{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:54:22Z","timestamp":1760234062078,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,3,25]],"date-time":"2021-03-25T00:00:00Z","timestamp":1616630400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In 2005, Philippe Guillot presented a new construction of Boolean functions using linear codes as an extension of the Maiorana\u2013McFarland\u2019s (MM) construction of bent functions. In this paper, we study a new family of Boolean functions with cryptographically strong properties, such as non-linearity, propagation criterion, resiliency, and balance. The construction of cryptographically strong Boolean functions is a daunting task, and there is currently a wide range of algebraic techniques and heuristics for constructing such functions; however, these methods can be complex, computationally difficult to implement, and not always produce a sufficient variety of functions. We present in this paper a construction of Boolean functions using algebraic codes following Guillot\u2019s work.<\/jats:p>","DOI":"10.3390\/axioms10020042","type":"journal-article","created":{"date-parts":[[2021,3,25]],"date-time":"2021-03-25T02:54:03Z","timestamp":1616640843000},"page":"42","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A New Family of Boolean Functions with Good Cryptographic Properties"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7793-896X","authenticated-orcid":false,"given":"Guillermo","family":"Sosa-G\u00f3mez","sequence":"first","affiliation":[{"name":"Facultad de Ciencias Econ\u00f3micas y Empresariales, Universidad Panamericana, \u00c1lvaro del Portillo 49, Zapopan, Jalisco 45010, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7069-1642","authenticated-orcid":false,"given":"Octavio","family":"Paez-Osuna","sequence":"additional","affiliation":[{"name":"Ronin Institute, Montclair, NJ 07043, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0681-3833","authenticated-orcid":false,"given":"Omar","family":"Rojas","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias Econ\u00f3micas y Empresariales, Universidad Panamericana, \u00c1lvaro del Portillo 49, Zapopan, Jalisco 45010, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5004-2960","authenticated-orcid":false,"given":"Evaristo Jos\u00e9","family":"Madarro-Cap\u00f3","sequence":"additional","affiliation":[{"name":"Institute of Cryptography, University of Havana, Havana 10400, Cuba"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,25]]},"reference":[{"key":"ref_1","unstructured":"Lachowicz, P. (2021, March 15). Walsh\u2013Hadamard Transform and Tests for Randomness of Financial Return- Series. Available online: https:\/\/quantatrisk.com\/2015\/04\/07\/walsh-hadamard-transform-python-tests-for-randomness-of-financial-return-series\/."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Menezes, A.J., Van Oorschot, P.C., and Vanstone, S.A. (2018). Handbook of Applied Cryptography, CRC Press.","DOI":"10.1201\/9781439821916"},{"key":"ref_3","unstructured":"Pasalic, E. (2003). On Boolean Functions in Symmetric-Key Ciphers, Lund University."},{"key":"ref_4","first-page":"774","article-title":"DES encryption and decryption algorithm implementation based on FPGA","volume":"18","author":"Zeebaree","year":"2020","journal-title":"Indones. J. Electr. Eng. Comput. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"131101","DOI":"10.1007\/s11432-018-9929-x","article-title":"Stream cipher designs: A review","volume":"63","author":"Jiao","year":"2020","journal-title":"Sci. China Inf. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Cusick, T.W., and Stanica, P. (2017). Cryptographic Boolean Functions and Applications, Academic Press.","DOI":"10.1016\/B978-0-12-811129-1.00005-5"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/BF00630563","article-title":"Differential cryptanalysis of DES-like cryptosystems","volume":"4","author":"Biham","year":"1991","journal-title":"J. Cryptol."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Langford, S.K., and Hellman, M.E. (1994). Differential-linear cryptanalysis. Annual International Cryptology Conference, Springer.","DOI":"10.1007\/3-540-48658-5_3"},{"key":"ref_9","unstructured":"Chuan-Kun, W., and Dengguo, F. (2016). Boolean Functions and Their Applications in Cryptography, Springer."},{"key":"ref_10","first-page":"50","article-title":"De la b\u00fasqueda de funciones booleanas con buenas propiedades criptogr\u00e1ficas","volume":"26","year":"2007","journal-title":"Cinvestav"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Chee, S., Lee, S., Lee, D., and Sung, S.H. (1996). On the correlation immune functions and their nonlinearity. International Conference on the Theory and Application of Cryptology and Information Security, Springer. AsiaCrypt.","DOI":"10.1007\/BFb0034850"},{"key":"ref_12","unstructured":"Forri\u00e9, R. (1988). The strict avalanche criterion: Spectral properties of Boolean functions and an extended definition. Conference on the Theory and Application of Cryptography, Springer."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1345","DOI":"10.1109\/18.21267","article-title":"A Note on Hermitian Codes Over GF(q2)","volume":"34","author":"Stichtenoth","year":"1988","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_14","unstructured":"Forney, G.D. (1966). Concatenated Codes, Citeseer."},{"key":"ref_15","first-page":"549","article-title":"A Larger Class of Cryptographic Boolean Functions via a Study of the Maiorana-McFarland Construction","volume":"Volume 2442","author":"Carlet","year":"2002","journal-title":"Advances in Cryptology"},{"key":"ref_16","first-page":"141","article-title":"Cryptographical boolean functions construction from linear codes","volume":"387","author":"Guillot","year":"2005","journal-title":"Boolean Funct. Cryptogr. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Wicker, S.B., and Bhargava, V.K. (1999). Reed-Solomon Codes and Their Applications, John Wiley & Sons.","DOI":"10.1109\/9780470546345"},{"key":"ref_18","unstructured":"Van Lint, J.H. (2012). Introduction to Coding Theory, Springer Science & Business Media."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/2\/42\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:40:44Z","timestamp":1760161244000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/10\/2\/42"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,25]]},"references-count":18,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["axioms10020042"],"URL":"https:\/\/doi.org\/10.3390\/axioms10020042","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2021,3,25]]}}}