New construction of Boolean functions which satisfy multiple cryptographic criteria

To resist various attacks, a Boolean function used in symmetric cipher systems should satisfy multiple cryptographic criteria. In this paper, a new generalized construction method for Boolean functions which satisfy multiple cryptographic criteria is provided. These multiple cryptographic criteria include balanced, high nonlinearity, high algebraic degree, propagation criterion of order l (PC(l)) and nonexistence of nonzero linear structures. The construction is based on the use of linear error-correcting code. Given a linear code and its dual code, we show that it is possible to obtain these cryptographic functions.