Mastering Blockchain - Second Edition

Elliptic Curve Digital Signature Algorithm

In order to sign and verify using the ECDSA scheme, first key pair needs to be generated:

1. First, define an elliptic curve E:

• • With modulus P
  • Coefficients a and b
  • Generator point A that forms a cyclic group of prime order q

2. An integer d is chosen randomly so that 0 < d < q.
3. Calculate public key B so that B = d A.

The public key is the sextuple in the form shown here:

Kpb = (p,a,b,q,A,B)

The private key, d is randomly chosen in step 2:

Kpr = d

Now the signature can be generated using the private and public key.

4. First, an ephemeral key K_e is chosen, where 0 < K_e < q. It should be ensured that K_e is truly random and that no two signatures have the same key; otherwise, the private key can be ...