17.10 APPLICATIONS OF FINITE FIELD MULTIPLIERS
The finite field multipliers we developed in the previous sections can be used to an advantage in cryptography. For example, elliptic curve encryption techniques require the following finite field operations:
1. Addition, which is simply performed by a bank of XOR gates;.
2. Multiplication, which was discussed before.
3. Squaring is a special case of multiplication.
(17.41)
Specialized and fast hardware structures for field squaring were developed by the author’s research group [111].
4. Inversion method based on Fermat’s theorem requires m − 1 squaring operations and m − 2 multiplication operations [112]. Performance can be improved by using the method proposed by Itoh and Tsujii [112].