This is denoted as .
As mentioned in the introduction, the padding scheme used in the Merkle–Damgård construction must be chosen carefully to ensure the security of the scheme. Mihir Bellare gives sufficient conditions for a padding scheme to possess to ensure that the MD construction is secure: the scheme must be "MD-compliant" (the original length-padding scheme used by Merkle is an example of MD-compliant padding).:145 Conditions:
- is a prefix of .
- If then .
- If then the last block of is different from the last block of .
With these conditions in place, we find a collision in the MD hash function exactly when we find a collision in the underlying compression function. Therefore, the Merkle–Damgård construction is provably secure when the underlying compression function is secure. :147