{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T10:20:47Z","timestamp":1772792447559,"version":"3.50.1"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T00:00:00Z","timestamp":1772755200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T00:00:00Z","timestamp":1772755200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cybersecurity"],"abstract":"Abstract<\/jats:title>\n \n Near collision attacks and fast near collision attacks on stream ciphers are controversial attack methods in the field of cryptography in recent years, and their attack results are based on reduced experimental observations and derivation of birthday collision theory. Due to the large-scale internal state of the stream cipher, it is difficult to conduct experiments on all internal states. This article systematically summarizes the principles of near collision attacks and fast near collision attacks, and conducts a complete near collision attack experiment on the nonlinear output function used in the Grain v1 cipher. It is found that there are significant deviations in the keystream output differences for only partial near collisions, while for other non-near collisions, the corresponding keystream output difference also has a large deviation. Combining the theories of derivative of Boolean functions, we find that the effectiveness of near collision attacks is correlated to the distribution of the derivative of the Boolean function the cipher used. At the same time, we provide a more accurate near collision attack method for the Grain v1 stream cipher. Furthermore, we present an indepth analysis of the attack presented at ACNS 2023. The results of this article have a memory and data complexity of\n \n \n $$2^{79}$$<\/jats:tex-math>\n \n \n 2<\/mml:mn>\n 79<\/mml:mn>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , a online time complexity of\n \n \n $$2^{69.3}$$<\/jats:tex-math>\n \n \n 2<\/mml:mn>\n \n 69.3<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , and a success probability of\n \n \n $$2^{-16.97}$$<\/jats:tex-math>\n \n \n 2<\/mml:mn>\n \n -<\/mml:mo>\n 16.97<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n .\n <\/jats:p>","DOI":"10.1186\/s42400-026-00562-x","type":"journal-article","created":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T07:36:36Z","timestamp":1772782596000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Some observations of near collision attacks on grain v1"],"prefix":"10.1186","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7433-5207","authenticated-orcid":false,"given":"Shaoyu","family":"Du","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weiping","family":"Gu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,3,6]]},"reference":[{"key":"562_CR1","doi-asserted-by":"crossref","unstructured":"Banik S, Collins D, Meier W (2023) Near Collision Attack Against Grain v1. In: Tibouchi, M., Wang, X. (eds) Applied cryptography and network security. ACNS 2023. Lecture Notes in Computer Science, 13905. Springer, Cham","DOI":"10.1007\/978-3-031-33488-7_7"},{"issue":"4","key":"562_CR2","doi-asserted-by":"publisher","first-page":"88","DOI":"10.46586\/tosc.v2020.i4.88-103","volume":"2020","author":"P Derbez","year":"2020","unstructured":"Derbez P, Fouque PA, Mollimard V (2020) Fake near collisions attacks. IACR Trans Symmet Cryptol 2020(4):88\u2013103","journal-title":"IACR Trans Symmet Cryptol"},{"key":"562_CR3","doi-asserted-by":"publisher","unstructured":"Ding Y, Wang Z, Li W (2007) Some cryptographic properties of Boolean function derivatives (in Chinese) 28(1):6. https:\/\/doi.org\/10.3969\/j.issn.1009-2102.2007.01.004","DOI":"10.3969\/j.issn.1009-2102.2007.01.004"},{"key":"562_CR4","doi-asserted-by":"crossref","unstructured":"Hell M, Johansson T, Meier W (2007) Grain: a stream cipher for constrained environments. Int J Wirel Mob Comput (IJWMC) 2(1), 86C93","DOI":"10.1504\/IJWMC.2007.013798"},{"issue":"2","key":"562_CR5","first-page":"110","volume":"33","author":"H Jing-lian","year":"2012","unstructured":"Jing-lian H, Zhuo W (2012) Relationship between correlation immune and weight of H Boolean functions. J Commun 33(2):110\u2013118","journal-title":"J Commun"},{"key":"562_CR6","doi-asserted-by":"publisher","first-page":"905","DOI":"10.1108\/03684921111142458","volume":"40","author":"W Li","year":"2011","unstructured":"Li W, Wang Z, Huang J (2011) The e-derivative of Boolean functions and its application in the fault detection and cryptographic system. Kybernetes 40:905\u2013911. https:\/\/doi.org\/10.1108\/03684921111142458","journal-title":"Kybernetes"},{"key":"562_CR7","doi-asserted-by":"crossref","unstructured":"TODO Y, ISOBE T, MEIER W, et al. (2018) Fast correlation attack revisited[C]. In: Advances in cryptology-CRYPTO , Part II. Springer Cham, 2018: 129\u2013159","DOI":"10.1007\/978-3-319-96881-0_5"},{"issue":"8","key":"562_CR8","first-page":"82","volume":"34","author":"LI Wei-wei","year":"2013","unstructured":"Wei-wei LI (2013) Correlation-immunity study of balanced H-Boolean functions. J Commun 34(8):82\u201387","journal-title":"J Commun"},{"key":"562_CR9","unstructured":"Yixian Y N-variable Boolean function (in Chinese). 1988(03):4\u201312. CNKI:SUN:BJYD.0.1988-03-000"},{"key":"562_CR10","unstructured":"Yixian Y, Yusen Y (1997) N-variable H-Boolean function (in Chinese), 19(2):3. CNKI:SUN:DZYX.0.1997-02-011"},{"issue":"6","key":"562_CR11","doi-asserted-by":"publisher","first-page":"812","DOI":"10.13868\/j.cnki.jcr.000408","volume":"7","author":"YJ Zhang","year":"2020","unstructured":"Zhang YJ, Hu L, Shi DP, Wang P, Sun SW, Wei R (2020) Improved fast correlation attack on Grain-v1. J Cryptol Res 7(6):812\u2013825. https:\/\/doi.org\/10.13868\/j.cnki.jcr.000408","journal-title":"J Cryptol Res"},{"key":"562_CR12","doi-asserted-by":"crossref","unstructured":"Zhang B, Li Z, Feng D, Lin D (2014) Near Collision Attack on the Grain v1 Stream Cipher. In: Moriai S (eds) Fast Software Encryption. FSE 2013. Lecture notes in computer science, vol 8424. Springer, Berlin, Heidelberg","DOI":"10.1007\/978-3-662-43933-3_27"},{"key":"562_CR13","doi-asserted-by":"crossref","unstructured":"Zhang B, Xu C, Meier W (2018) Fast near collision attack on the grain v1 stream cipher. In: Nielsen J, Rijmen V (eds) Advances in cryptology C EUROCRYPT 2018. EUROCRYPT 2018. Lecture notes in computer science, 10821. Springer, Cham","DOI":"10.1007\/978-3-319-78375-8_25"}],"container-title":["Cybersecurity"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s42400-026-00562-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s42400-026-00562-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s42400-026-00562-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T07:36:43Z","timestamp":1772782603000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1186\/s42400-026-00562-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,6]]},"references-count":13,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["562"],"URL":"https:\/\/doi.org\/10.1186\/s42400-026-00562-x","relation":{},"ISSN":["2523-3246"],"issn-type":[{"value":"2523-3246","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,6]]},"assertion":[{"value":"26 August 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 February 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 March 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that we have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"132"}}