4

What's the limit?

And what is the chance of someone guessing your keys?

8

1) As per Orbit Len's comment: Stellar uses ED25519 keypairs. There is only one public key that matches the given secret key. Source

2) Here is an example for bitcoin and someone trying to guess your private key:

"A Bitcoin private key is simply an integer between one and about 10^77. This may not seem like much of a selection, but for practical purposes it’s essentially infinite.

If you could process one trillion private keys per second, it would take more than one million times the age of the universe to count them all. Even worse, just enumerating these keys would consume more than the total energy output of the sun for 32 years. This vast keyspace plays a fundamental role in securing the Bitcoin network."

Source

7

Going by the actual source code, there are 32 secret keys that generate the exact same public key -- only 251 bits of the seed hash are used in the elliptic curve exponentiation. For signing, another two bits are used.

So all in all, 253 bits of entropy, or 1.4*10^76 unique keys.

The number of atoms in the observable universe is estimated to be around 10^80.

You pick one atom, have your friend guess which one. That's how unlikely it is to guess your private key.

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