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) c17e041

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].

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