Let's say my Bitcoin address is
1Nu5mzpUD9A7daZ76QJEsBfkBjCWVLh7pJ and I sign the message
random-challenge with its private key.
The result is :
Bitcoin uses a unique property of ECDSQ which allow to calculate the public key from the message and signature. So if I send to the recipient the above message and signatures he/she will be able to get my address
Now, if I send the same signature and a completely different message, will it derive all the time a valid random Bitcoin address ? And if yes, doesn't this have some serious security implication allowing people to prove they control an address without having the private key ?