The elliptic curves algorithm is based on the discrete logarithm problem discussed earlier but in the context of elliptic curves.
An elliptic curve is an algebraic cubic curve over a field, which can be defined by the following equation.
Smaller Keys, Stronger Security
The curve is non-singular, which means that it has no cusps or self-intersections.
It has two variables a and b, as well as a point of infinity.
Here, a and b are integers whose values are elements of the field on which the elliptic curve is defined.
Elliptic curves can be defined over real numbers, rational numbers, complex numbers, or finite fields.
For cryptographic purposes, an elliptic curve over prime finite fields is used instead of real numbers.
Different curves can be generated by varying the value of a and/or b.
Why This Matters for Blockchain Technology
The most prominently used cryptosystems based on elliptic curves are the Elliptic Curve Digital Signature Algorithm (ECDSA) and the Elliptic Curve Diffie-Hellman (ECDH) key exchange.
To understand public key cryptography, the key concept that needs to be explored is the concept of public and private keys.
Key Points to Remember
- Elliptic curves The elliptic curves algorithm is based on the discrete logarithm problem discussed earlier but in the context of elliptic curves.
- An elliptic curve is an algebraic cubic curve over a field, which can be defined by the following equation.
- The curve is non-singular, which means that it has no cusps or self-intersections.
- It has two variables a and b, as well as a point of infinity.
Conclusion
Elliptic curves 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.