Calculation of non-linearity and algebraic degree of constructed boolean function

In cryptography systems, to resist algebraic and fast algebraic attack (FAA), Boolean functionwould have high value of nonlinearity, high value of algebraic degree and large algebraic immunity (AIm(f)). We have calculated the nonlinearity ( nl(f)) of the constructed Boolean functionand proved the lower bound on nonlinearity, which are identical to best lower bound of known Boolean functionto resist linear, correlation and fast algebraic attacks. We have also calculated algebraic degree (Ad(f)) of constructed Boolean functionand its value is equal to Ad(f) of well known Boolean function. In this paper, definition of balancedness, nl(f), Ad(f) and AIm(f) are also defined in preliminaries.