Polynomial basis multipliers which are widely applied in public-key cryptosystems such as elliptic curve cryptosystem are suitable to be FPGA (Field Programmable Gate Array) and VLSI (Very Large Scale Integrated circuit) implementations due to their regularity and modularity properties. On-line error detection capability can provide a countermeasure to recently developed fault-based cryptanalysis. A novel polynomial basis multiplier using self-checking alternating logic (SCAL) method is developed. The proposed polynomial basis multiplier can provide both on-line error detection and off-line testability capabilities. Our proposed multiplier requires only one-third of the extra space complexity that existing multipliers require. Our proposed SCAL polynomial basis multiplier is the first polynomial basis multiplier over GF(2m) with both online error detection and off-line testability capabilities.