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.
How Identity and Authenticity Are Verified (Part 2)
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.
It should be ensured that K is truly random and e e e that no two signatures have the same key; otherwise, the private key can be calculated.
Another value R is calculated using R = K A; that is, by multiplying A (the generator point) and the random ephemeral key.
Initialize a variable r with the x coordinate value of point R so that r = xR.
The signature can be calculated as follows: Here, m is the message for which the signature is being computed, and h(m) is the hash of the message m.
Signature verification is carried out by following this process: 1.
Why This Matters for Blockchain Technology
Verification is carried out as follows: r, s is accepted as a valid signature if the x coordinate of point P calculated in step 4 has the same value as the signature parameter r mod q; that is: Xp = r mod q means valid signature Xp != r mod q means invalid signature Various practical examples are shown in the following subsections, which demonstrate how the RSA digital signature can be generated, used, and verified using OpenSSL.
Key Points to Remember
- 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.
- 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.
- It should be ensured that K is truly random and e e e that no two signatures have the same key; otherwise, the private key can be calculated.
Conclusion
Elliptic Curve Digital Signature represents one of the many innovative layers that make blockchain technology so powerful and transformative. As distributed systems continue to evolve, a solid understanding of these core concepts becomes increasingly valuable — not just for developers, but for anyone building, investing in, or working alongside blockchain-powered systems.
Whether you are just starting your blockchain journey or deepening existing expertise, mastering these fundamentals gives you the tools to think clearly about decentralized systems and make smarter decisions in this rapidly evolving space.