How Is the Specific Base Point for a Curve like Secp256k1 Chosen?
The base point (G) for a standardized curve like secp256k1 is not chosen arbitrarily but is part of the publicly defined parameters for that curve. It is selected to be a point on the curve that generates a subgroup of a very large prime order (n).
The specific coordinates of G are derived from a set of deterministic, verifiable procedures to ensure there are no backdoors or weaknesses. The choice is made to maximize the difficulty of solving the elliptic curve discrete logarithm problem.
Glossar
Order of the Base Point
Order ⎊ The order of the base point, denoted as $n$, is the smallest positive integer such that when the base point $G$ is added to itself $n$ times, the result is the point at infinity, the identity element of the elliptic curve group.
Base Point
Origin ⎊ A base point, within cryptocurrency and derivative markets, establishes a reference value against which subsequent price movements are measured; its initial determination is critical for accurate valuation and risk assessment.
Secp256k1
Cryptography ⎊ The Secp256k1 curve, a specific instance of elliptic curve cryptography, underpins the security of numerous cryptocurrency systems, notably Bitcoin.
Elliptic Curve Discrete Logarithm
Foundation ⎊ The presumed intractability of solving this problem over finite fields forms the bedrock of public-key cryptography utilized in digital signatures for asset control.
Point on the Curve
Calibration ⎊ A point on the curve, within cryptocurrency derivatives, represents a specific input value used to determine the theoretical price of an option or other derivative contract, reflecting market consensus on future volatility and underlying asset price movements.