{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,4]],"date-time":"2026-02-04T17:30:08Z","timestamp":1770226208128,"version":"3.49.0"},"publisher-location":"Cham","reference-count":28,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031159848","type":"print"},{"value":"9783031159855","type":"electronic"}],"license":[{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,1,1]],"date-time":"2022-01-01T00:00:00Z","timestamp":1640995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022]]},"DOI":"10.1007\/978-3-031-15985-5_12","type":"book-chapter","created":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T20:02:37Z","timestamp":1665432157000},"page":"329-358","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Moz$$\\mathbb {Z}_{2^k}$$arella: Efficient Vector-OLE and Zero-Knowledge Proofs over\u00a0$$\\mathbb {Z}_{2^k}$$"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7905-0198","authenticated-orcid":false,"given":"Carsten","family":"Baum","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9164-305X","authenticated-orcid":false,"given":"Lennart","family":"Braun","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1482-0064","authenticated-orcid":false,"given":"Alexander","family":"Munch-Hansen","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7937-8422","authenticated-orcid":false,"given":"Peter","family":"Scholl","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,10,11]]},"reference":[{"key":"12_CR1","doi-asserted-by":"publisher","unstructured":"Alekhnovich, M.: More on average case vs approximation complexity. In: 44th FOCS, pp. 298\u2013307. IEEE Computer Society Press, October 2003. https:\/\/doi.org\/10.1109\/SFCS.2003.1238204","DOI":"10.1109\/SFCS.2003.1238204"},{"key":"12_CR2","doi-asserted-by":"publisher","unstructured":"Ames, S., Hazay, C., Ishai, Y., Venkitasubramaniam, M.: Ligero: lightweight sublinear arguments without a trusted setup. In: Thuraisingham, B.M., Evans, D., Malkin, T., Xu, D. (eds.) ACM CCS 2017, pp. 2087\u20132104. ACM Press, October\/November 2017. https:\/\/doi.org\/10.1145\/3133956.3134104","DOI":"10.1145\/3133956.3134104"},{"key":"12_CR3","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, Part I. LNCS, vol. 10401, pp. 223\u2013254. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-63688-7_8"},{"key":"12_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1007\/978-3-642-22006-7_34","volume-title":"Automata, Languages and Programming","author":"S Arora","year":"2011","unstructured":"Arora, S., Ge, R.: New algorithms for learning in presence of errors. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part I. LNCS, vol. 6755, pp. 403\u2013415. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-22006-7_34"},{"key":"12_CR5","doi-asserted-by":"publisher","unstructured":"Baum, C., Braun, L., Munch-Hansen, A., Razet, B., Scholl, P.: Appenzeller to brie: efficient zero-knowledge proofs for mixed-mode arithmetic and Z2k. In: Vigna, G., Shi, E. (eds.) ACM CCS 2021, pp. 192\u2013211. ACM Press, November 2021. https:\/\/doi.org\/10.1145\/3460120.3484812","DOI":"10.1145\/3460120.3484812"},{"key":"12_CR6","doi-asserted-by":"crossref","unstructured":"Baum, C., Braun, L., Munch-Hansen, A., Scholl, P.: Moz$$\\mathbb{Z} _{2^k}$$arella: efficient vector-OLE and zero-knowledge proofs over $$\\mathbb{Z} _{2^k}$$. Cryptology ePrint Archive, Paper 2022\/819 (2022). https:\/\/eprint.iacr.org\/2022\/819, Full Version","DOI":"10.1007\/978-3-031-15985-5_12"},{"key":"12_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1007\/978-3-030-84259-8_4","volume-title":"Advances in Cryptology \u2013 CRYPTO 2021","author":"C Baum","year":"2021","unstructured":"Baum, C., Malozemoff, A.J., Rosen, M.B., Scholl, P.: $${\\sf Mac}^{\\prime }n^{\\prime }Cheese$$: zero-knowledge proofs for\u00a0boolean and arithmetic circuits with\u00a0nested disjunctions. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021. LNCS, vol. 12828, pp. 92\u2013122. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-84259-8_4"},{"key":"12_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"701","DOI":"10.1007\/978-3-030-26954-8_23","volume-title":"Advances in Cryptology \u2013 CRYPTO 2019","author":"E Ben-Sasson","year":"2019","unstructured":"Ben-Sasson, E., Bentov, I., Horesh, Y., Riabzev, M.: Scalable zero knowledge with no trusted setup. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019, Part III. LNCS, vol. 11694, pp. 701\u2013732. Springer, Cham (2019). https:\/\/doi.org\/10.1007\/978-3-030-26954-8_23"},{"key":"12_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"278","DOI":"10.1007\/3-540-48329-2_24","volume-title":"Advances in Cryptology \u2014 CRYPTO\u2019 93","author":"A Blum","year":"1994","unstructured":"Blum, A., Furst, M., Kearns, M., Lipton, R.J.: Cryptographic primitives based on hard learning problems. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 278\u2013291. Springer, Heidelberg (1994). https:\/\/doi.org\/10.1007\/3-540-48329-2_24"},{"key":"12_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"280","DOI":"10.1007\/978-3-642-42045-0_15","volume-title":"Advances in Cryptology - ASIACRYPT 2013","author":"D Boneh","year":"2013","unstructured":"Boneh, D., Waters, B.: Constrained pseudorandom functions and their applications. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 280\u2013300. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-42045-0_15"},{"key":"12_CR11","doi-asserted-by":"publisher","unstructured":"Boyle, E., Couteau, G., Gilboa, N., Ishai, Y.: Compressing vector OLE. In: Lie, D., Mannan, M., Backes, M., Wang, X. (eds.) ACM CCS 2018, pp. 896\u2013912. ACM Press, October 2018. https:\/\/doi.org\/10.1145\/3243734.3243868","DOI":"10.1145\/3243734.3243868"},{"key":"12_CR12","doi-asserted-by":"publisher","unstructured":"Boyle, E., et al.: Efficient two-round OT extension and silent non-interactive secure computation. In: Cavallaro, L., Kinder, J., Wang, X., Katz, J. (eds.) ACM CCS 2019, pp. 291\u2013308. ACM Press, November 2019. https:\/\/doi.org\/10.1145\/3319535.3354255","DOI":"10.1145\/3319535.3354255"},{"key":"12_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1007\/978-3-642-54631-0_29","volume-title":"Public-Key Cryptography \u2013 PKC 2014","author":"E Boyle","year":"2014","unstructured":"Boyle, E., Goldwasser, S., Ivan, I.: Functional signatures and pseudorandom functions. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 501\u2013519. Springer, Heidelberg (2014). https:\/\/doi.org\/10.1007\/978-3-642-54631-0_29"},{"key":"12_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1007\/978-3-030-84252-9_17","volume-title":"Advances in Cryptology \u2013 CRYPTO 2021","author":"G Couteau","year":"2021","unstructured":"Couteau, G., Rindal, P., Raghuraman, S.: Silver: silent VOLE and oblivious transfer from hardness of decoding structured LDPC codes. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021, Part III. LNCS, vol. 12827, pp. 502\u2013534. Springer, Cham (2021). https:\/\/doi.org\/10.1007\/978-3-030-84252-9_17"},{"key":"12_CR15","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, Part II. LNCS, vol. 10992, pp. 769\u2013798. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-96881-0_26"},{"key":"12_CR16","unstructured":"Dittmer, S., Ishai, Y., Ostrovsky, R.: Line-point zero knowledge and its applications. In: 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Schloss Dagstuhl-Leibniz-Zentrum f\u00fcr Informatik (2021)"},{"key":"12_CR17","unstructured":"Ganesh, C., Nitulescu, A., Soria-Vazquez, E.: Rinocchio: SNARKs for ring arithmetic. Cryptology ePrint Archive, Report 2021\/322 (2021). https:\/\/eprint.iacr.org\/2021\/322"},{"key":"12_CR18","doi-asserted-by":"publisher","unstructured":"Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions (extended abstract). In: 25th FOCS, pp. 464\u2013479. IEEE Computer Society Press, October 1984. https:\/\/doi.org\/10.1109\/SFCS.1984.715949","DOI":"10.1109\/SFCS.1984.715949"},{"issue":"4","key":"12_CR19","doi-asserted-by":"publisher","first-page":"792","DOI":"10.1145\/6490.6503","volume":"33","author":"O Goldreich","year":"1986","unstructured":"Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions. J. ACM (JACM) 33(4), 792\u2013807 (1986)","journal-title":"J. ACM (JACM)"},{"key":"12_CR20","doi-asserted-by":"publisher","unstructured":"Kiayias, A., Papadopoulos, S., Triandopoulos, N., Zacharias, T.: Delegatable pseudorandom functions and applications. In: Sadeghi, A.R., Gligor, V.D., Yung, M. (eds.) ACM CCS 2013, pp. 669\u2013684. ACM Press, November 2013. https:\/\/doi.org\/10.1145\/2508859.2516668","DOI":"10.1145\/2508859.2516668"},{"key":"12_CR21","unstructured":"Liu, H., Wang, X., Yang, K., Yu, Y.: The hardness of LPN over any integer ring and field for PCG applications. Cryptology ePrint Archive, Paper 2022\/712 (2022). https:\/\/eprint.iacr.org\/2022\/712"},{"key":"12_CR22","doi-asserted-by":"publisher","unstructured":"Maller, M., Bowe, S., Kohlweiss, M., Meiklejohn, S.: Sonic: zero-knowledge SNARKs from linear-size universal and updatable structured reference strings. In: Cavallaro, L., Kinder, J., Wang, X., Katz, J. (eds.) ACM CCS 2019, pp. 2111\u20132128. ACM Press, November 2019. https:\/\/doi.org\/10.1145\/3319535.3339817","DOI":"10.1145\/3319535.3339817"},{"key":"12_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"554","DOI":"10.1007\/978-3-319-76578-5_19","volume-title":"Public-Key Cryptography \u2013 PKC 2018","author":"P Scholl","year":"2018","unstructured":"Scholl, P.: Extending oblivious transfer with low communication via key-homomorphic PRFs. In: Abdalla, M., Dahab, R. (eds.) PKC 2018, Part I. LNCS, vol. 10769, pp. 554\u2013583. Springer, Cham (2018). https:\/\/doi.org\/10.1007\/978-3-319-76578-5_19"},{"key":"12_CR24","doi-asserted-by":"publisher","unstructured":"Schoppmann, P., Gasc\u00f3n, A., Reichert, L., Raykova, M.: Distributed vector-OLE: improved constructions and implementation. In: Cavallaro, L., Kinder, J., Wang, X., Katz, J. (eds.) ACM CCS 2019, pp. 1055\u20131072. ACM Press, November 2019. https:\/\/doi.org\/10.1145\/3319535.3363228","DOI":"10.1145\/3319535.3363228"},{"key":"12_CR25","doi-asserted-by":"publisher","unstructured":"Weng, C., Yang, K., Katz, J., Wang, X.: Wolverine: fast, scalable, and communication-efficient zero-knowledge proofs for boolean and arithmetic circuits. In: 2021 IEEE Symposium on Security and Privacy, pp. 1074\u20131091. IEEE Computer Society Press, May 2021. https:\/\/doi.org\/10.1109\/SP40001.2021.00056","DOI":"10.1109\/SP40001.2021.00056"},{"key":"12_CR26","doi-asserted-by":"publisher","unstructured":"Yang, K., Sarkar, P., Weng, C., Wang, X.: QuickSilver: efficient and affordable zero-knowledge proofs for circuits and polynomials over any field. In: Vigna, G., Shi, E. (eds.) ACM CCS 2021, pp. 2986\u20133001. ACM Press, November 2021. https:\/\/doi.org\/10.1145\/3460120.3484556","DOI":"10.1145\/3460120.3484556"},{"key":"12_CR27","doi-asserted-by":"publisher","unstructured":"Yang, K., Weng, C., Lan, X., Zhang, J., Wang, X.: Ferret: fast extension for correlated OT with small communication. In: Ligatti, J., Ou, X., Katz, J., Vigna, G. (eds.) ACM CCS 2020, pp. 1607\u20131626. ACM Press, November 2020. https:\/\/doi.org\/10.1145\/3372297.3417276","DOI":"10.1145\/3372297.3417276"},{"key":"12_CR28","unstructured":"Zichron, L.: Locally computable arithmetic pseudorandom generators. Master\u2019s thesis, School of Electrical Engineering, Tel Aviv University (2017). http:\/\/www.eng.tau.ac.il\/~bennyap\/pubs\/Zichron.pdf"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 CRYPTO 2022"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-15985-5_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:05:02Z","timestamp":1760133902000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-15985-5_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022]]},"ISBN":["9783031159848","9783031159855"],"references-count":28,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-15985-5_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022]]},"assertion":[{"value":"11 October 2022","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, CA","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":"2022","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15 August 2022","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 August 2022","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"42","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"crypto2022","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/crypto.iacr.org\/2022\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}