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This work develops a novel self-checking alternating logic (SCAL) bit-parallel Gaussian normal basis (GNB) multiplier with type-t over GF(2m). The proposed GNB multiplier is with both concurrent error-detection and off-line testing capabilities. The concurrent error-detection capability can give countermeasure to fault-based cryptanalysis. The off-line testing capability supports the design-for-test property. The proposed SCAL GNB multiplier can detect both permanent and transient faults. The proposed SCAL GNB is the first normal basis multiplier to have both on-line error-detection and off-line testing capabilities.