The elliptic curve equation is:
Y2 = X3 + aX + b
In the case of the secp256k1 curve used by bitcoin:
a=0
b=7
Therefore:
Y2 = X3 + 7
So, if you know X, you can use the curve equation to compute Y2.
A square root extraction will result in Y and -Y. The compressed point format includes the least significant bit of Y in the first byte. That bit is enough to know whether you got Y or -Y and adjust appropriately.
Y2 = X3 + aX + b
In the case of the secp256k1 curve used by bitcoin:
a=0
b=7
Therefore:
Y2 = X3 + 7
So, if you know X, you can use the curve equation to compute Y2.
A square root extraction will result in Y and -Y. The compressed point format includes the least significant bit of Y in the first byte. That bit is enough to know whether you got Y or -Y and adjust appropriately.
very beginner question... what's X and Y? the integer form of the key?
X and Y are the coordinates of the elliptic curve, in which bitcoin's elliptic curve cryptography operations take place. A public key is a point on that curve so it's stored as (X, Y), or (X, b) in compressed form.
Read this for an introduction http://www.coindesk.com/math-behind-bitcoin/
