The invention relates to a method and multiplier for multiplying two factors from the Galois field GF (2m*p), where each of the factors can be represented as a vector of p sub-blocks with a width of m bits and p, m are positive integers greater than 1. The method and multiplier allow for a polynomial multiplication to be performed quickly and efficiently with minimum requirements in respect of for storage space. Therefore, savings can thus be achieved in respect of power consumption, crystal surface and calculation time.