LUKS on-disk-formatThe LUKS on-disk-specification is available here: LUKS-on-disk-format.pdf It standardizes the on-disk format of a LUKS partition, as well as the semantic use of all LUKS specific objects. Reference implementationcryptsetup-luks is the reference implementation for the specification. Your implementation should be able to detect and open a cryptsetup-luks generated partition, if the underlaying cipher system supports the hashes and ciphers given in the partition header.
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Section 2.4.1 (definition of H_1) says |P| denotes the block size of the hash function. What is really meant is that |P| denotes the digest size of the hash function. The block size of SHA1 is 3.2 times its digest size.