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David · Accepted Answer

1. Galois field GF (p). We can define Elliptic curve over GF (p) for p > 3 as
following:
Let GF (p) be finite field and there are constants a, b ∈ GF (p) such that
4a3 + 27b2 ≡ 0(modp)
Now elliptic curve is defined as the trace of y2 = x3 + ax + b on GF (p),
together with a special point O, point at infinity. Similarly we can define
elliptic curve over GF (2m) for some m ≥ 1.

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