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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 
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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 
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Sugata Gangopadhyay, Constanza Riera, Pantelimon Stăniă. Gowers $ U_2 $ norm as a measure of nonlinearity for Boolean functions and their generalizations. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020056 
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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 
[4] 
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 
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Constanza Riera, Pantelimon Stănică. Landscape Boolean functions. Advances in Mathematics of Communications, 2019, 13 (4) : 613627. doi: 10.3934/amc.2019038 
[6] 
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 
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Claude Carlet, Serge Feukoua. Three basic questions on Boolean functions. Advances in Mathematics of Communications, 2017, 11 (4) : 837855. doi: 10.3934/amc.2017061 
[8] 
Sihem Mesnager, Gérard Cohen. Fast algebraic immunity of Boolean functions. Advances in Mathematics of Communications, 2017, 11 (2) : 373377. doi: 10.3934/amc.2017031 
[9] 
Bimal Mandal, Aditi Kar Gangopadhyay. A note on generalization of bent boolean functions. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020069 
[10] 
Kyril Tintarev. Is the TrudingerMoser nonlinearity a true critical nonlinearity?. Conference Publications, 2011, 2011 (Special) : 13781384. doi: 10.3934/proc.2011.2011.1378 
[11] 
Xingxing Liu, Zhijun Qiao, Zhaoyang Yin. On the Cauchy problem for a generalized CamassaHolm equation with both quadratic and cubic nonlinearity. Communications on Pure & Applied Analysis, 2014, 13 (3) : 12831304. doi: 10.3934/cpaa.2014.13.1283 
[12] 
QHeung Choi, Tacksun Jung. A nonlinear wave equation with jumping nonlinearity. Discrete & Continuous Dynamical Systems  A, 2000, 6 (4) : 797802. doi: 10.3934/dcds.2000.6.797 
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Yingshu Lü, Chunqin Zhou. Symmetry for an integral system with general nonlinearity. Discrete & Continuous Dynamical Systems  A, 2019, 39 (3) : 15331543. doi: 10.3934/dcds.2018121 
[14] 
Eugenia N. Petropoulou. On some difference equations with exponential nonlinearity. Discrete & Continuous Dynamical Systems  B, 2017, 22 (7) : 25872594. doi: 10.3934/dcdsb.2017098 
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[16] 
Claude Carlet, Serge Feukoua. Three parameters of Boolean functions related to their constancy on affine spaces. Advances in Mathematics of Communications, 2019 doi: 10.3934/amc.2020036 
[17] 
Yu Zhou. On the distribution of autocorrelation value of balanced Boolean functions. Advances in Mathematics of Communications, 2013, 7 (3) : 335347. doi: 10.3934/amc.2013.7.335 
[18] 
Tingting Pang, Nian Li, Li Zhang, Xiangyong Zeng. Several new classes of (balanced) Boolean functions with few Walsh transform values. Advances in Mathematics of Communications, 2020 doi: 10.3934/amc.2020095 
[19] 
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[20] 
Jong Uhn Kim. On the stochastic Burgers equation with a polynomial nonlinearity in the real line. Discrete & Continuous Dynamical Systems  B, 2006, 6 (4) : 835866. doi: 10.3934/dcdsb.2006.6.835 
2019 Impact Factor: 0.734
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