Detecting errors in a polynomial basis multiplier using multiple parity bits for both inputs

This paper investigates the concurrent detection of multiple-bit errors in polynomial basis (PB) multipliers over binary extension fields. To this end, multiple parity bits are considered for both inputs of the multiplier. For the multiplier architecture considered here, the two inputs go through considerably different sets of circuits and this allows us to use different number of parity bits with the inputs. In a bit-parallel implementation of a GF(2¹⁶³) PB multiplier with eight parity bits for the first input and three parity bits for the second input, the area overhead and the probability of error detection are approximately 55.59% and 0.997, respectively. Additionally, the average time overhead of the scheme implemented in a bit-parallel fashion is approximately 25%.