{"volume":15606,"oa_version":"Submitted Version","doi":"10.1007/978-3-031-91095-1_14","publication_status":"published","day":"28","conference":{"end_date":"2025-05-08","location":"Madrid, Spain","name":"EUROCRYPT: International Conference on the Theory and Applications of Cryptographic Techniques","start_date":"2025-05-04"},"publisher":"Springer Nature","department":[{"_id":"KrPi"}],"OA_type":"green","date_published":"2025-04-28T00:00:00Z","main_file_link":[{"url":"https://www.research-collection.ethz.ch/handle/20.500.11850/732894","open_access":"1"}],"type":"conference","abstract":[{"lang":"eng","text":"We study recent algebraic attacks (Briaud-Øygarden EC’23) on the Regular Syndrome Decoding (RSD) problem and the assumptions underlying the correctness of their attacks’ complexity estimates. By relating these assumptions to interesting algebraic-combinatorial problems, we prove that they do not hold in full generality. However, we show that they are (asymptotically) true for most parameter sets, supporting the soundness of algebraic attacks on RSD. Further, we prove—without any heuristics or assumptions—that RSD can be broken in polynomial time whenever the number of error blocks times the square of the size of error blocks is larger than 2 times the square of the dimension of the code.\r\nAdditionally, we use our methodology to attack a variant of the Learning With Errors problem where each error term lies in a fixed set of constant size. We prove that this problem can be broken in polynomial time, given a sufficient number of samples. This result improves on the seminal work by Arora and Ge (ICALP’11), as the attack’s time complexity is independent of the LWE modulus."}],"intvolume":"     15606","quality_controlled":"1","publication":"44th Annual International Conference on the Theory and Applications of Cryptographic Techniques","status":"public","corr_author":"1","date_updated":"2025-05-28T06:12:39Z","publication_identifier":{"isbn":["9783031910944"],"eissn":["1611-3349"],"eisbn":["9783031910951"],"issn":["0302-9743"]},"date_created":"2025-05-19T14:15:01Z","language":[{"iso":"eng"}],"citation":{"chicago":"Cueto Noval, Miguel, Simon-Philipp Merz, Patrick Stählin, and Akin Ünal. “On the Soundness of Algebraic Attacks against Code-Based Assumptions.” In <i>44th Annual International Conference on the Theory and Applications of Cryptographic Techniques</i>, 15606:385–415. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/978-3-031-91095-1_14\">https://doi.org/10.1007/978-3-031-91095-1_14</a>.","apa":"Cueto Noval, M., Merz, S.-P., Stählin, P., &#38; Ünal, A. (2025). On the soundness of algebraic attacks against code-based assumptions. In <i>44th Annual International Conference on the Theory and Applications of Cryptographic Techniques</i> (Vol. 15606, pp. 385–415). Madrid, Spain: Springer Nature. <a href=\"https://doi.org/10.1007/978-3-031-91095-1_14\">https://doi.org/10.1007/978-3-031-91095-1_14</a>","mla":"Cueto Noval, Miguel, et al. “On the Soundness of Algebraic Attacks against Code-Based Assumptions.” <i>44th Annual International Conference on the Theory and Applications of Cryptographic Techniques</i>, vol. 15606, Springer Nature, 2025, pp. 385–415, doi:<a href=\"https://doi.org/10.1007/978-3-031-91095-1_14\">10.1007/978-3-031-91095-1_14</a>.","short":"M. Cueto Noval, S.-P. Merz, P. Stählin, A. Ünal, in:, 44th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Springer Nature, 2025, pp. 385–415.","ieee":"M. Cueto Noval, S.-P. Merz, P. Stählin, and A. Ünal, “On the soundness of algebraic attacks against code-based assumptions,” in <i>44th Annual International Conference on the Theory and Applications of Cryptographic Techniques</i>, Madrid, Spain, 2025, vol. 15606, pp. 385–415.","ista":"Cueto Noval M, Merz S-P, Stählin P, Ünal A. 2025. On the soundness of algebraic attacks against code-based assumptions. 44th Annual International Conference on the Theory and Applications of Cryptographic Techniques. EUROCRYPT: International Conference on the Theory and Applications of Cryptographic Techniques, LNCS, vol. 15606, 385–415.","ama":"Cueto Noval M, Merz S-P, Stählin P, Ünal A. On the soundness of algebraic attacks against code-based assumptions. In: <i>44th Annual International Conference on the Theory and Applications of Cryptographic Techniques</i>. Vol 15606. Springer Nature; 2025:385-415. doi:<a href=\"https://doi.org/10.1007/978-3-031-91095-1_14\">10.1007/978-3-031-91095-1_14</a>"},"author":[{"orcid":"0000-0002-2505-4246","id":"ffc563a3-f6e0-11ea-865d-e3cce03d17cc","last_name":"Cueto Noval","first_name":"Miguel","full_name":"Cueto Noval, Miguel"},{"last_name":"Merz","first_name":"Simon-Philipp","full_name":"Merz, Simon-Philipp"},{"last_name":"Stählin","first_name":"Patrick","full_name":"Stählin, Patrick"},{"orcid":"0000-0002-8929-0221","first_name":"Akin","full_name":"Ünal, Akin","id":"f6b56fb6-dc63-11ee-9dbf-f6780863a85a","last_name":"Ünal"}],"title":"On the soundness of algebraic attacks against code-based assumptions","oa":1,"scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","alternative_title":["LNCS"],"_id":"19712","article_processing_charge":"No","OA_place":"repository","page":"385-415","year":"2025","acknowledgement":"We thank Pierre Briaud and Morten Øygarden for helpful discussions on algebraic attacks on RSD, and the EC reviewers for helpful comments.","month":"04"}