{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,22]],"date-time":"2025-04-22T04:02:02Z","timestamp":1745294522396,"version":"3.40.4"},"reference-count":27,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AMC"],"published-print":{"date-parts":[[2025]]},"DOI":"10.3934\/amc.2025003","type":"journal-article","created":{"date-parts":[[2025,1,24]],"date-time":"2025-01-24T11:56:11Z","timestamp":1737719771000},"page":"1433-1459","source":"Crossref","is-referenced-by-count":0,"title":["A digital signature scheme based on the vector space factorization problem and the MPC-in-the-Head paradigm"],"prefix":"10.3934","volume":"19","author":[{"given":"Philippe","family":"Gaborit","sequence":"first","affiliation":[]},{"given":"Mercedes","family":"Haiech","sequence":"additional","affiliation":[{"name":"University of Limoges, France"}]},{"given":"Romaric","family":"Neveu","sequence":"additional","affiliation":[{"name":"University of Limoges, France"}]}],"member":"2321","reference":[{"key":"key-10.3934\/amc.2025003-1","unstructured":"<p>C. Aguilar-Melchor, T. Feneuil, N. Gama, S. Gueron, J. Howe, D. Joseph, A. Joux, E. Persichetti, T. Randrianarisoa, M. Rivain and D. Yue, <i>SD-in-the-Head Signature Scheme<\/i>, Submission to the 1st round of the NIST additional signatures project. 2023. <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/sdith.org\/\">https:\/\/sdith.org\/<\/ext-link>.<\/p>"},{"key":"key-10.3934\/amc.2025003-2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-30589-4_20"},{"key":"key-10.3934\/amc.2025003-3","unstructured":"<p>N. Aragon, L. Bidoux, J. Chi-Dom\u00ednguez, T. Feneuil, P. Gaborit, R. Neveu and M. Rivain, MIRA: a Digital Signature Scheme based on the MinRank problem and the MPC-in-the-Head paradigm, 2023. <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/pqc-mira.org\/index.html\">https:\/\/pqc-mira.org\/index.html<\/ext-link>.<\/p>"},{"key":"key-10.3934\/amc.2025003-4","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2019.2933535"},{"key":"key-10.3934\/amc.2025003-5","unstructured":"<p>Aumasson, J., Bernstein, D., Beullens, W., Dobraunig, C., Eichlseder, M., Fluhrer, S., Gazdag, S., H\u00fclsing, A., Kampanakis, P., K\u00a8olbl, S., Lange, T., Lauridsen, M., Mendel, F., Niederhagen, R., Rechberger, C., Rijneveld, J., Schwabe, P. and Westerbaan, B., SPHINCS+, Submission to the 3rd round of the NIST post-quantum project., 2023. <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/sphincs.org\/\">https:\/\/sphincs.org\/<\/ext-link>.<\/p>"},{"key":"key-10.3934\/amc.2025003-6","unstructured":"<p>S. Bai, L. Ducas, E. Kiltz, T. Lepoint, V. Lyubashevsky, P. Schwabe, G. Seiler and D. Stehl\u00e9, CRYSTALS-Dilithium, Submission to the 3rd round of the NIST post-quantum project, 2022. <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/pq-crystals.org\/dilithium\/index.shtml\">https:\/\/pq-crystals.org\/dilithium\/index.shtml<\/ext-link>.<\/p>"},{"key":"key-10.3934\/amc.2025003-7","unstructured":"<p>G. Banegas, K. Carrier, A. Chailloux, A. Couvreur, T. Debris-Alazard, P. Gaborit, P. Karpman, J. Loyer, R. Niederhagen, N. Sendrier, B. Smith and J. Tillich, WAVE, Submission to the 1st round of the NIST additional signatures project, 2023. <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/wave-sign.org\/\">https:\/\/wave-sign.org\/<\/ext-link>.<\/p>"},{"key":"key-10.3934\/amc.2025003-8","doi-asserted-by":"crossref","unstructured":"<p>C. Baum, W. Beullens, S. Mukherjee, E. Orsini, S. Ramacher, C. Rechberger, L. Roy and P. Scholl, <i>One Tree to Rule Them All: Optimizing GGM Trees and OWFs for Post-Quantum Signatures<\/i>, Chung, KM., Sasaki, Y. (eds) Advances in Cryptology \u2013 ASIACRYPT 2024. Lecture Notes in Computer Science, vol 15484. Springer Nature Singapore, 2024.<\/p>","DOI":"10.1007\/978-981-96-0875-1_15"},{"key":"key-10.3934\/amc.2025003-9","doi-asserted-by":"crossref","unstructured":"<p>J. Berthomieu, C. Eder and M. Safey El Din, Msolve: A library for solving polynomial systems, <i>2021 International Symposium On Symbolic And Algebraic Computation<\/i>, Association for Computing Machinery (ACM), New York, (2021), 51-58.<\/p>","DOI":"10.1145\/3452143.3465545"},{"key":"key-10.3934\/amc.2025003-10","unstructured":"<p>W. Beullens, M. Chen, J. Ding, B. Gong, M. Kannwischer, J. Patarin, B. Peng, D. Schmidt, C. Shih, C. Tao and B. Yang, Unbalanced Oil and Vinegar, Submission to the 1st round of the NIST additional signatures project, <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/www.uovsig.org\/\">https:\/\/www.uovsig.org\/<\/ext-link>, 2023.<\/p>"},{"key":"key-10.3934\/amc.2025003-11","doi-asserted-by":"crossref","unstructured":"<p>L. Bidoux, J. Chi-Dom\u00ednguez, T. Feneuil, P. Gaborit, A. Joux, M. Rivain and A. Vin\u00e7otte, RYDE: A digital signature scheme based on rank-syndrome-decoding problem with mpcith paradigm, <i>Designs, Codes and Cryptography<\/i>, (2025), 1573-7586<\/p>","DOI":"10.1007\/s10623-024-01544-1"},{"key":"key-10.3934\/amc.2025003-12","doi-asserted-by":"crossref","unstructured":"<p>L. Bidoux, T. Feneuil, P. Gaborit, R. Neveu and M. Rivain, Dual Support Decomposition in the Head: Shorter Signatures from Rank SD and MinRank, <i>Chung, KM., Sasaki, Y. (eds) Advances in Cryptology \u2013 ASIACRYPT 2024. Lecture Notes in Computer Science<\/i>, Springer Nature Singapore, <b>15484<\/b> (2024), 38-69.<\/p>","DOI":"10.1007\/978-981-96-0888-1_2"},{"key":"key-10.3934\/amc.2025003-13","unstructured":"<p>M. Bros, Algebraic cryptanalysis and contributions to post-quantum cryptography based on error-correcting codes in the rank-metric, Ph.D Thesis, Universit\u00e9 de Limoges, 2022.<\/p>"},{"key":"key-10.3934\/amc.2025003-14","doi-asserted-by":"crossref","unstructured":"<p>T. Chien Lau and C. How Tan, Rank preserving code-based signature, <i>2020 IEEE International Symposium On Information Theory (ISIT)<\/i>, (2020), 846-851.<\/p>","DOI":"10.1109\/ISIT44484.2020.9174058"},{"key":"key-10.3934\/amc.2025003-15"},{"key":"key-10.3934\/amc.2025003-16","doi-asserted-by":"crossref","unstructured":"<p>T. Feneuil, Building MPCitH-based signatures from MQ, MinRank, and Rank SD, <i>Applied cryptography and network security. Part I, <\/i>  Lecture Notes in Comput. Sci., <b>14583<\/b> (2024), 403\u2013431.<\/p>","DOI":"10.1007\/978-3-031-54770-6_16"},{"key":"key-10.3934\/amc.2025003-17","doi-asserted-by":"crossref","unstructured":"<p>T. Feneuil, A. Joux and M. Rivain, Syndrome decoding in the head: Shorter signatures from zero-knowledge proofs, <i>Advances In Cryptology \u2013 CRYPTO 2022<\/i>, Lecture Notes in Comput. Sci., <b>13508<\/b> (2022), 541-572.<\/p>","DOI":"10.1007\/978-3-031-15979-4_19"},{"key":"key-10.3934\/amc.2025003-18","unstructured":"<p>T. Feneuil and M. Rivain, <i>Threshold Computation in the Head: Improved Framework for Post-Quantum Signatures and Zero-Knowledge Arguments<\/i>, Cryptology ePrint Archive, Paper 2023\/1573, 2023.<\/p>"},{"key":"key-10.3934\/amc.2025003-19","doi-asserted-by":"crossref","unstructured":"<p>T. Feneuil and M. Rivain, Threshold linear secret sharing to the rescue of mpc-in-the-head, <i>Advances In Cryptology \u2013 ASIACRYPT 2023<\/i>, Lecture Notes in Comput. Sci., <b>14438<\/b> (2023), 441-473.<\/p>","DOI":"10.1007\/978-981-99-8721-4_14"},{"key":"key-10.3934\/amc.2025003-20","doi-asserted-by":"crossref","unstructured":"<p>A. Fiat and A. Shamir, How to prove yourself: Practical solutions to identification and signature problems, <i>Advances in Cryptology\u2014CRYPTO '86 (Santa Barbara, Calif., 1986), <\/i>  <i>Lecture Notes in Comput. Sci.<\/i>, Springer-Verlag, Berlin, <b>263<\/b> (1987), 186-194.<\/p>","DOI":"10.1007\/3-540-47721-7_12"},{"key":"key-10.3934\/amc.2025003-21","unstructured":"<p>P. Fouque, J. Hoffstein, P. Kirchner, V. Lyubashevsky, T. Pornin, T. Prest, T. Ricosset, G. Seiler, W. Whyte and Z. Zhang, Falcon: Fast-Fourier Lattice-based Compact Signatures over NTRU, Submission to the 3rd round of the NIST post-quantum project, (<ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/falcon-sign.info\/\">https:\/\/falcon-sign.info\/<\/ext-link> 2022).<\/p>"},{"key":"key-10.3934\/amc.2025003-22","unstructured":"<p>A. Hauteville, D\u00e9codage en m\u00e9trique rang et attaques sur un syst\u00e8me de chiffrement \u00e0 base de codes LRPC, Universit\u00e9 de Limoges, France, <ext-link ext-link-type=\"uri\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/inria.hal.science\/hal-01755842\">https:\/\/inria.hal.science\/hal-01755842<\/ext-link>, 2014.<\/p>"},{"key":"key-10.3934\/amc.2025003-23","doi-asserted-by":"crossref","unstructured":"<p>Y. Ishai, E. Kushilevitz, R. Ostrovsky and A. Sahai, Zero-knowledge from secure multiparty computation, <i>STOC'07\u2014Proceedings of the 39th Annual ACM Symposium on Theory of Computing<\/i>, Association for Computing Machinery (ACM), New York, (2007), 21-30.<\/p>","DOI":"10.1145\/1250790.1250794"},{"key":"key-10.3934\/amc.2025003-24","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-65411-5_1"},{"key":"key-10.3934\/amc.2025003-25","doi-asserted-by":"crossref","unstructured":"<p>J. Katz, V. Kolesnikov and X. Wang, Improved non-interactive zero knowledge with applications to post-quantum signatures, <i>Proceedings Of The 2018 ACM SIGSAC Conference On Computer And Communications Security<\/i>, (2018), 525-537<\/p>","DOI":"10.1145\/3243734.3243805"},{"key":"key-10.3934\/amc.2025003-26","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-54074-6_6"},{"key":"key-10.3934\/amc.2025003-27","unstructured":"<p>R. Perlner and D. Smith-Tone, <i>Rainbow Band Separation is Better than we Thought,<\/i> Cryptology ePrint Archive, Paper 2020\/702, 2020.<\/p>"}],"container-title":["Advances in Mathematics of Communications"],"original-title":[],"deposited":{"date-parts":[[2025,4,21]],"date-time":"2025-04-21T09:37:13Z","timestamp":1745228233000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.aimsciences.org\/\/article\/doi\/10.3934\/amc.2025003"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":27,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025]]}},"URL":"https:\/\/doi.org\/10.3934\/amc.2025003","relation":{},"ISSN":["1930-5346","1930-5338"],"issn-type":[{"type":"print","value":"1930-5346"},{"type":"electronic","value":"1930-5338"}],"subject":[],"published":{"date-parts":[[2025]]}}}