Constructing odd Variable Boolean Functions with Optimal Algebraic Immunity

Based on Carlet-Feng functions, we present a method to construct odd variable Boolean functions with optimal algebraic immunity in this paper. The proposed functions can have the highest algebraic ...

[1]  Yingpu Deng,et al.  A conjecture about binary strings and its applications on constructing Boolean functions with optimal algebraic immunity , 2011, Des. Codes Cryptogr..

[2]  Nicolas Courtois Fast Algebraic Attacks on Stream Ciphers with Linear Feedback , 2003, CRYPTO.

[3]  Yuan Li,et al.  A Note on "On the Construction of Boolean Functions with Optimal Algebraic Immunity" , 2008, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[4]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .

[5]  H. Niederreiter,et al.  Finite Fields: Encyclopedia of Mathematics and Its Applications. , 1997 .

[6]  Lei Hu,et al.  More Balanced Boolean Functions With Optimal Algebraic Immunity and Good Nonlinearity and Resistance to Fast Algebraic Attacks , 2011, IEEE Transactions on Information Theory.

[7]  Lei Hu,et al.  Further properties of several classes of Boolean functions with optimum algebraic immunity , 2009, Des. Codes Cryptogr..

[8]  Claude Carlet,et al.  Algebraic Attacks and Decomposition of Boolean Functions , 2004, EUROCRYPT.

[9]  Subhamoy Maitra,et al.  Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity , 2006, Des. Codes Cryptogr..

[10]  Frederik Armknecht,et al.  Improving Fast Algebraic Attacks , 2004, FSE.

[11]  Claude Carlet,et al.  Algebraic immunity for cryptographically significant Boolean functions: analysis and construction , 2006, IEEE Transactions on Information Theory.

[12]  Wen-Feng Qi,et al.  Construction and Analysis of Boolean Functions of 2t+1 Variables with Maximum Algebraic Immunity , 2006, ASIACRYPT.

[13]  O. S. Rothaus,et al.  On "Bent" Functions , 1976, J. Comb. Theory, Ser. A.

[14]  Rudolf Lide,et al.  Finite fields , 1983 .

[15]  J. Dillon Elementary Hadamard Difference Sets , 1974 .

[16]  Claude Carlet,et al.  An Infinite Class of Balanced Functions with Optimal Algebraic Immunity, Good Immunity to Fast Algebraic Attacks and Good Nonlinearity , 2008, ASIACRYPT.