{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T17:15:00Z","timestamp":1760116500605,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,8]],"date-time":"2024-11-08T00:00:00Z","timestamp":1731024000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Council of Science and Industrial Research"},{"name":"Amrita Vishwa Vidyapeetham"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Boolean functions are fundamental building blocks in both discrete mathematics and computer science, with applications spanning from cryptography to coding theory. Bent functions, a subset of Boolean functions with maximal nonlinearity, are particularly valuable in cryptographic applications. This study introduces a novel equivalence relation among all Boolean functions and presents an algorithm to generate bent functions based on this relation. We systematically generated a collection of 10,000 bent functions over eight variables, all originating from the same equivalence class, and analyzed their structural complexity through rank determination. Our findings revealed the presence of at least five distinct affine classes of bent functions within this collection. By employing this construction, we devised an algorithm to generate a filter function capable of combining Boolean functions. This filter function can be dynamically adjusted based on a key, offering potential applications in symmetric cipher design, such as enhancing security or improving efficiency.<\/jats:p>","DOI":"10.3390\/sym16111501","type":"journal-article","created":{"date-parts":[[2024,11,12]],"date-time":"2024-11-12T03:53:14Z","timestamp":1731383594000},"page":"1501","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Generating Bent Functions and Dynamic Filters: A Novel Equivalence-Based Approach"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7775-1529","authenticated-orcid":false,"given":"Joseph","family":"Nelson","sequence":"first","affiliation":[{"name":"Department of Mathematics, Amrita School of Physical Sciences, Coimbatore 641112, Amrita Vishwa Vidyapeetham, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chungath","family":"Srinivasan","sequence":"additional","affiliation":[{"name":"TIFAC-CORE in Cyber Security, Amrita School of Engineering, Coimbatore 641112, Amrita Vishwa Vidyapeetham, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anand R.","family":"Nair","sequence":"additional","affiliation":[{"name":"TIFAC-CORE in Cyber Security, Amrita School of Engineering, Coimbatore 641112, Amrita Vishwa Vidyapeetham, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lakshmy","family":"Koduvayur Viswanathan","sequence":"additional","affiliation":[{"name":"TIFAC-CORE in Cyber Security, Amrita School of Engineering, Coimbatore 641112, Amrita Vishwa Vidyapeetham, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/s10623-022-01097-1","article-title":"Bent functions in the partial spread class generated by linear recurring sequences","volume":"91","author":"Gadouleau","year":"2023","journal-title":"Des. Codes Cryptogr."},{"key":"ref_2","unstructured":"Dillon, J.F. (1974). Elementary Hadamard Difference-Sets, University of Maryland."},{"key":"ref_3","unstructured":"Carlet, C. (1993). Two new classes of bent functions. Workshop on the Theory and Application of Cryptographic Techniques, Springer."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Carlet, C. (1996). A Construction of Bent Functions, Cambridge University Press.","DOI":"10.1017\/CBO9780511525988.006"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Carlet, C. (2004). On the secondary constructions of resilient and bent functions. 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Theory"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"305","DOI":"10.3934\/amc.2012.6.305","article-title":"Secondary constructions of bent functions and their enforcement","volume":"6","author":"Carlet","year":"2012","journal-title":"Adv. Math. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s10623-015-0145-8","article-title":"Four decades of research on bent functions","volume":"78","author":"Carlet","year":"2016","journal-title":"Des. Codes Cryptogr."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2398","DOI":"10.1016\/j.disc.2008.05.017","article-title":"Results on rotation symmetric bent functions","volume":"309","author":"Dalai","year":"2009","journal-title":"Discret. Math."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1016\/j.jcta.2005.07.009","article-title":"Construction of bent functions via Niho power functions","volume":"113","author":"Dobbertin","year":"2006","journal-title":"J. Comb. Theory Ser. A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"6979","DOI":"10.1109\/TIT.2012.2206557","article-title":"Further results on Niho bent functions","volume":"58","author":"Budaghyan","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1016\/0097-3165(76)90024-8","article-title":"On \u201cbent\u201d functions","volume":"20","author":"Rothaus","year":"1976","journal-title":"J. Comb. Theory Ser. A"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1109\/TIT.2005.862121","article-title":"Monomial bent functions","volume":"52","author":"Leander","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1818","DOI":"10.1109\/TIT.2012.2229782","article-title":"Several new classes of bent functions from Dillon exponents","volume":"59","author":"Li","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/s12095-015-0144-7","article-title":"Further constructions of infinite families of bent functions from new permutations and their duals","volume":"8","author":"Mesnager","year":"2016","journal-title":"Cryptogr. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2295","DOI":"10.3906\/mat-2104-5","article-title":"Secondary constructions of (non)-weakly regular plateaued functions over finite fields","volume":"45","author":"Mesnager","year":"2021","journal-title":"Turk. J. Math."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1515\/jmc-2016-0042","article-title":"Affine equivalence of monomial rotation symmetric Boolean functions: A P\u00f3lya\u2019s theorem approach","volume":"10","author":"Cusick","year":"2016","journal-title":"J. Math. Cryptol."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Mesnager, S., and Mesnager, S. (2016). Bent Functions, Springer International Publishing.","DOI":"10.1007\/978-3-319-32595-8"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1080\/00207160.2012.669832","article-title":"Construction of bent functions of 2k variables from a basis of","volume":"89","author":"Climent","year":"2012","journal-title":"Int. J. Comput. Math."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Nyberg, K. (1990). Constructions of bent functions and difference sets.  Advances in Cryptology\u2014EUROCRYPT\u201990, Springer.","DOI":"10.1007\/3-540-46877-3_13"},{"key":"ref_23","unstructured":"Meier, W., and Staffelbach, O. (1989). Nonlinearity criteria for cryptographic functions. Workshop on the Theory and Application of Cryptographic Techniques, Springer."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1096","DOI":"10.1016\/j.ffa.2007.03.001","article-title":"On the ranks of bent functions","volume":"13","author":"Weng","year":"2007","journal-title":"Finite Fields Their Appl."},{"key":"ref_25","first-page":"520","article-title":"Weight and nonlinearity of Boolean functions","volume":"36","author":"Ciungu","year":"2012","journal-title":"Turk. J. Math."},{"key":"ref_26","first-page":"1040","article-title":"An Algorithm for Constructing Support of Bent Functions by Extending a Set","volume":"8","author":"Nelson","year":"2023","journal-title":"Int. J. Math. Eng. Manag. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/S0045-7825(97)00192-8","article-title":"On the least-squares method","volume":"152","author":"Jiang","year":"1998","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_28","unstructured":"Pandey, S.K., and Mishra, P.R. (2024, September 01). Count of Rotational Symmetric Bent Boolean Functions; Cryptology ePrint Archive, Paper 2019\/873. Available online: https:\/\/eprint.iacr.org\/2019\/873."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.dam.2024.05.037","article-title":"Construction and enumeration of balanced rotation symmetric Boolean functions","volume":"357","author":"Zeenath","year":"2024","journal-title":"Discret. Appl. Math."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.dam.2013.12.016","article-title":"Counting rotation symmetric functions using Polya\u2019s theorem","volume":"169","author":"Lakshmy","year":"2014","journal-title":"Discret. Appl. Math."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s10623-010-9455-z","article-title":"Counting all bent functions in dimension eight 99270589265934370305785861242880","volume":"59","author":"Langevin","year":"2011","journal-title":"Des. Codes Cryptogr."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"609","DOI":"10.3934\/amc.2011.5.609","article-title":"On the number of bent functions from iterative constructions: Lower bounds and hypotheses","volume":"5","author":"Tokareva","year":"2011","journal-title":"Adv. Math. Commun."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Lamba, C.S. (2010, January 26\u201328). Design and analysis of stream cipher for network security. Proceedings of the 2010 Second International Conference on Communication Software and Networks, Washington, DC, USA.","DOI":"10.1109\/ICCSN.2010.113"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/11\/1501\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:29:06Z","timestamp":1760113746000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/11\/1501"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,8]]},"references-count":33,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2024,11]]}},"alternative-id":["sym16111501"],"URL":"https:\/\/doi.org\/10.3390\/sym16111501","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,11,8]]}}}