{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T14:38:29Z","timestamp":1769524709392,"version":"3.49.0"},"publisher-location":"Cham","reference-count":28,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030648398","type":"print"},{"value":"9783030648404","type":"electronic"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"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":[[2020]]},"DOI":"10.1007\/978-3-030-64840-4_6","type":"book-chapter","created":{"date-parts":[[2020,12,4]],"date-time":"2020-12-04T15:06:04Z","timestamp":1607094364000},"page":"151-180","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Asymptotically Good Multiplicative LSSS over Galois Rings and Applications to MPC over $$\\mathbb {Z}\/p^k\\mathbb {Z} $$"],"prefix":"10.1007","author":[{"given":"Mark","family":"Abspoel","sequence":"first","affiliation":[]},{"given":"Ronald","family":"Cramer","sequence":"additional","affiliation":[]},{"given":"Ivan","family":"Damg\u00e5rd","sequence":"additional","affiliation":[]},{"given":"Daniel","family":"Escudero","sequence":"additional","affiliation":[]},{"given":"Matthieu","family":"Rambaud","sequence":"additional","affiliation":[]},{"given":"Chaoping","family":"Xing","sequence":"additional","affiliation":[]},{"given":"Chen","family":"Yuan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,12,5]]},"reference":[{"key":"6_CR1","doi-asserted-by":"crossref","unstructured":"Abspoel, M., et al.: Asymptotically good multiplicative LSSS over Galois rings and applications to MPC over $$\\mathbb{Z}\/p^k\\mathbb{Z}$$. Cryptology ePrint Archive (2020)","DOI":"10.1007\/978-3-030-64840-4_6"},{"key":"6_CR2","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 Galois rings. In: Hofheinz, D., Rosen, A. (eds.) TCC 2019. LNCS, vol. 11891, pp. 471\u2013501. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-36030-6_19"},{"key":"6_CR3","unstructured":"Abspoel, M., Dalskov, A., Escudero, D., Nof, A.: An efficient passive-to-active compiler for honest-majority MPC over rings. Cryptology ePrint Archive, Report 2019\/1298 (2019). https:\/\/eprint.iacr.org\/2019\/1298"},{"key":"6_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1007\/11681878_16","volume-title":"Theory of Cryptography","author":"Z Beerliov\u00e1-Trub\u00edniov\u00e1","year":"2006","unstructured":"Beerliov\u00e1-Trub\u00edniov\u00e1, Z., Hirt, M.: Efficient multi-party computation with dispute control. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 305\u2013328. Springer, Heidelberg (2006). https:\/\/doi.org\/10.1007\/11681878_16"},{"key":"6_CR5","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":"6_CR6","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). https:\/\/doi.org\/10.1007\/978-3-642-32009-5_39"},{"key":"6_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/978-3-030-26954-8_3","volume-title":"Advances in Cryptology \u2013 CRYPTO 2019","author":"D Boneh","year":"2019","unstructured":"Boneh, D., Boyle, E., Corrigan-Gibbs, H., Gilboa, N., Ishai, Y.: Zero-Knowledge proofs on secret-shared data via fully linear PCPs. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11694, pp. 67\u201397. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-26954-8_3"},{"key":"6_CR8","doi-asserted-by":"crossref","unstructured":"Boyle, E., Gilboa, N., Ishai, Y., Nof, A.: Practical fully secure three-party computation via sublinear distributed zero-knowledge proofs. In: Cavallaro, L., Kinder, J., Wang, X., Katz, J. (eds.) ACM CCS 2019, pp. 869\u2013886. ACM Press (2019)","DOI":"10.1145\/3319535.3363227"},{"key":"6_CR9","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. LNCS, vol. 10993, pp. 395\u2013426. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-96878-0_14"},{"key":"6_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1007\/978-3-540-72540-4_17","volume-title":"Advances in Cryptology - EUROCRYPT 2007","author":"H Chen","year":"2007","unstructured":"Chen, H., Cramer, R., Goldwasser, S., de Haan, R., Vaikuntanathan, V.: Secure computation from random error correcting codes. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 291\u2013310. Springer, Heidelberg (2007). https:\/\/doi.org\/10.1007\/978-3-540-72540-4_17"},{"key":"6_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1007\/978-3-319-96878-0_2","volume-title":"Advances in Cryptology \u2013 CRYPTO 2018","author":"K Chida","year":"2018","unstructured":"Chida, K., et al.: Fast large-scale honest-majority MPC for malicious adversaries. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10993, pp. 34\u201364. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-96878-0_2"},{"key":"6_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"769","DOI":"10.1007\/978-3-319-96881-0_26","volume-title":"Advances in Cryptology \u2013 CRYPTO 2018","author":"R Cramer","year":"2018","unstructured":"Cramer, R., Damg\u00e5rd, I., Escudero, D., Scholl, P., Xing, C.: SPD $$\\mathbb{Z}_{2^k}$$: efficient MPC mod $$2^k$$ for dishonest majority. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 769\u2013798. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-96881-0_26"},{"key":"6_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1007\/3-540-45539-6_22","volume-title":"Advances in Cryptology \u2014 EUROCRYPT 2000","author":"R Cramer","year":"2000","unstructured":"Cramer, R., Damg\u00e5rd, I., Maurer, U.: 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"},{"key":"6_CR14","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 \u2014 EUROCRYPT 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":"6_CR15","first-page":"832","volume":"2019","author":"R Cramer","year":"2019","unstructured":"Cramer, R., Rambaud, M., Xing, C.: Asymptotically-good arithmetic secret sharing over $$\\mathbb{Z}\/p^k\\mathbb{Z}$$ with strong multiplication and its applications to efficient MPC. IACR Cryptol. ePrint Arch. 2019, 832 (2019)","journal-title":"IACR Cryptol. ePrint Arch."},{"key":"6_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/978-3-030-26951-7_3","volume-title":"Advances in Cryptology \u2013 CRYPTO 2019","author":"I Damg\u00e5rd","year":"2019","unstructured":"Damg\u00e5rd, I., Larsen, K.G., Nielsen, J.B.: Communication lower bounds for statistically secure MPC, with or without preprocessing. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11693, pp. 61\u201384. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-26951-7_3"},{"key":"6_CR17","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":"6_CR18","doi-asserted-by":"crossref","unstructured":"Damg\u00e5rd, I., Escudero, D., Frederiksen, T., Keller, M., Scholl, P., Volgushev, N.: New primitives for actively-secure MPC over rings with applications to private machine learning. In: 2019 IEEE Symposium on Security and Privacy (SP), Los Alamitos, CA, USA, May 2019, pp. 1325\u20131343. IEEE Computer Society (2019)","DOI":"10.1109\/SP.2019.00078"},{"issue":"1","key":"6_CR19","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1007\/BF01884295","volume":"121","author":"A Garcia","year":"1995","unstructured":"Garcia, A., Stichtenoth, H.: A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound. Inventiones mathematicae 121(1), 211\u2013222 (1995)","journal-title":"Inventiones mathematicae"},{"key":"6_CR20","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 ACM STOC, pp. 495\u2013504. ACM Press (2014)","DOI":"10.1145\/2591796.2591861"},{"key":"6_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1007\/978-3-030-26951-7_4","volume-title":"Advances in Cryptology \u2013 CRYPTO 2019","author":"V Goyal","year":"2019","unstructured":"Goyal, V., Liu, Y., Song, Y.: Communication-efficient unconditional MPC with guaranteed output delivery. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11693, pp. 85\u2013114. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-26951-7_4"},{"key":"6_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"618","DOI":"10.1007\/978-3-030-56880-1_22","volume-title":"Advances in Cryptology \u2013 CRYPTO 2020","author":"V Goyal","year":"2020","unstructured":"Goyal, V., Song, Y., Zhu, C.: Guaranteed output delivery comes free in honest majority MPC. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020. LNCS, vol. 12171, pp. 618\u2013646. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-56880-1_22"},{"key":"6_CR23","doi-asserted-by":"crossref","unstructured":"Lamport, L., Shostak, R., Pease, M.: The byzantine generals problem. In: Concurrency: The Works of Leslie Lamport, pp. 203\u2013226 (2019)","DOI":"10.1145\/3335772.3335936"},{"key":"6_CR24","doi-asserted-by":"crossref","unstructured":"Lindell, Y., Nof, A.: A framework for constructing fast MPC over arithmetic circuits with malicious adversaries and an honest-majority. In: Thuraisingham, B.M., Evans, D., Malkin, T., Xu, D. (eds.) ACM CCS 2017, pp. 259\u2013276. ACM Press (2017)","DOI":"10.1145\/3133956.3133999"},{"key":"6_CR25","unstructured":"Massey, J.L.: Some applications of coding theory in cryptography. In: Farrell, P.F. (ed.) Codes and Ciphers, Cryptography and Coding IV, pp. 33\u201347. Formara Lt., Esses (1995)"},{"key":"6_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/978-3-319-93387-0_17","volume-title":"Applied Cryptography and Network Security","author":"PS Nordholt","year":"2018","unstructured":"Nordholt, P.S., Veeningen, M.: Minimising communication in honest-majority MPC by batchwise multiplication verification. In: Preneel, B., Vercauteren, F. (eds.) ACNS 2018. LNCS, vol. 10892, pp. 321\u2013339. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-93387-0_17"},{"issue":"5","key":"6_CR27","doi-asserted-by":"publisher","first-page":"2218","DOI":"10.1109\/TIT.2006.872986","volume":"52","author":"H Stichtenoth","year":"2006","unstructured":"Stichtenoth, H.: Transitive and self-dual codes attaining the Tsfasman-Vl\u0103du\u0163-Zink bound. IEEE Trans. Inf. Theor. 52(5), 2218\u20132224 (2006)","journal-title":"IEEE Trans. Inf. Theor."},{"key":"6_CR28","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-76878-4","volume-title":"Algebraic Function Fields and Codes","author":"H Stichtenoth","year":"2008","unstructured":"Stichtenoth, H.: Algebraic Function Fields and Codes, 2nd edn. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-76878-4","edition":"2"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 ASIACRYPT 2020"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-64840-4_6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,12]],"date-time":"2024-03-12T19:06:37Z","timestamp":1710270397000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-64840-4_6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030648398","9783030648404"],"references-count":28,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-64840-4_6","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"5 December 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"ASIACRYPT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on the Theory and Application of Cryptology and Information Security","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Daejeon","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Korea (Republic of)","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"7 December 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 December 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"26","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"asiacrypt2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/asiacrypt.iacr.org\/2020\/","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":"websubrev","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"316","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":"85","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":"27% - 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":"19","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":"The conference will take place virtually due to the COVID-19 pandemic.","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"}]}}