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Padding has two primary uses in cryptography, ensuring messages are the proper length necessary for certain ciphers (e.g., block ciphers) or to provide assurances not built into the core cipher (e.g., semantic security)
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Necessity of all three MD-Compliant padding conditions
For Merkle-Damgård hashing, MD-compliant padding is defined as any padding scheme satisfying:
$M$ is a prefix of $\text{Pad}(M)$
$|M_1|=|M_2|\Rightarrow |\text{Pad}(M_1)|=|\text{Pad}(M_2)|$
$|M_1|\neq … I can see how different length messages having the last padding block could lead to collisions, for example. …