\u2013662. Springer, Heidelberg (2012)"},{"key":"16_CR17","doi-asserted-by":"crossref","unstructured":"Feige, U., Kilian, J., Naor, M.: A minimal model for secure computation (extended abstract). In: 26th Annual ACM Symposium on Theory of Computing, pp. 554\u2013563. ACM Press, May 1994","DOI":"10.1145\/195058.195408"},{"key":"16_CR18","doi-asserted-by":"crossref","unstructured":"Franklin, M.K., Yung, M.: Communication complexity of secure computation (extended abstract). In: 24th Annual ACM Symposium on Theory of Computing, pp. 699\u2013710. ACM Press, May 1992","DOI":"10.1145\/129712.129780"},{"key":"16_CR19","doi-asserted-by":"crossref","unstructured":"Genkin, D., Ishai, Y., Prabhakaran, M., Sahai, A., Tromer, E.: Circuits resilient to additive attacks with applications to secure computation. In: Shmoys, D.B. (ed.) 46th Annual ACM Symposium on Theory of Computing, pp. 495\u2013504. ACM Press, May \/ June 2014","DOI":"10.1145\/2591796.2591861"},{"key":"16_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1007\/978-3-662-48000-7_35","volume-title":"Advances in Cryptology \u2013 CRYPTO 2015","author":"D Genkin","year":"2015","unstructured":"Genkin, D., Ishai, Y., Polychroniadou, A.: Efficient multi-party computation: from passive to active security via secure SIMD circuits. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9216, pp. 721\u2013741. Springer, Heidelberg (2015)"},{"key":"16_CR21","doi-asserted-by":"crossref","unstructured":"G\u00e1l, A., Ros\u00e9n, A.: Lower bounds on the amount of randomness in private computation. In: 35th Annual ACM Symposium on Theory of Computing, pp. 659\u2013666. ACM Press, June 2003","DOI":"10.1145\/780542.780638"},{"key":"16_CR22","doi-asserted-by":"crossref","unstructured":"Ishai, Y., Kushilevitz, E.: Randomizing polynomials: A new representation with applications to round-efficient secure computation. In: 41st Annual Symposium on Foundations of Computer Science, pp. 294\u2013304. IEEE Computer Society Press, November 2000","DOI":"10.1109\/SFCS.2000.892118"},{"key":"16_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1007\/978-3-642-36594-2_34","volume-title":"Theory of Cryptography","author":"Y Ishai","year":"2013","unstructured":"Ishai, Y., Kushilevitz, E., Meldgaard, S., Orlandi, C., Paskin-Cherniavsky, A.: On the power of correlated randomness in secure computation. In: Sahai, A. (ed.) TCC 2013. LNCS, vol. 7785, pp. 600\u2013620. Springer, Heidelberg (2013)"},{"key":"16_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1007\/978-3-642-00457-5_18","volume-title":"Theory of Cryptography","author":"Y Ishai","year":"2009","unstructured":"Ishai, Y., Prabhakaran, M., Sahai, A.: Secure arithmetic computation with no honest majority. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 294\u2013314. Springer, Heidelberg (2009)"},{"issue":"4","key":"16_CR25","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1137\/S0895480196306130","volume":"10","author":"E Kushilevitz","year":"1997","unstructured":"Kushilevitz, E., Mansour, Y.: Randomness in private computations. SIAM J. Discrete Math. 10(4), 647\u2013661 (1997)","journal-title":"SIAM J. Discrete Math."},{"key":"16_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1007\/3-540-48658-5_36","volume-title":"Advances in Cryptology - CRYPTO \u201994","author":"E Kushilevitz","year":"1994","unstructured":"Kushilevitz, E., Ros\u00e9n, A.: A randomness-rounds tradeoff in private computation. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 397\u2013410. Springer, Heidelberg (1994)"},{"issue":"2","key":"16_CR27","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1137\/0405021","volume":"5","author":"E Kushilevitz","year":"1992","unstructured":"Kushilevitz, E.: Privacy and communication complexity. SIAM J. Discrete Math. 5(2), 273\u2013284 (1992)","journal-title":"SIAM J. Discrete Math."},{"key":"16_CR28","doi-asserted-by":"crossref","unstructured":"Naor, M., Nissim, K.: Communication preserving protocols for secure function evaluation. In: 33rd Annual ACM Symposium on Theory of Computing, pp. 590\u2013599. ACM Press, July 2001","DOI":"10.1145\/380752.380855"},{"key":"16_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"681","DOI":"10.1007\/978-3-642-32009-5_40","volume-title":"Advances in Cryptology \u2013 CRYPTO 2012","author":"JB Nielsen","year":"2012","unstructured":"Nielsen, J.B., Nordholt, P.S., Orlandi, C., Burra, S.S.: A new approach to practical active-secure two-party computation. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 681\u2013700. Springer, Heidelberg (2012)"},{"key":"16_CR30","doi-asserted-by":"crossref","unstructured":"Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority (extended abstract). In: 21st Annual ACM Symposium on Theory of Computing, pp. 73\u201385. ACM Press, May 1989","DOI":"10.1145\/73007.73014"},{"key":"16_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"707","DOI":"10.1007\/978-3-642-14623-7_38","volume-title":"Advances in Cryptology \u2013 CRYPTO 2010","author":"S Winkler","year":"2010","unstructured":"Winkler, S., Wullschleger, J.: On the efficiency of classical and quantum oblivious transfer reductions. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 707\u2013723. Springer, Heidelberg (2010)"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 CRYPTO 2016"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-53008-5_16","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,3]],"date-time":"2025-06-03T23:00:11Z","timestamp":1748991611000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-53008-5_16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783662530078","9783662530085"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-53008-5_16","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016]]},"assertion":[{"value":"21 July 2016","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CRYPTO","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Annual International Cryptology Conference","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Santa Barbara","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"USA","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2016","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 August 2016","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 August 2016","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"36","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"crypto2016","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}