Abstract: Signature monitoring is an effective technique to detect the control flow errors. Different signature functions cause significantly different overheads in memory and processor performance. In order to reduce the overhead, a new signature function is presented for the detection of control flow errors in this paper. This signature function is defined in Galois field （GF）. An algorithm is presented to assign state codes and compute state signatures. The assignment of values to the states is carried out by matrix inversion instead of using exhaustive search methods. In this algorithm, the computation of the signature requires only one addition operation and one multiplication operation at each transition of states. This signature function can be implemented as one dimensional table while the previous signature function needs to be implemented as two dimensional table. So this signature function allows lower overhead than the previous signatures. A method is also presented to further reduce the overhead caused by this signature function while guaranteeing a given delay for control flow error detection. This signature function can be efficiently implemented in both hardware and software.