Finite field division implementation

A generalized version of the plus-minus algorithm is used for implementing dividers over GF(p/sup n/). Generic dividers have been synthesized in the general case of GF(p/sup n/) and in the particular cases of GF(2/sup n/) and GF(p). The theoretical costs are O(logN) being N the number of field elements, and the theoretical computation times are O(logN) in the case of dividers over GF(p/sup n/) and GF(2/sup n/), and O((logN)/sup 2/) in the case of dividers over GF(p). Finally, the results of FPGA implementations are reported, and a comparison is made between dividers over GF(p), GF(2/sup n/) and GF(p/sup n/).