How to Tell if a Public Key's Y Value is Positive or Negative?

So, I got a public key (x, y) and its inverse (x, -y). How do we figure out which is positive and which is negative? Like, is there a simple way to tell?

Here’s an example. For my private key 1 -> (x, y): x = 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798L y = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8L And for -y: -y = 0xb7c52588d95c3b9aa25b0403f1eef75702e84bb7597aabe663b82f6f04ef2777L What can we do with this?

What about large numbers or private keys? Anyone got tips?

To check even or odd, just look at the least significant bit. The LSB for Y and -Y are opposites. So it’s really about even/odd, not positive/negative, you know?

So, what you’re saying is there’s no positive or negative? All numbers are technically positive?

If you want a simple way to get the pubkey from the private key, divide the known pubkey. But first, check if it’s even or odd. Hope the thread creator is still around after all this time.

Yup, odd means y mod 2 == 1 and even means y mod 2 == 0. For negative, keep subtracting P until y < 0. Positive? Just add P until y > 0.

Wait, what’s the connection with scalar parity and y being odd/even? It seems like there’s no proof either way. Maybe a super-computer will figure it out someday.

I don’t get it... Like, if I subtract 21 10 = 11, how does -10 end up being -19? Is there a transition from positive to negative?

In secp256k1, 1/2 gives a huge number. Just checking if that method actually helps with odd/even pubkey definitions. Tried a bunch but patterns stay the same.

But think about this: 7/2 1/2 = 3, and when I subtract, 7 3 is odd. So, what gives?

Just remember, we’re working with the pubkey as our known variable. No decimals or private key involved.

I’m talking about this example: 1/2 = 57896044618658097711785492504343953926418782139537452191302581570759080747169 7/2 = 57896044618658097711785492504343953926418782139537452191302581570759080747172