{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T14:26:21Z","timestamp":1761402381007,"version":"3.40.3"},"publisher-location":"Cham","reference-count":29,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031828515"},{"type":"electronic","value":"9783031828522"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"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":[[2025]]},"DOI":"10.1007\/978-3-031-82852-2_3","type":"book-chapter","created":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T13:01:40Z","timestamp":1741784500000},"page":"54-83","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Generation of\u00a0Authenticated Secret-Shared Scaled Unit Vectors for\u00a0Beaver Triples"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-8694-7260","authenticated-orcid":false,"given":"Vincent","family":"Rieder","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,13]]},"reference":[{"key":"3_CR1","doi-asserted-by":"publisher","unstructured":"Abram, D., Scholl, P.: Low-communication multiparty triple generation for SPDZ from ring-LPN. In: Hanaoka, G., Shikata, J., Watanabe, Y. (eds.) Public-Key Cryptography \u2013 PKC 2022, pp. 221\u2013251. Springer International Publishing, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-030-97121-2_9","DOI":"10.1007\/978-3-030-97121-2_9"},{"key":"3_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/978-3-319-63688-7_8","volume-title":"Advances in Cryptology \u2013 CRYPTO 2017","author":"B Applebaum","year":"2017","unstructured":"Applebaum, B., Damg\u00e5rd, I., Ishai, Y., Nielsen, M., Zichron, L.: Secure arithmetic computation with constant computational overhead. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 223\u2013254. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-63688-7_8"},{"key":"3_CR3","doi-asserted-by":"publisher","unstructured":"Baum, C., Cozzo, D., Smart, N.P.: Using TopGear in overdrive: a more efficient ZKPoK for SPDZ. In: Paterson, K., Stebila, D. (eds.) Selected Areas in Cryptography \u2013 SAC 2019, pp. 274\u2013302. Springer International Publishing, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-38471-5_12","DOI":"10.1007\/978-3-030-38471-5_12"},{"key":"3_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"420","DOI":"10.1007\/3-540-46766-1_34","volume-title":"Advances in Cryptology \u2014 CRYPTO 1991","author":"D Beaver","year":"1992","unstructured":"Beaver, D.: Efficient multiparty protocols using circuit randomization. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 420\u2013432. Springer, Heidelberg (1992). https:\/\/doi.org\/10.1007\/3-540-46766-1_34"},{"key":"3_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1007\/978-3-642-20465-4_11","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2011","author":"R Bendlin","year":"2011","unstructured":"Bendlin, R., Damg\u00e5rd, I., Orlandi, C., Zakarias, S.: Semi-homomorphic encryption and multiparty computation. In: Paterson, K.G. (ed.) EUROCRYPT 2011. LNCS, vol. 6632, pp. 169\u2013188. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-20465-4_11"},{"key":"3_CR6","doi-asserted-by":"publisher","unstructured":"Bombar, M., Couteau, G., Couvreur, A., Ducros, C.: Correlated Pseudorandomness from the Hardness of quasi-abelian decoding. In: Handschuh, H., Lysyanskaya, A. (eds.) Advances in Cryptology \u2013 CRYPTO 2023, pp. 567\u2013601. Springer Nature Switzerland, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-38551-3_18","DOI":"10.1007\/978-3-031-38551-3_18"},{"key":"3_CR7","doi-asserted-by":"crossref","unstructured":"Boyle, E., Couteau, G., Gilboa, N., Ishai, Y.: Compressing vector ole. In: Proceedings of the 2018 ACM SIGSAC Conference on Computer and Communications Security, CCS 2018, pp. 896\u2013912, New York, NY, USA, 2018. Association for Computing Machinery (2018)","DOI":"10.1145\/3243734.3243868"},{"key":"3_CR8","doi-asserted-by":"publisher","unstructured":"Boyle, E., et al.: Correlated pseudorandomness from expand-accumulate codes. In: Advances in Cryptology \u2013 CRYPTO 2022: 42nd Annual International Cryptology Conference, CRYPTO 2022, Santa Barbara, CA, USA, 15\u201318 August 2022, Proceedings, Part II, pp. 603\u2013633. Springer-Verlag, Heidelberg, (2022). https:\/\/doi.org\/10.1007\/978-3-031-15979-4_21","DOI":"10.1007\/978-3-031-15979-4_21"},{"key":"3_CR9","doi-asserted-by":"crossref","unstructured":"Boyle, E., Couteau, G., Gilboa, N., Ishai, Y., Kohl, L., Rindal, P., Scholl, P.: Efficient two-round OT extension and silent non-interactive secure computation. In: Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security, CCS 2019, pp. 291\u2013308, New York, NY, USA, 2019. Association for Computing Machinery (2019)","DOI":"10.1145\/3319535.3354255"},{"key":"3_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1007\/978-3-030-26954-8_16","volume-title":"Advances in Cryptology \u2013 CRYPTO 2019","author":"E Boyle","year":"2019","unstructured":"Boyle, E., Couteau, G., Gilboa, N., Ishai, Y., Kohl, L., Scholl, P.: Efficient pseudorandom correlation generators: silent OT extension and more. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11694, pp. 489\u2013518. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-26954-8_16"},{"key":"3_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1007\/978-3-030-56880-1_14","volume-title":"Advances in Cryptology \u2013 CRYPTO 2020","author":"E Boyle","year":"2020","unstructured":"Boyle, E., Couteau, G., Gilboa, N., Ishai, Y., Kohl, L., Scholl, P.: Efficient\u00a0pseudorandom\u00a0correlation\u00a0generators from ring-LPN. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020. LNCS, vol. 12171, pp. 387\u2013416. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-56880-1_14"},{"key":"3_CR12","doi-asserted-by":"crossref","unstructured":"Boyle, E., Gilboa, N., Ishai, Y.: Function secret sharing: improvements and extensions. In: CCS, pp. 1292\u20131303. ACM (2016)","DOI":"10.1145\/2976749.2978429"},{"key":"3_CR13","doi-asserted-by":"crossref","unstructured":"Canetti, R.: Universally composable security: a new paradigm for cryptographic protocols. In: Proceedings 42nd IEEE Symposium on Foundations of Computer Science, pp. 136\u2013145 (2001)","DOI":"10.1109\/SFCS.2001.959888"},{"key":"3_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1007\/978-3-662-54970-4_10","volume-title":"Financial Cryptography and Data Security","author":"I Damg\u00e5rd","year":"2017","unstructured":"Damg\u00e5rd, I., Damg\u00e5rd, K., Nielsen, K., Nordholt, P.S., Toft, T.: Confidential benchmarking based on multiparty computation. In: Grossklags, J., Preneel, B. (eds.) FC 2016. LNCS, vol. 9603, pp. 169\u2013187. Springer, Heidelberg (2017). https:\/\/doi.org\/10.1007\/978-3-662-54970-4_10"},{"key":"3_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-40203-6_1","volume-title":"Computer Security \u2013 ESORICS 2013","author":"I Damg\u00e5rd","year":"2013","unstructured":"Damg\u00e5rd, I., Keller, M., Larraia, E., Pastro, V., Scholl, P., Smart, N.P.: Practical covertly secure MPC for dishonest majority \u2013 Or: breaking the SPDZ limits. In: Crampton, J., Jajodia, S., Mayes, K. (eds.) ESORICS 2013. LNCS, vol. 8134, pp. 1\u201318. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-40203-6_1"},{"key":"3_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). https:\/\/doi.org\/10.1007\/978-3-642-32009-5_38"},{"key":"3_CR17","doi-asserted-by":"crossref","unstructured":"Doerner, J., Shelat, A.: Scaling ORAM for secure computation. In: CCS, pp. 523\u2013535. ACM (2017)","DOI":"10.1145\/3133956.3133967"},{"key":"3_CR18","doi-asserted-by":"publisher","unstructured":"Escudero, D., Xing, C., Yuan, C.: More efficient dishonest majority secure computation over $$\\mathbb{Z}_{2^k}$$ via galois rings. In: Dodis, Y., Shrimpton, T. (eds.) Advances in Cryptology \u2013 CRYPTO 2022, pp. 383\u2013412. Springer Nature Switzerland, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-031-15802-5_14","DOI":"10.1007\/978-3-031-15802-5_14"},{"key":"3_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"640","DOI":"10.1007\/978-3-642-55220-5_35","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2014","author":"N Gilboa","year":"2014","unstructured":"Gilboa, N., Ishai, Y.: Distributed point functions and their applications. In: Nguyen, P.Q., Oswald, E. (eds.) EUROCRYPT 2014. LNCS, vol. 8441, pp. 640\u2013658. Springer, Heidelberg (2014). https:\/\/doi.org\/10.1007\/978-3-642-55220-5_35"},{"key":"3_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"598","DOI":"10.1007\/978-3-319-70694-8_21","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2017","author":"C Hazay","year":"2017","unstructured":"Hazay, C., Scholl, P., Soria-Vazquez, E.: Low cost constant round MPC combining BMR and oblivious transfer. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10624, pp. 598\u2013628. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-70694-8_21"},{"key":"3_CR21","doi-asserted-by":"crossref","unstructured":"Keller, M.: MP-SPDZ: a versatile framework for multi-party computation. In: Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security, CCS 2020, pp. 1575\u20131590, New York, NY, USA, 2020. Association for Computing Machinery (2020)","DOI":"10.1145\/3372297.3417872"},{"key":"3_CR22","doi-asserted-by":"crossref","unstructured":"Keller, M., Orsini, E., Scholl, P.: Mascot: faster malicious arithmetic secure computation with oblivious transfer. In: Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, CCS 2016, page 830\u2013842, New York, NY, USA, 2016. Association for Computing Machinery (2016)","DOI":"10.1145\/2976749.2978357"},{"key":"3_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1007\/978-3-319-78372-7_6","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2018","author":"M Keller","year":"2018","unstructured":"Keller, M., Pastro, V., Rotaru, D.: Overdrive: making SPDZ great again. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 158\u2013189. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-78372-7_6"},{"key":"3_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-10433-6_1","volume-title":"Cryptology and Network Security","author":"V Kolesnikov","year":"2009","unstructured":"Kolesnikov, V., Sadeghi, A.-R., Schneider, T.: Improved garbled circuit building blocks and applications to auctions and computing minima. In: Garay, J.A., Miyaji, A., Otsuka, A. (eds.) CANS 2009. LNCS, vol. 5888, pp. 1\u201320. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-10433-6_1"},{"key":"3_CR25","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). https:\/\/doi.org\/10.1007\/978-3-642-32009-5_40"},{"key":"3_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1007\/978-3-030-40186-3_12","volume-title":"Topics in Cryptology \u2013 CT-RSA 2020","author":"E Orsini","year":"2020","unstructured":"Orsini, E., Smart, N.P., Vercauteren, F.: Overdrive2k: efficient secure MPC over $$\\mathbb{Z}_{2^k}$$ from somewhat homomorphic encryption. In: Jarecki, S. (ed.) CT-RSA 2020. LNCS, vol. 12006, pp. 254\u2013283. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-40186-3_12"},{"key":"3_CR27","doi-asserted-by":"crossref","unstructured":"Schoppmann, P., Gasc\u00f3n, A., Reichert, L., Raykova, M.: Distributed vector-ole: improved constructions and implementation. In: Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security, CCS 2019, pp. 1055\u20131072, New York, NY, USA, 2019. Association for Computing Machinery (2019)","DOI":"10.1145\/3319535.3363228"},{"key":"3_CR28","doi-asserted-by":"crossref","unstructured":"Hasler, S., Reisert, P., Rivinius, M., K\u00fcsters, R.: Multipars: reduced-communication MPC over z2k. In: Proceedings on Privacy Enhancing Technologies (2024)","DOI":"10.56553\/popets-2024-0038"},{"key":"3_CR29","doi-asserted-by":"crossref","unstructured":"Yang, K., Weng, C., Lan, X., Zhang, J. and Wang, X.: Ferret: fast extension for correlated OT with small communication. In: CCS, pp. 1607\u20131626. ACM (2020)","DOI":"10.1145\/3372297.3417276"}],"container-title":["Lecture Notes in Computer Science","Selected Areas in Cryptography \u2013 SAC 2024"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-82852-2_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T13:01:55Z","timestamp":1741784515000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-82852-2_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031828515","9783031828522"],"references-count":29,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-82852-2_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"13 March 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The author has no competing interests to declare that are relevant to the content of this article.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"SAC","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Selected Areas in Cryptography","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Montreal, QC","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Canada","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"29 August 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"31 August 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"31","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"sacrypt2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/sacworkshop.org\/SAC24\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}