ECDSA Public key randomness If I have a 256bit ECDSA public key how likely is it that the same public key will be generated by another person. Will it take on average 2^256 tries to generate same public key? If I xor the first 32bytes of the public key over the second 32bytes and only have 32bytes is it now 2^128 tries to generate the same 32byte data? Or less? Thanks
ECC public keys are not random numbers.

They are generated through a scalar multiplication of a random scalar with a known/public point on the curve, called Generator.

The entropy lies entirely in the random scalar. Two public keys will collide if the random scalars collide.

When you say "256bit ECDSA  public key" you probably mean that your elliptic curve curve is defined over a finite field whose size is approximatively $2^{256}$. This would explain why you are mentioning a public key of 64 bytes in your question.

Now, in cryptographic secure elliptic curves, that size is closely related to the size of order of the generator, which is actually the size of your random scalar.

Therefore, without knowing the exact curve you are using I can't exactly answer the question. But approximatively the expected probability is: $\frac1{2^{256}}$

This has nothing to do with the encoding, so xoring the key over itself doesn't really make sense to me, or I didn't understand it.