Bitcoin's mini private key format works by brute forcing random data to produce a secret so that when appending
? and then hashing with sha256 it will produce a hash that starts with
0x00. This way the user knows the secret is well formed and can proceed to hash it without appending
? to produce their private key.
This technique could be extended to include useful data in the hash "header", up to 2 bytes could be brute forced in a second or two.
However it seems that this scheme is reducing entropy of the secret i.e. if the attacker knows that a key is not valid by using a cheap sha256 hash, she will skip the expensive private to public key calculations. When the hash header is 1 byte around 99.6% of the random candidate keys were rejected, for 2 bytes it was 99.9983282%.
So does this scheme reduces the entropy of initial secret? If so how much?