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

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.

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