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On an improved correlation analysis of stream ciphers using multioutput Boolean functions and the related generalized notion of nonlinearity
1.  Université Paris 8, Département de mathématiques, 2, rue de la Liberté, 93526  SAINTDENIS cedex 02, France 
2.  DSO National Laboratories, 20 Science Park Drive S118230, Singapore, Singapore, Singapore 
[1] 
Qian Liu. The lower bounds on the secondorder nonlinearity of three classes of Boolean functions. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2020136 
[2] 
Claude Carlet. Parameterization of Boolean functions by vectorial functions and associated constructions. Advances in Mathematics of Communications, 2022 doi: 10.3934/amc.2022013 
[3] 
Jian Liu, Sihem Mesnager, Lusheng Chen. Variation on correlation immune Boolean and vectorial functions. Advances in Mathematics of Communications, 2016, 10 (4) : 895919. doi: 10.3934/amc.2016048 
[4] 
Sugata Gangopadhyay, Constanza Riera, Pantelimon Stănică. Gowers $ U_2 $ norm as a measure of nonlinearity for Boolean functions and their generalizations. Advances in Mathematics of Communications, 2021, 15 (2) : 241256. doi: 10.3934/amc.2020056 
[5] 
SelÇuk Kavut, Seher Tutdere. Highly nonlinear (vectorial) Boolean functions that are symmetric under some permutations. Advances in Mathematics of Communications, 2020, 14 (1) : 127136. doi: 10.3934/amc.2020010 
[6] 
Sugata Gangopadhyay, Goutam Paul, Nishant Sinha, Pantelimon Stǎnicǎ. Generalized nonlinearity of $ S$boxes. Advances in Mathematics of Communications, 2018, 12 (1) : 115122. doi: 10.3934/amc.2018007 
[7] 
Jundong Wang, Lijun Zhang, Elena Shchepakina, Vladimir Sobolev. Solitary waves of singularly perturbed generalized KdV equation with high order nonlinearity. Discrete and Continuous Dynamical Systems  S, 2022 doi: 10.3934/dcdss.2022124 
[8] 
Constanza Riera, Pantelimon Stănică. Landscape Boolean functions. Advances in Mathematics of Communications, 2019, 13 (4) : 613627. doi: 10.3934/amc.2019038 
[9] 
Yang Yang, Xiaohu Tang, Guang Gong. Even periodic and odd periodic complementary sequence pairs from generalized Boolean functions. Advances in Mathematics of Communications, 2013, 7 (2) : 113125. doi: 10.3934/amc.2013.7.113 
[10] 
Junchao Zhou, Yunge Xu, Lisha Wang, Nian Li. Nearly optimal codebooks from generalized Boolean bent functions over $ \mathbb{Z}_{4} $. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020121 
[11] 
Sihem Mesnager, Gérard Cohen. Fast algebraic immunity of Boolean functions. Advances in Mathematics of Communications, 2017, 11 (2) : 373377. doi: 10.3934/amc.2017031 
[12] 
Claude Carlet, Serge Feukoua. Three basic questions on Boolean functions. Advances in Mathematics of Communications, 2017, 11 (4) : 837855. doi: 10.3934/amc.2017061 
[13] 
Bimal Mandal, Aditi Kar Gangopadhyay. A note on generalization of bent boolean functions. Advances in Mathematics of Communications, 2021, 15 (2) : 329346. doi: 10.3934/amc.2020069 
[14] 
Kyril Tintarev. Is the TrudingerMoser nonlinearity a true critical nonlinearity?. Conference Publications, 2011, 2011 (Special) : 13781384. doi: 10.3934/proc.2011.2011.1378 
[15] 
Xingxing Liu, Zhijun Qiao, Zhaoyang Yin. On the Cauchy problem for a generalized CamassaHolm equation with both quadratic and cubic nonlinearity. Communications on Pure and Applied Analysis, 2014, 13 (3) : 12831304. doi: 10.3934/cpaa.2014.13.1283 
[16] 
Rui Zhang, Sihong Su. A new construction of weightwise perfectly balanced Boolean functions. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021020 
[17] 
Makram Hamouda, Mohamed Ali Hamza, Alessandro Palmieri. A note on the nonexistence of global solutions to the semilinear wave equation with nonlinearity of derivativetype in the generalized Einsteinde Sitter spacetime. Communications on Pure and Applied Analysis, 2021, 20 (11) : 37033721. doi: 10.3934/cpaa.2021127 
[18] 
QHeung Choi, Tacksun Jung. A nonlinear wave equation with jumping nonlinearity. Discrete and Continuous Dynamical Systems, 2000, 6 (4) : 797802. doi: 10.3934/dcds.2000.6.797 
[19] 
Yingshu Lü, Chunqin Zhou. Symmetry for an integral system with general nonlinearity. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 15331543. doi: 10.3934/dcds.2018121 
[20] 
Eugenia N. Petropoulou. On some difference equations with exponential nonlinearity. Discrete and Continuous Dynamical Systems  B, 2017, 22 (7) : 25872594. doi: 10.3934/dcdsb.2017098 
2020 Impact Factor: 0.935
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