How Does the Curve Equation Define the Possible Points for the Key Pair? ⎊ Path

How Does the Curve Equation Define the Possible Points for the Key Pair?

The elliptic curve equation, such as y2 = x3 + ax + b (mod p), defines the set of all valid points (x, y) that lie on the curve over a finite field (p). All public keys and the generator point must satisfy this equation.

The private key is a scalar, but the public key is a point on the curve. The equation establishes the mathematical space in which all ECDSA operations take place, ensuring consistency and cryptographic properties.

What Is the Relationship between a Public Key and a Private Key in ECDSA?

How Does the Order of the Base Point Relate to the Private Key Space?

What Is the ‘R’ Value in an ECDSA Signature and How Is It Derived from ‘K’?

What Is the Discrete Logarithm Problem?

What Is the ‘Base Point’ in the Context of Elliptic Curve Cryptography?

How Does the Size of the Nonce Field Affect the Mining Process?

How Does Elliptic Curve Cryptography Secure Private Keys?

Explain the Relationship between a Private Key, Public Key, and Wallet Address