user131513: I am reading about ECDSA, and I find that the private key must be in (0,n), with n = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141.
Is n the total number of points on the secp256k1 curve? (plus the 0 point)
And how does n limit the range of private keys?
What if a private key is bigger than n?

user208: n is the number of points on the curve (including the point at infinity). Private keys are numbers between 1 and n-1, inclusive. 0 is not a valid private key, because its corresponding point would be the point at infinity.
If you'd naively try to compute the public key corresponding to private key d and private key d+n, you'd obtain the same public keys. That means the public key for private key n would also be infinity (same as for private key 0).
For this reason, private keys are restricted to range 1 to n-1: that guarantees that for every non-infinity point on the curve there is exactly one private key.

131513: <p>I am reading about <a href="https://en.bitcoin.it/wiki/Secp256k1#:%7E:text=n%20%3D%20FFFFFFFF%20FFFFFFFF%20FFFFFFFF%20FFFFFFFE%20BAAEDCE6%20AF48A03B%20BFD25E8C%20D0364141" rel="nofollow noreferrer">ECDSA</a>, and I find that the private key must be in <code>(0,n)</code>, with <code>n = FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141</code>.</p>
<p>Is <code>n</code> the total number of points on the secp256k1 curve? (plus the 0 point)</p>
<p>And how does <code>n</code> limit the range of private keys?</p>
<p>What if a private key is bigger than <code>n</code>?</p>
 208: <p>n is the number of points on the curve (including the point at infinity). Private keys are numbers between 1 and n-1, inclusive. 0 is not a valid private key, because its corresponding point would be the point at infinity.</p>
<p>If you'd naively try to compute the public key corresponding to private key d and private key d+n, you'd obtain the same public keys. That means the public key for private key n would also be infinity (same as for private key 0).</p>
<p>For this reason, private keys are restricted to range 1 to n-1: that guarantees that for every non-infinity point on the curve there is exactly one private key.</p>
