user139993: I'm reading the spending section of BIP47:

Alice calculates a scalar shared secret using the x value of S:
s = SHA256(Sx).
If the value of s is not in the secp256k1 group, Alice MUST increment the index used to derive Bob's public key and try again.

Where S is a point on the elliptic curve and s is an integer to be used as a private key in subsequent sections.
My question is

What does it mean for the integer s to be in a group of points?


user208: I believe it simply means: if s, when interpreted as an integer, is larger or equal to the curve order, one needs to restart and increment. The probability for this happening is negligible, as the curve order for secp256k1 is very close to 2256.

139993: <p>I'm reading <a href="https://github.com/bitcoin/bips/blob/master/bip-0047.mediawiki#sending" rel="nofollow noreferrer">the spending section of BIP47</a>:</p>
<blockquote>
<p>Alice calculates a scalar shared secret using the x value of S:
s = SHA256(Sx).
If the value of s is not in the secp256k1 group, Alice MUST increment the index used to derive Bob's public key and try again.</p>
</blockquote>
<p>Where <code>S</code> is a <strong>point</strong> on the elliptic curve and <code>s</code> is an <strong>integer</strong> to be used as a private key in subsequent sections.</p>
<p>My question is</p>
<ul>
<li>What does it mean for the <strong>integer</strong> <code>s</code> to be <strong>in a group of points</strong>?</li>
</ul>
 208: <p>I believe it simply means: if <code>s</code>, when interpreted as an integer, is larger or equal to the curve order, one needs to restart and increment. The probability for this happening is negligible, as the curve order for secp256k1 is very close to 2<sup>256</sup>.</p>
