{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T20:51:27Z","timestamp":1771102287235,"version":"3.50.1"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,4,1]],"date-time":"2025-04-01T00:00:00Z","timestamp":1743465600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,4,1]],"date-time":"2025-04-01T00:00:00Z","timestamp":1743465600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62206312"],"award-info":[{"award-number":["62206312"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cybersecurity"],"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>In CRYPTO 2019, Gohr built a bridge between machine learning and differential cryptanalysis, which show that machine learning-aided methods have advantages over classical differential cryptanalysis. Yet, for linear cryptanalysis, there is lack of effective works showing that machine learning-aided cryptanalysis can reach the benchmark of traditional counterparts and also lack of an effective universal framework using\u00a0machine learning to\u00a0assist linear cryptanalysis. In this paper, we mainly focus on machine learning-aided linear cryptanalysis and application to <jats:sc>Des<\/jats:sc>. First, we propose a machine learning-aided model to distinguish different Bernoulli distributions and demonstrate the validity of the model through experiments and theoretical analysis. Based on the model, we propose a new machine learning-aided linear cryptanalysis framework, which can be applied to one bit and multiple bits key-recovery attacks. As applications, we perform one bit attacks on 3-, 4-, 5-, 6-round <jats:sc>Des<\/jats:sc> and multiple bits attack on 8-round <jats:sc>Des<\/jats:sc>. Compared with the previous works about machine learning-aided linear cryptanalysis, the results improve the success rate and the complexity. Most importantly, more rounds are covered in our work. Besides, the work indicates that machine learning-aided cryptanalysis can achieve the same or marginally better performance than classical methods.<\/jats:p>","DOI":"10.1186\/s42400-024-00327-4","type":"journal-article","created":{"date-parts":[[2025,4,1]],"date-time":"2025-04-01T03:07:17Z","timestamp":1743476837000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Improved machine learning-aided linear cryptanalysis: application to DES"],"prefix":"10.1186","volume":"8","author":[{"given":"Zezhou","family":"Hou","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2223-4329","authenticated-orcid":false,"given":"Jiongjiong","family":"Ren","sequence":"additional","affiliation":[]},{"given":"Shaozhen","family":"Chen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,1]]},"reference":[{"key":"327_CR1","unstructured":"Abadi M, Andersen DG (2016) Learning to protect communications with adversarial neural cryptography. Preprintat at. https:\/\/arxiv.org\/abs\/1610.06918"},{"key":"327_CR2","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1007\/978-3-031-22963-3_11","volume-title":"Advances in cryptology - ASIACRYPT 2022\u201328th International conference on the theory and application of cryptology and information security","author":"Z Bao","year":"2022","unstructured":"Bao Z, Guo J, Liu M, Ma L, Tu Y (2022) Enhancing differential-neural cryptanalysis. In: Agrawal S, Lin D (eds) Advances in cryptology - ASIACRYPT 2022\u201328th International conference on the theory and application of cryptology and information security. Springer, Heidelberg, pp 318\u2013347. https:\/\/doi.org\/10.1007\/978-3-031-22963-3_11"},{"key":"327_CR3","unstructured":"Bao Z, Guo J, Liu M, Ma L, Tu Y (2021) Enhancing differential-neural cryptanalysis. IACR Cryptol. ePrint Arch. 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Springer, Heidelberg, pp 805\u2013835. https:\/\/doi.org\/10.1007\/978-3-030-77870-5_28"},{"key":"327_CR6","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1007\/978-3-540-28628-8_18","volume-title":"Advances in cryptology - CRYPTO 2004, 24th annual international cryptology conference","author":"E Biham","year":"2004","unstructured":"Biham E, Chen R (2004) Near-collisions of SHA-0. In: Franklin MK (ed) Advances in cryptology - CRYPTO 2004, 24th annual international cryptology conference, vol 3152. Springer, Heidelberg, pp 290\u2013305. https:\/\/doi.org\/10.1007\/978-3-540-28628-8_18"},{"key":"327_CR7","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/978-3-540-28628-8_","volume-title":"Advances in cryptology - CRYPTO 2004, 24th annual international cryptology conference","author":"NT Courtois","year":"2004","unstructured":"Courtois NT (2004) Feistel schemes and bi-linear cryptanalysis. 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