{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,21]],"date-time":"2025-12-21T01:36:53Z","timestamp":1766281013394,"version":"3.40.3"},"publisher-location":"Cham","reference-count":23,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030842444"},{"type":"electronic","value":"9783030842451"}],"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\/978-3-030-84245-1_12","type":"book-chapter","created":{"date-parts":[[2021,8,10]],"date-time":"2021-08-10T23:04:26Z","timestamp":1628636666000},"page":"335-364","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Efficient Information-Theoretic Multi-party Computation over Non-commutative Rings"],"prefix":"10.1007","author":[{"given":"Daniel","family":"Escudero","sequence":"first","affiliation":[]},{"given":"Eduardo","family":"Soria-Vazquez","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,8,11]]},"reference":[{"key":"12_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1007\/978-3-030-36030-6_19","volume-title":"Theory of Cryptography","author":"M Abspoel","year":"2019","unstructured":"Abspoel, M., Cramer, R., Damg\u00e5rd, I., Escudero, D., Yuan, C.: Efficient information-theoretic secure multiparty computation over $$\\mathbb{Z}\/p^k\\mathbb{Z}$$ via\u00a0Galois rings. In: Hofheinz, D., Rosen, A. (eds.) TCC 2019, Part I. LNCS, vol. 11891, pp. 471\u2013501. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-36030-6_19"},{"key":"12_CR2","unstructured":"Baccarini, A., Blanton, M., Yuan, C.: Multi-party replicated secret sharing over a ring with applications to privacy-preserving machine learning. Cryptology ePrint Archive, Report 2020\/1577 (2020). https:\/\/eprint.iacr.org\/2020\/1577"},{"key":"12_CR3","doi-asserted-by":"crossref","unstructured":"Ben-Or, M., Cleve, R.: Computing algebraic formulas using a constant number of registers. SIAM J. Comput. 21(1), 54\u201358 (1992)","DOI":"10.1137\/0221006"},{"key":"12_CR4","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 ACM STOC, pp. 1\u201310. ACM Press (May 1988)","DOI":"10.1145\/62212.62213"},{"key":"12_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"530","DOI":"10.1007\/978-3-030-21568-2_26","volume-title":"Applied Cryptography and Network Security","author":"A Ben-Efraim","year":"2019","unstructured":"Ben-Efraim, A., Nielsen, M., Omri, E.: Turbospeedz: double your online SPDZ! improving SPDZ using function dependent preprocessing. In: Deng, R.H., Gauthier-Uma\u00f1a, V., Ochoa, M., Yung, M. (eds.) ACNS 2019. LNCS, vol. 11464, pp. 530\u2013549. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-21568-2_26"},{"key":"12_CR6","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). https:\/\/doi.org\/10.1007\/978-3-540-78524-8_13"},{"key":"12_CR7","doi-asserted-by":"crossref","unstructured":"Canetti, R., Universally composable security: a new paradigm for cryptographic protocols. In: 42nd FOCS, pp. 136\u2013145. IEEE Computer Society Press, October 2001","DOI":"10.1109\/SFCS.2001.959888"},{"key":"12_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1007\/978-3-319-96878-0_14","volume-title":"Advances in Cryptology \u2013 CRYPTO 2018","author":"I Cascudo","year":"2018","unstructured":"Cascudo, I., Cramer, R., Xing, C., Yuan, C.: Amortized complexity of information-theoretically secure MPC revisited. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018, Part III. LNCS, vol. 10993, pp. 395\u2013426. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-96878-0_14"},{"key":"12_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1007\/978-3-642-40084-1_11","volume-title":"Advances in Cryptology \u2013 CRYPTO 2013","author":"G Cohen","year":"2013","unstructured":"Cohen, G., et al.: Efficient multiparty protocols via log-depth threshold formulae. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part II. LNCS, vol. 8043, pp. 185\u2013202. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-40084-1_11"},{"key":"12_CR10","doi-asserted-by":"publisher","unstructured":"Cramer, R., Damg\u00e5rd, I., Maurer, U.M.: General secure multi-party computation from any linear secret-sharing scheme. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 316\u2013334. Springer, Heidelberg (2000). https:\/\/doi.org\/10.1007\/3-540-45539-6_22","DOI":"10.1007\/3-540-45539-6_22"},{"key":"12_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"596","DOI":"10.1007\/3-540-39200-9_37","volume-title":"Advances in Cryptology\u2014EUROCRYPT 2003","author":"R Cramer","year":"2003","unstructured":"Cramer, R., Fehr, S., Ishai, Y., Kushilevitz, E.: Efficient multi-party computation over rings. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 596\u2013613. Springer, Heidelberg (2003). https:\/\/doi.org\/10.1007\/3-540-39200-9_37"},{"key":"12_CR12","unstructured":"Cramer, R., Rambaud, M., Xing, C.: Asymptotically-good arithmetic secret sharing over $$\\mathbb{Z}\/p^{\\ell } \\mathbb{Z}$$ with strong multiplication and its applications to efficient MPC. Cryptology ePrint Archive, Report 2019\/832 (2019). https:\/\/eprint.iacr.org\/2019\/832"},{"key":"12_CR13","unstructured":"Dalskov, A., Escudero, D., Keller, M.: Fantastic four: honest-majority four-party secure computation with malicious security. In: USENIX 2021 (2021)"},{"key":"12_CR14","doi-asserted-by":"crossref","unstructured":"Dawar, A., Kopczynski, E., Holm, B., Gr\u00e4del, E., Pakusa, W.: Definability of linear equation systems over groups and rings. arXiv preprint arXiv:1204.3022 (2012)","DOI":"10.2168\/LMCS-9(4:12)2013"},{"key":"12_CR15","doi-asserted-by":"publisher","unstructured":"Dalskov, A.P.K., Lee, E., Soria-Vazquez, E.: Circuit amortization friendly encodings and their application to statistically secure multiparty computation. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020, Part III. LNCS, vol. 12493, pp. 213\u2013243. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-64840-4_8","DOI":"10.1007\/978-3-030-64840-4_8"},{"key":"12_CR16","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). https:\/\/doi.org\/10.1007\/978-3-540-74143-5_32"},{"key":"12_CR17","doi-asserted-by":"crossref","unstructured":"Desmedt, Y., et al.: Graph coloring applied to secure computation in non-abelian groups. J. Cryptol. 25(4), 557\u2013600 (2012)","DOI":"10.1007\/s00145-011-9104-3"},{"key":"12_CR18","unstructured":"Escudero, D., Dalskov, A.: Honest majority MPC with abort with minimal online communication. Cryptology ePrint Archive, Report 2020\/1556 (2020). https:\/\/eprint.iacr.org\/2020\/1556"},{"key":"12_CR19","doi-asserted-by":"crossref","unstructured":"Lamport, L., Shostak, R., Pease, M.: The byzantine generals problem. ACM Trans. Program. Lang. Syst. 4(3), 382\u2013401 (1982)","DOI":"10.1145\/357172.357176"},{"key":"12_CR20","doi-asserted-by":"crossref","unstructured":"Ore, O.: Linear equations in non-commutative fields. Ann. Math. 32, 463\u2013477 (1931)","DOI":"10.2307\/1968245"},{"key":"12_CR21","doi-asserted-by":"crossref","unstructured":"Quintin, G., Barbier, M., Chabot, C.: On generalized Reed-Solomon codes over commutative and noncommutative rings. IEEE Trans. Inf. Theory 59(9), 5882\u20135897 (2013)","DOI":"10.1109\/TIT.2013.2264797"},{"key":"12_CR22","doi-asserted-by":"crossref","unstructured":"Shamir, A.: How to share a secret. Commun. Assoc. Comput. Mach. 22(11), 612\u2013613 (1979)","DOI":"10.1145\/359168.359176"},{"key":"12_CR23","doi-asserted-by":"crossref","unstructured":"Sontag, E.D.: On linear systems and noncommutative rings. Math. Syst. Theory 9(4), 327\u2013344 (1975)","DOI":"10.1007\/BF01715359"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 CRYPTO 2021"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-84245-1_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,11]],"date-time":"2024-08-11T00:13:34Z","timestamp":1723335214000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-84245-1_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030842444","9783030842451"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-84245-1_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"11 August 2021","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":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16 August 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"20 August 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"41","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"crypto2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/crypto.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":"426","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":"103","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":"24% - 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":"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":"20.9","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":"1 invited paper is also included.","order":10,"name":"additional_info_on_review_process","label":"Additional Info on Review Process","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"}]}}