A testable implementation of bit parallel multiplier over the finite field GF(2m) is proposed. A function independent test set of length (2m+4), which detects all the single stuck-at faults in an m bit GF(2m) multiplier circuit, is also presented. Test set can be determined readily from the corresponding algebraic forms without running an ATPG tool. The test complexity is lower than ATPG generated or algorithmic test set. The test set provides 100 percent single stuck-at fault coverage. The gate counts of the proposed testable multiplier as a function of degree m has been analyzed. The testable circuit realization requires only two extra inputs for controllability and some additional EX ns and need field testing, built-in self-test (BIST) circuit may be used to generate test pattern internally for detecting faults in the multiplier circuits