{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T08:43:53Z","timestamp":1765961033351,"version":"3.41.0"},"publisher-location":"Cham","reference-count":20,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319790626"},{"type":"electronic","value":"9783319790633"}],"license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018]]},"DOI":"10.1007\/978-3-319-79063-3_6","type":"book-chapter","created":{"date-parts":[[2018,3,31]],"date-time":"2018-03-31T14:23:38Z","timestamp":1522506218000},"page":"121-141","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Implementing Joux-Vitse\u2019s Crossbred Algorithm for Solving $${\\mathcal M\\mathcal Q}$$ Systems over $${\\mathbb F}_2$$ on GPUs"],"prefix":"10.1007","author":[{"given":"Ruben","family":"Niederhagen","sequence":"first","affiliation":[]},{"given":"Kai-Chun","family":"Ning","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9362-5282","authenticated-orcid":false,"given":"Bo-Yin","family":"Yang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,4,1]]},"reference":[{"key":"6_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/11761679_8","volume-title":"Advances in Cryptology - EUROCRYPT 2006","author":"C Berbain","year":"2006","unstructured":"Berbain, C., Gilbert, H., Patarin, J.: QUAD: a practical stream cipher with provable security. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 109\u2013128. Springer, Heidelberg (2006)"},{"key":"6_CR2","unstructured":"Bernstein, D.J.: The saber cluster. https:\/\/blog.cr.yp.to\/20140602-saber.html"},{"key":"6_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/978-3-642-15031-9_14","volume-title":"Cryptographic Hardware and Embedded Systems, CHES 2010","author":"C Bouillaguet","year":"2010","unstructured":"Bouillaguet, C., Chen, H.-C., Cheng, C.-M., Chou, T., Niederhagen, R., Shamir, A., Yang, B.-Y.: Fast exhaustive search for polynomial systems in $${\\mathbb{F}_2}$$. In: Mangard, S., Standaert, F.-X. (eds.) CHES 2010. LNCS, vol. 6225, pp. 203\u2013218. Springer, Heidelberg (2010)"},{"key":"6_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1007\/978-3-662-43414-7_11","volume-title":"Selected Areas in Cryptography \u2013 SAC 2013","author":"C Bouillaguet","year":"2014","unstructured":"Bouillaguet, C., Cheng, C.-M., Chou, T., Niederhagen, R., Yang, B.-Y.: Fast exhaustive search for quadratic systems in $$\\mathbb{F}_{2}$$ on FPGAs. In: Lange, T., Lauter, K., Lison\u011bk, P. (eds.) SAC 2013. LNCS, vol. 8282, pp. 205\u2013222. Springer, Heidelberg (2014)"},{"key":"6_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1007\/978-3-642-00862-7_17","volume-title":"Topics in Cryptology \u2013 CT-RSA 2009","author":"C Clough","year":"2009","unstructured":"Clough, C., Baena, J., Ding, J., Yang, B.-Y., Chen, M.: Square, a new multivariate encryption scheme. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 252\u2013264. Springer, Heidelberg (2009)"},{"key":"6_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1007\/11496137_12","volume-title":"Applied Cryptography and Network Security","author":"J Ding","year":"2005","unstructured":"Ding, J., Schmidt, D.: Rainbow, a new multivariable polynomial signature scheme. In: Ioannidis, J., Keromytis, A., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 164\u2013175. Springer, Heidelberg (2005)"},{"key":"6_CR7","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/S0022-4049(99)00005-5","volume":"139","author":"JC Faug\u00e8re","year":"1999","unstructured":"Faug\u00e8re, J.C.: A new efficient algorithm for computing Gr\u00f6bner bases ($$F_4$$). J. Pure Appl. Algebra 139, 61\u201388 (1999)","journal-title":"J. Pure Appl. Algebra"},{"key":"6_CR8","doi-asserted-by":"crossref","unstructured":"Faug\u00e8re, J.C.: A new efficient algorithm for computing Gr\u00f6bner bases without reduction to zero ($$F_5$$). In: International Symposium on Symbolic and Algebraic Computation \u2013 ISSAC 2002, pp. 75\u201383. ACM Press (2002)","DOI":"10.1145\/780506.780516"},{"key":"6_CR9","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1017\/S0960129508007251","volume":"19","author":"G Fusco","year":"2009","unstructured":"Fusco, G., Bach, E.: Phase transition of multivariate polynomial systems. Math. Struct. Comput. Sci. 19, 9\u201323 (2009)","journal-title":"Math. Struct. Comput. Sci."},{"key":"6_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/3-540-68339-9_4","volume-title":"Advances in Cryptology\u2014EUROCRYPT \u201996","author":"J Patarin","year":"1996","unstructured":"Patarin, J.: Hidden Fields Equations (HFE) and Isomorphisms of Polynomials (IP): two new families of asymmetric algorithms. In: Maurer, U. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 33\u201348. Springer, Heidelberg (1996)"},{"key":"6_CR11","doi-asserted-by":"crossref","unstructured":"Joux, A., Vitse, V.: A crossbred algorithm for solving boolean polynomial systems. IACR Cryptology ePrint Archive (2017). https:\/\/eprint.iacr.org\/2017\/372","DOI":"10.1007\/978-3-319-76620-1_1"},{"key":"6_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1007\/3-540-48910-X_15","volume-title":"Advances in Cryptology\u2014EUROCRYPT \u201999","author":"A Kipnis","year":"1999","unstructured":"Kipnis, A., Patarin, J., Goubin, L.: Unbalanced oil and vinegar signature schemes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 206\u2013222. Springer, Heidelberg (1999)"},{"key":"6_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"282","DOI":"10.1007\/3-540-45353-9_21","volume-title":"Topics in Cryptology\u2014CT-RSA 2001","author":"J Patarin","year":"2001","unstructured":"Patarin, J., Courtois, N., Goubin, L.: QUARTZ, 128-bit long digital signatures. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 282\u2013297. Springer, Heidelberg (2001)"},{"key":"6_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/978-3-319-11659-4_14","volume-title":"Post-Quantum Cryptography","author":"J Porras","year":"2014","unstructured":"Porras, J., Baena, J., Ding, J.: ZHFE, a new multivariate public key encryption scheme. In: Mosca, M. (ed.) PQCrypto 2014. LNCS, vol. 8772, pp. 229\u2013245. Springer, Cham (2014)"},{"key":"6_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"706","DOI":"10.1007\/978-3-642-22792-9_40","volume-title":"Advances in Cryptology \u2013 CRYPTO 2011","author":"K Sakumoto","year":"2011","unstructured":"Sakumoto, K., Shirai, T., Hiwatari, H.: Public-key identification schemes based on multivariate quadratic polynomials. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 706\u2013723. Springer, Heidelberg (2011)"},{"key":"6_CR16","doi-asserted-by":"crossref","unstructured":"Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Foundations of Computer Science, pp. 124\u2013134. IEEE (1994)","DOI":"10.1109\/SFCS.1994.365700"},{"issue":"2","key":"6_CR17","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1137\/S0036144598347011","volume":"41","author":"PW Shor","year":"1999","unstructured":"Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303\u2013332 (1999)","journal-title":"SIAM Rev."},{"key":"6_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1007\/978-3-319-29360-8_12","volume-title":"Post-Quantum Cryptography","author":"A Szepieniec","year":"2016","unstructured":"Szepieniec, A., Ding, J., Preneel, B.: Extension field cancellation: a new central trapdoor for multivariate quadratic systems. In: Takagi, T. (ed.) PQCrypto 2016. LNCS, vol. 9606, pp. 182\u2013196. Springer, Cham (2016)"},{"key":"6_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/11496618_7","volume-title":"Information Security and Cryptology \u2013 ICISC 2004","author":"B-Y Yang","year":"2005","unstructured":"Yang, B.-Y., Chen, J.-M.: All in the XL family: theory and practice. In: Park, C., Chee, S. (eds.) ICISC 2004. LNCS, vol. 3506, pp. 67\u201386. Springer, Heidelberg (2005)"},{"key":"6_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1007\/978-3-540-74619-5_19","volume-title":"Fast Software Encryption","author":"B-Y Yang","year":"2007","unstructured":"Yang, B.-Y., Chen, O.C.-H., Bernstein, D.J., Chen, J.-M.: Analysis of QUAD. In: Biryukov, A. (ed.) FSE 2007. LNCS, vol. 4593, pp. 290\u2013308. Springer, Heidelberg (2007)"}],"container-title":["Lecture Notes in Computer Science","Post-Quantum Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-79063-3_6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T08:52:43Z","timestamp":1751532763000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-79063-3_6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"ISBN":["9783319790626","9783319790633"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-79063-3_6","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2018]]},"assertion":[{"value":"1 April 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"PQCrypto","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Post-Quantum Cryptography","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Fort Lauderdale","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":"2018","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"9 April 2018","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 April 2018","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"9","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"pqcrypto2018","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.math.fau.edu\/pqcrypto2018\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}