Tu, Z. and Deng, Y. (2010) A conjecture about binary strings and its applications on constructing Boolean functions with optimal algebraic immunity. Designs, Codes and Cryptography, 1-14.
T-D猜想上多输出布尔函数构造Construction of Vectorial Boolean Function Based on T-D Conjecture
多输出布尔函数, 代数免疫度, Bent函数, 平衡性, 非线性度Vectorial Boolean Functions, Algebraic Immunity, Bent Function, Balancedness, Nonlinearity
《Advances in Applied Mathematics》, Vol.3 No.2, 2014-05-16
An improvement has been made on the construction method of Boolean Functions and the relevant conclusions of combinatorial conjecture proposed by Ziran Tu. We generalized their results and extended to the vectorial case. A class of bent Boolean functions F with the maximum algebraic immunity is presented by a more general construction method. Then by modifying F, we get new vectorial balanced functions with optimum algebraic degree, good nonlinearity and good algebraic immunity even maximum algebraic immunity for some cases.