Abstract: A new spectrum of Boolean function was presented by monomial trace function instead of linear function. The new spectrum was called as d Walsh cyclic spectrum. Trace function monomials best approximation of Boolean function was investigated and found by computing d Walsh cyclic spectrum and the computational complexity was just  2²ⁿ /n. By monomial trace function approximating the feedforward function of stream cipher, it is possible to commit a decimation attack on stream cipher, which may have important implications for cipher design and analysis.