Quote from: NUFCrichard on January 11, 2017, 09:38:31 AM

Did you use an online vanitygen? I wouldn't trust that as far as I could throw it!

There is a way to combine public or private keys that commutes with the algorithm for generating public keys from private keys.
In particular, if we have two private keys P and Q, and the function f to generate their public keys:
p=f[P]
q=f[Q]
p and q are the respective public keys.
Call the function that combines keys together "*", it could be a different function when used for public and private keys, but I will still represent it with the same symbol.
R=P*Q
R is a private key produced by combining P and Q.
The function can also be used to combine public keys.
r=p*q
And now for the commutativity property:
r=f[R]
The algorithm for generating the address is a hash of the public key:
p'=H[p]
q'=H[q]
r'=H[r]
Reputable vanity generators work in the following fasion:
1. The client generates a private key P, its public key p=f[P], and sends p to the vanity miner.
2. The client chooses a pattern the address must follow, usually a word it has to start with, and sends this to the vanity miner.
3. The vanity miner chooses an arbitrary private key Q.
4. The vanity miner finds its public key q=f[Q].
5. The vanity miner combines its key with the one provided by the client r=p*q.
6. The vanity miner hashes r to get r'=H[r].
7. The vanity miner checks r' against the pattern, if it does not pass, the vanity miner goes back to step 4, steps 4-7 are the loop, and the miner does them a very large number of times.
8. When an address comes through that fits the pattern, the vanity miner sends the successful partial private key Q to the client.
9. The client combines P and Q to get the final private key R=P*Q, and derives the final address r'=H[f[R]], r' now fits the pattern.
Now the client has a vanity address and its private key, and the vanity miner cannot hack it because P is never sent to the vanity miner.
The only security disadvantage of this scheme is the fact that the public key r is known to the vanity miner, and is vulnerable to quantum computing, hashes are quite resistant to quantum attack, but the number-theoretical elliptic curve algorithm is quite vulnerable. Normally, a quantum attacker only has the time between broadcasting and confirmation to hack ECDSA, but with a vanity address, the hacker can start as soon as the address is generated.
Note that reusing an address that was already sent from, as well as using an address to sign messages, create the same quantum vulnurability as using a vanity address.