ECC Trivia: There Are Two Elliptic Curve Points For Every x-Axis Point

So, what’s the square root of 9? You, might say it is 3, but that not the right answer … as the right answer is 3 and -3. What has that go to do with cybersecurity, well, I’ll explain.

So, let me do a bit of trivia here. In ECC (Elliptic Curve Cryptography), we have a point on a curve and we operate on it. If we call that point P. Then we might add P to itself to get 2P (a point doubling). And so with 2P, I can’t reverse the operation to find P. That’s the core of the security of ECC, in that we can’t reverse an adding (or multiplying operation). We can then have a random value of n — known as a scalar value, and then compute: Q =nP. In this case, we should not be able to compute n, even though we know the points P and Q. For this, we can then define n as our secret (or private key), and Q as our public key. If we then standardize P as a generator point (G), we know have a public key system.

But, did you know we actually end up with two possible points?

Going back to my roots

ECC involves uses an equation such as:

y²=x³+ax + b (mod p)

and where p is a prime number. One example is the Bitcoin curve (secp256k1) of: