7. Discussion

Building tables for Zech's logarithm requires a lot of space and time at least proportional to the size of corresponding field. In theory of coding such algorithms are called exponential, since order of magnitudes are compared with the degree of the field, as a measure of the length of elementary messages.

Thus these tables are not an «immediate» tool for code breaking, and related problems. But allowing fast calculus in some subfields is ever welcome, and can be a piece of some more sophisticated attack.

Let us discuss maximal field size that can be attained. Storing in internal memory some table of natural integers is easy up to some mega-octets, leading to . With the Huber's method, a space/time bargain can be done with factor . Thus, only are requested for and for .

For multiplications, divisions or exponentiations in , a storage capacity of will be requested, with storage accesses in the average case, or a capacity of with accesses. It i clear that, at the present moment, such a field's size is rather beyond the limits of general purpose hardware. For comparison, a VLSI processor specially designed for computing in [1], enables multiplications and inversions in, respectively, 4 and 70 s.