{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T15:33:49Z","timestamp":1772120029620,"version":"3.50.1"},"reference-count":14,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2023,2,14]],"date-time":"2023-02-14T00:00:00Z","timestamp":1676332800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,2,14]],"date-time":"2023-02-14T00:00:00Z","timestamp":1676332800000},"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":["Cryptogr. Commun."],"published-print":{"date-parts":[[2023,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Subterranean 2.0 is a permutation-based cipher suite which works with a 257 bit-state. It is designed for lightweight cryptography, and it scores very well with respect to energy consumption. Its security has been investigated by the designers against well-known attack vectors. A possible point of concern is the relatively low order of its linear layer, which equals 256. In the past, such properties have been exploited by invariant subspace attacks. We define linear mappings with a similar structure as the linear layer of Subterranean as SC-compositions. In this work, we explore finding SC-compositions with a higher order than 256. We rely on concepts from abstract algebra and number theory to understand the relation between the order and the bit-states of SC-compositions. Using a 257 bit-state as done in Subterranean is an unfortunate choice for designing such SC-compositions with a high order. We present two examples with different bit-states, each having a significantly higher order than 256.<\/jats:p>","DOI":"10.1007\/s12095-023-00630-w","type":"journal-article","created":{"date-parts":[[2023,2,14]],"date-time":"2023-02-14T03:41:51Z","timestamp":1676346111000},"page":"1053-1067","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["An algebraic approach to symmetric linear layers in cryptographic primitives"],"prefix":"10.1007","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5534-2655","authenticated-orcid":false,"given":"Robert Christian","family":"Subroto","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,2,14]]},"reference":[{"key":"630_CR1","unstructured":"Armstrong, M.A.: Groups and symmetry. Springer Sci. Bus. Media (1997)"},{"key":"630_CR2","unstructured":"Baldi, M., Barenghi, A., Chiaraluce, F., Pelosi, G., Santini, P.: Ledacrypt : low-density parity-check code-based cryptographic systems. NIST round, 2 (2019)"},{"key":"630_CR3","doi-asserted-by":"publisher","unstructured":"Beierle, C., Canteaut, A., Leander, G., Rotella, Y.: Proving resistance against invariant attacks : How to choose the round constants. In: Katz, J., Shacham, H. (eds.) Advances in Cryptology - CRYPTO 2017 - 37th Annual International Cryptology Conference, Santa Barbara, CA, USA, August 20-24, 2017, Proceedings, Part II. Lecture Notes in Computer Science, vol. 10402, pp. 647\u2013678. Springer. https:\/\/doi.org\/10.1007\/978-3-319-63715-0_22 (2017)","DOI":"10.1007\/978-3-319-63715-0_22"},{"key":"630_CR4","doi-asserted-by":"crossref","unstructured":"Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J.M., Schwabe, P., Seiler, G., Stehl\u00e9, D.: Crystals-kyber: a Cca-secure module-lattice-based kem. In: 2018 IEEE European Symposium on Security and Privacy (Euros&P). pp. 353\u2013367. IEEE (2018)","DOI":"10.1109\/EuroSP.2018.00032"},{"issue":"S1","key":"630_CR5","doi-asserted-by":"publisher","first-page":"262","DOI":"10.46586\/tosc.v2020.iS1.262-294","volume":"2020","author":"J Daemen","year":"2020","unstructured":"Daemen, J., Massolino, P.M.C., Mehrdad, A., Rotella, Y.: The subterranean 2.0 cipher suite. IACR Trans. Symmetric Cryptol. 2020(S1), 262\u2013294 (2020). https:\/\/doi.org\/10.13154\/tosc.v2020.iS1.262-294","journal-title":"IACR Trans. Symmetric Cryptol."},{"key":"630_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-60769-5","volume-title":"The Design of Rijndael - The Advanced Encryption Standard (AES). Information Security and Cryptography","author":"J Daemen","year":"2020","unstructured":"Daemen, J., Rijmen, V.: The Design of Rijndael - The Advanced Encryption Standard (AES). Information Security and Cryptography, 2nd edn. Springer, New York (2020). https:\/\/doi.org\/10.1007\/978-3-662-60769-5","edition":"2nd edn."},{"key":"630_CR7","unstructured":"Ehrlich, G.: Fundamental concepts of abstract algebra. Courier Corporation (2011)"},{"key":"630_CR8","doi-asserted-by":"crossref","unstructured":"Hoffstein, J., Pipher, J., Silverman, J.H.: Ntru : a ring-based public key cryptosystem. In: International Algorithmic Number Theory Symposium, pp. 267\u2013288. Springer (1998)","DOI":"10.1007\/BFb0054868"},{"issue":"3","key":"630_CR9","first-page":"368","volume":"59","author":"I Kra","year":"2012","unstructured":"Kra, I., Simanca, S.R.: On circulant matrices. Notices of the AMS 59(3), 368\u2013377 (2012)","journal-title":"Notices of the AMS"},{"key":"630_CR10","unstructured":"Lang, S.: Algebra, volume 211 of. Graduate Texts in Mathematics (2004)"},{"key":"630_CR11","volume-title":"Finite fields. No. 20","author":"R Lidl","year":"1997","unstructured":"Lidl, R., Niederreiter, H.: Finite fields. No. 20. Cambridge University Press, Cambridge (1997)"},{"key":"630_CR12","unstructured":"Lyubashevsky, V., Ducas, L., Kiltz, E., Lepoint, T., Schwabe, P., Seiler, G., Stehl\u00e9, D., Bai, S.: Crystals-dilithium. Submission to the NIST Post-Quantum Cryptography Standardization [NIS] (2017)"},{"key":"630_CR13","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1016\/j.jalgebra.2015.04.006","volume":"435","author":"K Mahatab","year":"2015","unstructured":"Mahatab, K., Sampath, K.: Chinese remainder theorem for cyclotomic polynomials in z [x]. J. Algebra 435, 223\u2013262 (2015)","journal-title":"J. Algebra"},{"key":"630_CR14","doi-asserted-by":"crossref","unstructured":"D\u2019Anvers, JP, Karmakar, A, Roy, SS, Vercauteren, F: Saber: Module-LWR based key exchange, CPA-secure encryption and CCA-secure KEM, IACR Cryptol. ePrint Arch. pp. 230. http:\/\/eprint.iacr.org\/2018\/230 (2018)","DOI":"10.1007\/978-3-319-89339-6_16"}],"container-title":["Cryptography and Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-023-00630-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12095-023-00630-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-023-00630-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,3]],"date-time":"2024-06-03T12:23:32Z","timestamp":1717417412000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12095-023-00630-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,14]]},"references-count":14,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2023,11]]}},"alternative-id":["630"],"URL":"https:\/\/doi.org\/10.1007\/s12095-023-00630-w","relation":{"has-preprint":[{"id-type":"doi","id":"10.21203\/rs.3.rs-2178150\/v1","asserted-by":"object"}]},"ISSN":["1936-2447","1936-2455"],"issn-type":[{"value":"1936-2447","type":"print"},{"value":"1936-2455","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,14]]},"assertion":[{"value":"18 October 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 January 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 February 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}