{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,7]],"date-time":"2025-12-07T21:15:41Z","timestamp":1765142141325,"version":"3.40.3"},"publisher-location":"Cham","reference-count":34,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031683756"},{"type":"electronic","value":"9783031683763"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"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":[[2024]]},"DOI":"10.1007\/978-3-031-68376-3_2","type":"book-chapter","created":{"date-parts":[[2024,8,15]],"date-time":"2024-08-15T21:02:07Z","timestamp":1723755727000},"page":"39-70","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["MPC in\u00a0the\u00a0Head Using the\u00a0Subfield Bilinear Collision Problem"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-1052-0353","authenticated-orcid":false,"given":"Janik","family":"Huth","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2682-6508","authenticated-orcid":false,"given":"Antoine","family":"Joux","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,8,16]]},"reference":[{"key":"2_CR1","unstructured":"Adj, G., Rivera-Zamarripa, L., Verbel, J.: MinRank in the head: Short signatures from zero-knowledge proofs. Cryptology ePrint Archive, Report 2022\/1501 (2022). https:\/\/eprint.iacr.org\/2022\/1501"},{"key":"2_CR2","doi-asserted-by":"publisher","unstructured":"Aguilar-Melchor, C., Gama, N., Howe, J., H\u00fclsing, A., Joseph, D., Yue, D.: The return of the SDitH. In: Hazay, C., Stam, M. (eds.) EUROCRYPT\u00a02023, Part\u00a0V. LNCS, vol. 14008, pp. 564\u2013596. Springer, Heidelberg (2023). https:\/\/doi.org\/10.1007\/978-3-031-30589-4_20","DOI":"10.1007\/978-3-031-30589-4_20"},{"key":"2_CR3","unstructured":"Aragon, N., et al.: MIRA. Tech. rep., National Institute of Standards and Technology (2023). https:\/\/csrc.nist.gov\/Projects\/pqc-dig-sig\/round-1-additional-signatures"},{"key":"2_CR4","unstructured":"Barbulescu, R., Gaudry, P., Joux, A., Thom\u00e9, E.: A quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic. Cryptology ePrint Archive, Report 2013\/400 (2013). https:\/\/eprint.iacr.org\/2013\/400"},{"key":"2_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1007\/978-3-030-64837-4_17","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2020","author":"M Bardet","year":"2020","unstructured":"Bardet, M., et al.: Improvements of algebraic attacks for solving the rank decoding and MinRank problems. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12491, pp. 507\u2013536. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-64837-4_17"},{"key":"2_CR6","unstructured":"Bettale, L., Kahrobaei, D., Perret, L., Verbel, J.: Biscuit. Tech. rep., National Institute of Standards and Technology (2023). https:\/\/csrc.nist.gov\/Projects\/pqc-dig-sig\/round-1-additional-signatures"},{"key":"2_CR7","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. LNCS, vol. 8270, pp. 280\u2013300. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-42045-0_15"},{"key":"2_CR8","unstructured":"Bui, D., Carozza, E., Couteau, G., Goudarzi, D., Joux, A.: Short Signatures from Regular Syndrome Decoding, Revisited. Cryptology ePrint Archive, Paper 2024\/252 (2024). https:\/\/eprint.iacr.org\/2024\/252"},{"key":"2_CR9","doi-asserted-by":"publisher","unstructured":"Buss, J.F., Frandsen, G.S., Shallit, J.O.: The Computational Complexity of Some Problems of Linear Algebra. BRICS Rep. Ser. 3(33) (1996). https:\/\/doi.org\/10.7146\/brics.v3i33.20013","DOI":"10.7146\/brics.v3i33.20013"},{"issue":"6","key":"2_CR10","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1109\/TIT.1976.1055638","volume":"22","author":"W Diffie","year":"1976","unstructured":"Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Trans. Inf. Theory 22(6), 644\u2013654 (1976). https:\/\/doi.org\/10.1109\/TIT.1976.1055638","journal-title":"IEEE Trans. Inf. Theory"},{"key":"2_CR11","series-title":"Advances in Information Security","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-0716-0987-3","volume-title":"Multivariate Public Key Cryptosystems","author":"J Ding","year":"2020","unstructured":"Ding, J., Petzoldt, A., Schmidt, D.S.: Multivariate Public Key Cryptosystems. AIS, vol. 80. Springer, New York (2020). https:\/\/doi.org\/10.1007\/978-1-0716-0987-3"},{"key":"2_CR12","doi-asserted-by":"publisher","unstructured":"Faug\u00e8re, J.C.: A new efficient algorithm for computing gr\u00f6bner bases without reduction to zero (F5). In: Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation, pp. 75\u201383. ISSAC \u201902, ACM, New York, NY, USA (2002). https:\/\/doi.org\/10.1145\/780506.780516","DOI":"10.1145\/780506.780516"},{"key":"2_CR13","doi-asserted-by":"publisher","unstructured":"Faug\u00e8re, J.C., Safey El Din, M., Spaenlehauer, P.J.: Gr\u00f6bner bases of bihomogeneous ideals generated by polynomials of bidegree (1,1): Algorithms and complexity. J. Symbolic Comput. 46(4), 406\u2013437 (2011). https:\/\/doi.org\/10.1016\/j.jsc.2010.10.014","DOI":"10.1016\/j.jsc.2010.10.014"},{"key":"2_CR14","doi-asserted-by":"publisher","unstructured":"Feneuil, T., Joux, A., Rivain, M.: Syndrome decoding in the head: Shorter signatures from zero-knowledge proofs. In: Dodis, Y., Shrimpton, T. (eds.) CRYPTO\u00a02022, Part\u00a0II. LNCS, vol. 13508, pp. 541\u2013572. Springer, Heidelberg (2022). https:\/\/doi.org\/10.1007\/978-3-031-15979-4_19","DOI":"10.1007\/978-3-031-15979-4_19"},{"key":"2_CR15","unstructured":"Feneuil, T., Rivain, M.: MQOM \u2014 MQ on my Mind. Tech. rep., National Institute of Standards and Technology (2023). https:\/\/csrc.nist.gov\/Projects\/pqc-dig-sig\/round-1-additional-signatures"},{"key":"2_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1007\/3-540-47721-7_12","volume-title":"Advances in Cryptology \u2014 CRYPTO\u2019 86","author":"A Fiat","year":"1987","unstructured":"Fiat, A., Shamir, A.: How to prove yourself: practical solutions to identification and signature problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186\u2013194. Springer, Heidelberg (1987). https:\/\/doi.org\/10.1007\/3-540-47721-7_12"},{"key":"2_CR17","doi-asserted-by":"crossref","unstructured":"Goldreich, O.: The Foundations of Cryptography - Volume 1: Basic Techniques. Cambridge University Press (2001)","DOI":"10.1017\/CBO9780511546891"},{"issue":"4","key":"2_CR18","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 33(4), 792\u2013807 (1986). https:\/\/doi.org\/10.1145\/6490.6503","journal-title":"J. ACM"},{"key":"2_CR19","doi-asserted-by":"crossref","unstructured":"G\u00f6lo\u011flu, F., Joux, A.: A simplified approach to rigorous degree 2 elimination in discrete logarithm algorithms. Cryptology ePrint Archive, Report 2018\/430 (2018). https:\/\/eprint.iacr.org\/2018\/430","DOI":"10.1090\/mcom\/3404"},{"key":"2_CR20","doi-asserted-by":"publisher","unstructured":"Grover, L.K.: A fast quantum mechanical algorithm for database search. In: 28th ACM STOC, pp. 212\u2013219. ACM Press (1996). https:\/\/doi.org\/10.1145\/237814.237866","DOI":"10.1145\/237814.237866"},{"key":"2_CR21","doi-asserted-by":"publisher","unstructured":"Guo, X., et al.: Half-tree: Halving the cost of tree expansion in COT and DPF. In: Hazay, C., Stam, M. (eds.) EUROCRYPT\u00a02023, Part\u00a0I. LNCS, vol. 14004, pp. 330\u2013362. Springer, Heidelberg (Apr 2023). https:\/\/doi.org\/10.1007\/978-3-031-30545-0_12","DOI":"10.1007\/978-3-031-30545-0_12"},{"key":"2_CR22","unstructured":"Huth, J., Joux, A.: MPC in the head using the subfield bilinear collision problem. Cryptology ePrint Archive, Paper 2023\/1685 (2023). https:\/\/eprint.iacr.org\/2023\/1685"},{"key":"2_CR23","doi-asserted-by":"publisher","unstructured":"Ishai, Y., Kushilevitz, E., Ostrovsky, R., Sahai, A.: Zero-knowledge from secure multiparty computation. In: Johnson, D.S., Feige, U. (eds.) 39th ACM STOC, pp. 21\u201330. ACM Press (2007). https:\/\/doi.org\/10.1145\/1250790.1250794","DOI":"10.1145\/1250790.1250794"},{"key":"2_CR24","doi-asserted-by":"publisher","unstructured":"Johnson, C.R., \u0160migoc, H., Yang, D.: Solution theory for systems of bilinear equations. Linear Multilinear Algebra 62(12), 1553\u20131566 (2013). https:\/\/doi.org\/10.1080\/03081087.2013.839670","DOI":"10.1080\/03081087.2013.839670"},{"key":"2_CR25","doi-asserted-by":"publisher","unstructured":"Joux, A., , Pierrot, C.: Algorithmic aspects of elliptic bases in finite field discrete logarithm algorithms. Adv. Math. Commun. (2022). https:\/\/doi.org\/10.3934\/amc.2022085","DOI":"10.3934\/amc.2022085"},{"key":"2_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1007\/978-3-662-43414-7_18","volume-title":"Selected Areas in Cryptography \u2013 SAC 2013","author":"A Joux","year":"2014","unstructured":"Joux, A.: A new index calculus algorithm with complexity $$L(1\/4+o(1))$$ in small characteristic. In: Lange, T., Lauter, K., Lison\u011bk, P. (eds.) SAC 2013. LNCS, vol. 8282, pp. 355\u2013379. Springer, Heidelberg (2014). https:\/\/doi.org\/10.1007\/978-3-662-43414-7_18"},{"key":"2_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"378","DOI":"10.1007\/978-3-662-45611-8_20","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2014","author":"A Joux","year":"2014","unstructured":"Joux, A., Pierrot, C.: Improving the polynomial time precomputation of Frobenius representation discrete logarithm algorithms. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8873, pp. 378\u2013397. Springer, Heidelberg (2014). https:\/\/doi.org\/10.1007\/978-3-662-45611-8_20"},{"issue":"1","key":"2_CR28","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/s10623-015-0147-6","volume":"78","author":"A Joux","year":"2016","unstructured":"Joux, A., Pierrot, C.: Technical history of discrete logarithms in small characteristic finite fields - the road from Subexponential to quasi-polynomial complexity. DCC 78(1), 73\u201385 (2016). https:\/\/doi.org\/10.1007\/s10623-015-0147-6","journal-title":"DCC"},{"key":"2_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-030-65411-5_1","volume-title":"Cryptology and Network Security","author":"D Kales","year":"2020","unstructured":"Kales, D., Zaverucha, G.: An attack on some signature schemes constructed from five-pass identification schemes. In: Krenn, S., Shulman, H., Vaudenay, S. (eds.) CANS 2020. LNCS, vol. 12579, pp. 3\u201322. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-65411-5_1"},{"key":"2_CR30","doi-asserted-by":"crossref","unstructured":"Katz, J., Kolesnikov, V., Wang, X.: Improved non-interactive zero knowledge with applications to post-quantum signatures. Cryptology ePrint Archive, Report 2018\/475 (2018). https:\/\/eprint.iacr.org\/2018\/475","DOI":"10.1145\/3243734.3243805"},{"key":"2_CR31","doi-asserted-by":"crossref","unstructured":"Katz, J., Lindell, Y.: Introduction to Modern Cryptography, Second Edition. Chapman & Hall\/CRC, 2nd edn., New York (2014)","DOI":"10.1201\/b17668"},{"key":"2_CR32","doi-asserted-by":"publisher","unstructured":"Lang, S.: Algebra. Springer New York (2002). https:\/\/doi.org\/10.1007\/978-1-4613-0041-0","DOI":"10.1007\/978-1-4613-0041-0"},{"key":"2_CR33","doi-asserted-by":"publisher","unstructured":"Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: 35th FOCS, pp. 124\u2013134. IEEE Computer Society Press (1994). https:\/\/doi.org\/10.1109\/SFCS.1994.365700","DOI":"10.1109\/SFCS.1994.365700"},{"key":"2_CR34","unstructured":"Spaenlehauer, P.J.: Solving multi-homogeneous and determinantal systems: algorithms, complexity, applications. Phd thesis, Universit\u00e9 Pierre et Marie Curie (Univ. Paris 6) (2012)"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 CRYPTO 2024"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-68376-3_2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,15]],"date-time":"2024-08-15T21:02:46Z","timestamp":1723755766000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-68376-3_2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031683756","9783031683763"],"references-count":34,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-68376-3_2","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"16 August 2024","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":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 August 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"22 August 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"44","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"crypto2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/crypto.iacr.org\/2024\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}