user134226: Let's first define a valid Bitcoin private key as a number in the range of [1, 115792089237316195423570985008687907852837564279074904382605163141518161494336], and a valid Bitcoin public key as a public key derived from a valid Bitcoin private key.
Then my question is: Is there a way to determine whether a specific point on the secp256k1 curve is a valid Bitcoin public key?

user208: The secp256k1 curve has cofactor one, so every point on the curve can be written as a multiple of the generator. As a result, there are exactly as many points on the curve (excluding the point at infinity) as there are valid (nonzero) private keys.
In short: yes, every point on the curve is a valid public key.

134226: <p>Let's first define a <code>valid Bitcoin private key</code> as a number in the range of [1, 115792089237316195423570985008687907852837564279074904382605163141518161494336], and a <code>valid Bitcoin public key</code> as a public key derived from a valid Bitcoin private key.</p>
<p>Then my question is: Is there a way to determine whether a specific point on the secp256k1 curve is a valid Bitcoin public key?</p>
 208: <p>The secp256k1 curve has cofactor one, so every point on the curve can be written as a multiple of the generator. As a result, there are exactly as many points on the curve (excluding the point at infinity) as there are valid (nonzero) private keys.</p>
<p>In short: yes, every point on the curve is a valid public key.</p>
