user26602: Take a bitcoin public key (x, y) and its additive inverse (x, -y). How do you identify which is the positive point and which is the negative point?
Example
Private key 1 -> (x, y)
x =  0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798L
y =  0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8L
-y =  0xb7c52588d95c3b9aa25b0403f1eef75702e84bb7597aabe663b82f6f04ef2777L
Private key 2 -> (x, y)
x =  0xc6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee5L
y =  0x1ae168fea63dc339a3c58419466ceaeef7f632653266d0e1236431a950cfe52aL
-y =  0xe51e970159c23cc65c3a7be6b99315110809cd9acd992f1edc9bce55af301705L
Private key 3 -> (x, y)
x =  0xf9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9L
y =  0x388f7b0f632de8140fe337e62a37f3566500a99934c2231b6cb9fd7584b8e672L
-y =  0xc77084f09cd217ebf01cc819d5c80ca99aff5666cb3ddce4934602897b4715bdL

Also, how can you identify which pub key is odd and which is even?
ex: private key 1 x,y is odd , private key 2 x,y is even

user18196: There is no concrete determination that makes one 'y' value negative or not in an EC point. Feel free to make your own convention, like y-values <= than half of p are negative, and > half of p are positive. That's just a convention, though.
Related:

What does the curve used in Bitcoin, secp256k1, look like?



Also, how can you identify which pub key is odd and which is even?
ex: private key 1 x,y is odd , private key 2 x,y is even

You can't! Not without knowing the private key itself. If you could, you would be part of the way towards solving the discrete log problem.

26602: <p>Take a bitcoin public key (x, y) and its additive inverse (x, -y). How do you identify which is the positive point and which is the negative point?</p>

<p><strong>Example</strong></p>

<p><strong>Private key 1 -> (x, y)</strong></p>

<p>x =  0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798L</p>

<p>y =  0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8L</p>

<p>-y =  0xb7c52588d95c3b9aa25b0403f1eef75702e84bb7597aabe663b82f6f04ef2777L</p>

<p><strong>Private key 2 -> (x, y)</strong></p>

<p>x =  0xc6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee5L</p>

<p>y =  0x1ae168fea63dc339a3c58419466ceaeef7f632653266d0e1236431a950cfe52aL</p>

<p>-y =  0xe51e970159c23cc65c3a7be6b99315110809cd9acd992f1edc9bce55af301705L</p>

<p><strong>Private key 3 -> (x, y)</strong></p>

<p>x =  0xf9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9L</p>

<p>y =  0x388f7b0f632de8140fe337e62a37f3566500a99934c2231b6cb9fd7584b8e672L</p>

<p>-y =  0xc77084f09cd217ebf01cc819d5c80ca99aff5666cb3ddce4934602897b4715bdL</p>

<hr>

<p>Also, how can you identify which pub key is odd and which is even?</p>

<p>ex: private key 1 x,y is odd , private key 2 x,y is even</p>
 18196: <p>There is no concrete determination that makes one 'y' value negative or not in an EC point. Feel free to make your own convention, like y-values &lt;= than half of p are negative, and &gt; half of p are positive. That's just a convention, though.</p>
<p>Related:</p>
<ul>
<li><a href="https://bitcoin.stackexchange.com/questions/21907/what-does-the-curve-used-in-bitcoin-secp256k1-look-like">What does the curve used in Bitcoin, secp256k1, look like?</a></li>
</ul>
<hr>
<blockquote>
<p>Also, how can you identify which pub key is odd and which is even?</p>
<p>ex: private key 1 x,y is odd , private key 2 x,y is even</p>
</blockquote>
<p>You can't! Not without knowing the private key itself. If you could, you would be part of the way towards solving the <a href="https://en.wikipedia.org/wiki/Discrete_logarithm" rel="noreferrer">discrete log problem</a>.</p>
