{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T07:31:06Z","timestamp":1767339066579,"version":"3.40.3"},"publisher-location":"Cham","reference-count":36,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030305291"},{"type":"electronic","value":"9783030305307"}],"license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019]]},"DOI":"10.1007\/978-3-030-30530-7_5","type":"book-chapter","created":{"date-parts":[[2019,9,9]],"date-time":"2019-09-09T13:03:55Z","timestamp":1568034235000},"page":"86-105","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["On the Fast Algebraic Immunity of Majority Functions"],"prefix":"10.1007","author":[{"given":"Pierrick","family":"M\u00e9aux","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,9,9]]},"reference":[{"key":"5_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1007\/978-3-319-56620-7_6","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2017","author":"P Ananth","year":"2017","unstructured":"Ananth, P., Sahai, A.: Projective arithmetic functional encryption and indistinguishability obfuscation from degree-5 multilinear maps. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10210, pp. 152\u2013181. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-56620-7_6"},{"key":"5_CR2","doi-asserted-by":"crossref","unstructured":"Applebaum, B., Lovett, S.: Algebraic attacks against random local functions and their countermeasures. In: Wichs, D., Mansour, Y. (eds.) 48th ACM STOC. ACM Press, June 2016","DOI":"10.1145\/2897518.2897554"},{"issue":"1","key":"5_CR3","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1137\/16M1085942","volume":"47","author":"B Applebaum","year":"2018","unstructured":"Applebaum, B., Lovett, S.: Algebraic attacks against random local functions and their countermeasures. SIAM J. Comput. 47(1), 52\u201379 (2018)","journal-title":"SIAM J. Comput."},{"key":"5_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/11761679_10","volume-title":"Advances in Cryptology - EUROCRYPT 2006","author":"F Armknecht","year":"2006","unstructured":"Armknecht, F., Carlet, C., Gaborit, P., K\u00fcnzli, S., Meier, W., Ruatta, O.: Efficient computation of algebraic immunity for algebraic and fast algebraic attacks. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 147\u2013164. Springer, Heidelberg (2006). https:\/\/doi.org\/10.1007\/11761679_10"},{"key":"5_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1007\/11596219_4","volume-title":"Progress in Cryptology - INDOCRYPT 2005","author":"A Braeken","year":"2005","unstructured":"Braeken, A., Preneel, B.: On the algebraic immunity of symmetric Boolean functions. In: Maitra, S., Veni Madhavan, C.E., Venkatesan, R. (eds.) INDOCRYPT 2005. LNCS, vol. 3797, pp. 35\u201348. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/11596219_4"},{"issue":"8","key":"5_CR6","doi-asserted-by":"publisher","first-page":"2791","DOI":"10.1109\/TIT.2005.851743","volume":"51","author":"A Canteaut","year":"2005","unstructured":"Canteaut, A., Videau, M.: Symmetric Boolean functions. IEEE Trans. Inf. Theor. 51(8), 2791\u20132811 (2005)","journal-title":"IEEE Trans. Inf. Theor."},{"issue":"9","key":"5_CR7","doi-asserted-by":"publisher","first-page":"2178","DOI":"10.1109\/TIT.2004.833361","volume":"50","author":"C Carlet","year":"2004","unstructured":"Carlet, C.: On the degree, nonlinearity, algebraic thickness, and nonnormality of Boolean functions, with developments on symmetric functions. IEEE Trans. Inf. Theor. 50(9), 2178\u20132185 (2004)","journal-title":"IEEE Trans. Inf. Theor."},{"key":"5_CR8","doi-asserted-by":"crossref","unstructured":"Carlet, C.: Boolean functions for cryptography and error-correcting codes. In: Encyclopedia of Mathematics and Its Applications, pp. 257\u2013397, Cambridge University Press (2010)","DOI":"10.1017\/CBO9780511780448.011"},{"key":"5_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1007\/978-3-540-89255-7_26","volume-title":"Advances in Cryptology - ASIACRYPT 2008","author":"C Carlet","year":"2008","unstructured":"Carlet, C., Feng, K.: An Infinite class of balanced functions with optimal algebraic immunity, good immunity to fast algebraic attacks and good nonlinearity. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 425\u2013440. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-89255-7_26"},{"key":"5_CR10","doi-asserted-by":"crossref","unstructured":"Carlet, C., M\u00e9aux, P.: Boolean functions for homomorphic-friendly stream ciphers (2019, to appear)","DOI":"10.1007\/978-3-030-36237-9_10"},{"key":"5_CR11","doi-asserted-by":"crossref","unstructured":"Chen, Y., Guo, F., Zhang, L.: Fast algebraic immunity of $$2^m+2$$ and $$2^m+3$$ variables majority function. Cryptology ePrint Archive, Report 2019\/286 (2019)","DOI":"10.1109\/ACCESS.2019.2923456"},{"key":"5_CR12","doi-asserted-by":"publisher","unstructured":"Climent, J.J., Garc\u00eda, F., Requena, V.: The degree of a Boolean function and some algebraic properties of its support. 45, 25\u201336 (2013). https:\/\/doi.org\/10.2495\/DATA130031","DOI":"10.2495\/DATA130031"},{"key":"5_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"176","DOI":"10.1007\/978-3-540-45146-4_11","volume-title":"Advances in Cryptology - CRYPTO 2003","author":"NT Courtois","year":"2003","unstructured":"Courtois, N.T.: Fast algebraic attacks on stream ciphers with linear feedback. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 176\u2013194. Springer, Heidelberg (2003). https:\/\/doi.org\/10.1007\/978-3-540-45146-4_11"},{"key":"5_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1007\/3-540-39200-9_21","volume-title":"Advances in Cryptology \u2014 EUROCRYPT 2003","author":"NT Courtois","year":"2003","unstructured":"Courtois, N.T., Meier, W.: Algebraic attacks on stream ciphers with linear feedback. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 345\u2013359. Springer, Heidelberg (2003). https:\/\/doi.org\/10.1007\/3-540-39200-9_21"},{"key":"5_CR15","unstructured":"Cusick, T.: Simpler proof for nonlinearity of majority function. arXiv:1710.02034v2 (2018)"},{"key":"5_CR16","unstructured":"Dalai, D.K.: Computing the rank of incidence matrix and the algebraic immunity of Boolean functions. Cryptology ePrint Archive, Report 2013\/273 (2013). http:\/\/eprint.iacr.org\/2013\/273"},{"key":"5_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1007\/11502760_7","volume-title":"Fast Software Encryption","author":"DK Dalai","year":"2005","unstructured":"Dalai, D.K., Gupta, K.C., Maitra, S.: Cryptographically significant Boolean functions: construction and analysis in terms of algebraic immunity. In: Gilbert, H., Handschuh, H. (eds.) FSE 2005. LNCS, vol. 3557, pp. 98\u2013111. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/11502760_7"},{"issue":"1","key":"5_CR18","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/s10623-005-6300-x","volume":"40","author":"DK Dalai","year":"2006","unstructured":"Dalai, D.K., Maitra, S., Sarkar, S.: Basic theory in construction of Boolean functions with maximum possible annihilator immunity. Des. Codes Crypt. 40(1), 41\u201358 (2006)","journal-title":"Des. Codes Crypt."},{"key":"5_CR19","unstructured":"Faug\u00e8re, J.C.: A new efficient algorithm for computing Grobner bases without reduction to zero. In: Workshop on application of Groebner Bases 2002, Catania, Spain (2002). https:\/\/hal.inria.fr\/inria-00100997"},{"key":"5_CR20","doi-asserted-by":"crossref","unstructured":"Gentry, C.: Fully homomorphic encryption using ideal lattices. In: Mitzenmacher, M. (ed.) 41st ACM STOC, pp. 169\u2013178. ACM Press, May\/June 2009","DOI":"10.1145\/1536414.1536440"},{"key":"5_CR21","doi-asserted-by":"crossref","unstructured":"Goldreich, O.: Candidate one-way functions based on expander graphs. Electron. Colloq. Comput. Complex. (ECCC) 7(90), 76\u201387 (2000)","DOI":"10.1007\/978-3-642-22670-0_10"},{"key":"5_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1007\/978-3-540-28628-8_24","volume-title":"Advances in Cryptology \u2013 CRYPTO 2004","author":"P Hawkes","year":"2004","unstructured":"Hawkes, P., Rose, G.G.: Rewriting variables: the complexity of fast algebraic attacks on stream ciphers. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 390\u2013406. Springer, Heidelberg (2004). https:\/\/doi.org\/10.1007\/978-3-540-28628-8_24"},{"key":"5_CR23","unstructured":"Hongjun, W.: A lightweight authenticated cipher (2016). https:\/\/competitions.cr.yp.to\/round3\/acornv3.pdf"},{"key":"5_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"630","DOI":"10.1007\/978-3-319-63688-7_21","volume-title":"Advances in Cryptology \u2013 CRYPTO 2017","author":"H Lin","year":"2017","unstructured":"Lin, H., Tessaro, S.: Indistinguishability obfuscation from trilinear maps and block-wise local PRGs. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10401, pp. 630\u2013660. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-63688-7_21"},{"key":"5_CR25","doi-asserted-by":"publisher","unstructured":"Lin, H., Vaikuntanathan, V.: Indistinguishability obfuscation from DDH-like assumptions on constant-degree graded encodings. In: Dinur, I. (ed.) 57th FOCS, pp. 11\u201320. IEEE Computer Society Press, October 2016. https:\/\/doi.org\/10.1109\/FOCS.2016.11","DOI":"10.1109\/FOCS.2016.11"},{"key":"5_CR26","doi-asserted-by":"publisher","unstructured":"Liu, M., Lin, D.: Almost perfect algebraic immune functions with good nonlinearity. In: 2014 IEEE International Symposium on Information Theory, pp. 1837\u20131841, June 2014. https:\/\/doi.org\/10.1109\/ISIT.2014.6875151","DOI":"10.1109\/ISIT.2014.6875151"},{"key":"5_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1007\/978-3-642-34961-4_12","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2012","author":"M Liu","year":"2012","unstructured":"Liu, M., Zhang, Y., Lin, D.: Perfect algebraic immune functions. In: Wang, X., Sako, K. (eds.) ASIACRYPT 2012. LNCS, vol. 7658, pp. 172\u2013189. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-34961-4_12"},{"key":"5_CR28","unstructured":"M\u00e9aux, P., Carlet, C., Journault, A., Standaert, F.X.: Improved filter permutators: combining symmetric encryption design, Boolean functions, low complexity cryptography, and homomorphic encryption, for private delegation of computations. Cryptology ePrint Archive, Report 2019\/483 (2019). https:\/\/eprint.iacr.org\/2019\/483"},{"key":"5_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/978-3-662-49890-3_13","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2016","author":"P M\u00e9aux","year":"2016","unstructured":"M\u00e9aux, P., Journault, A., Standaert, F.-X., Carlet, C.: Towards stream ciphers for efficient FHE with low-noise ciphertexts. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9665, pp. 311\u2013343. Springer, Heidelberg (2016). https:\/\/doi.org\/10.1007\/978-3-662-49890-3_13"},{"issue":"5","key":"5_CR30","doi-asserted-by":"publisher","first-page":"2406","DOI":"10.1109\/TIT.2009.2015999","volume":"55","author":"L Qu","year":"2009","unstructured":"Qu, L., Feng, K., Liu, F., Wang, L.: Constructing symmetric Boolean functions with maximum algebraic immunity. IEEE Trans. Inf. Theor. 55(5), 2406\u20132412 (2009)","journal-title":"IEEE Trans. Inf. Theor."},{"issue":"8","key":"5_CR31","doi-asserted-by":"publisher","first-page":"2908","DOI":"10.1109\/TIT.2007.901189","volume":"53","author":"L Qu","year":"2007","unstructured":"Qu, L., Li, C., Feng, K.: A note on symmetric Boolean functions with maximum algebraic immunity in odd number of variables. IEEE Trans. Inf. Theor. 53(8), 2908\u20132910 (2007)","journal-title":"IEEE Trans. Inf. Theor."},{"issue":"1","key":"5_CR32","first-page":"99","volume":"46","author":"PR Geffe","year":"1973","unstructured":"Geffe, P.R.: How to protect data with ciphers that are really hard to break. Electronics 46(1), 99\u2013101 (1973)","journal-title":"Electronics"},{"issue":"19\u201320","key":"5_CR33","doi-asserted-by":"publisher","first-page":"2351","DOI":"10.1016\/j.disc.2006.08.008","volume":"307","author":"P Sarkar","year":"2007","unstructured":"Sarkar, P., Maitra, S.: Balancedness and correlation immunity of symmetric Boolean functions. Discrete Math. 307(19\u201320), 2351\u20132358 (2007)","journal-title":"Discrete Math."},{"key":"5_CR34","doi-asserted-by":"publisher","unstructured":"Tang, D., Carlet, C., Tang, X., Zhou, Z.: Construction of highly nonlinear 1-resilient Boolean functions with optimal algebraic immunity and provably high fast algebraic immunity. IEEE Trans. Inf. Theor. 63(9), 6113\u20136125 (2017). https:\/\/doi.org\/10.1109\/TIT.2017.2725918","DOI":"10.1109\/TIT.2017.2725918"},{"issue":"1","key":"5_CR35","doi-asserted-by":"publisher","first-page":"653","DOI":"10.1109\/TIT.2012.2217476","volume":"59","author":"Deng Tang","year":"2013","unstructured":"Tang, D., Carlet, C., Tang, X.: Highly nonlinear Boolean functions with optimal algebraic immunity and good behavior against fast algebraic attacks. IEEE Trans. Inf. Theor. 63(9), 653\u2013664 (2013). https:\/\/doi.org\/10.1109\/TIT.2012.2217476","journal-title":"IEEE Transactions on Information Theory"},{"issue":"11","key":"5_CR36","doi-asserted-by":"publisher","first-page":"2084","DOI":"10.1587\/transfun.E99.A.2084","volume":"99","author":"D Tang","year":"2016","unstructured":"Tang, D., Luo, R., Du, X.: The exact fast algebraic immunity of two subclasses of the majority function. IEICE Trans. 99(11), 2084\u20132088 (2016)","journal-title":"IEICE Trans."}],"container-title":["Lecture Notes in Computer Science","Progress in Cryptology \u2013 LATINCRYPT 2019"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-30530-7_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,23]],"date-time":"2024-07-23T00:02:34Z","timestamp":1721692954000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-30530-7_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019]]},"ISBN":["9783030305291","9783030305307"],"references-count":36,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-30530-7_5","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2019]]},"assertion":[{"value":"9 September 2019","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"LATINCRYPT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Cryptology and Information Security in Latin America","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Santiago de Chile","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Chile","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2019","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2 October 2019","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"4 October 2019","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"6","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"latincrypt2019","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/latincrypt2019.cryptojedi.org\/index.shtml","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Double-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"WebSubRev","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"40","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"18","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"45% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.35","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.35","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}