G is a basepoint on a curve.
Alice picks a key; d_{A} and a corresponding pub key; Q_{A} = d_{A} * G

Calculate e = HASH(m), where HASH is a cryptographic hash function, such as SHA-2.
Let z be the L_{n} leftmost bits of e, where L_{n} is the bit length of the group order n.
Select a cryptographically secure random integer k from [1,n-1].
Calculate the curve point (x_1, y_1) = k * G.
Calculate r = x_1 mod n. If r = 0, go back to step 3.
Calculate  s=k^-1(z+rd_{A}) mod n. If s=0, go back to step 3.
The signature is the pair (r,s).