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  • $\begingroup$ You say about Merkle–Damgård constructions, does the same applies to Merkle tree based hash functions? $\endgroup$ Commented Oct 19, 2022 at 1:54
  • $\begingroup$ @phantomcraft: It think the situation with a Merkle tree based hash is in between that for a Merkle–Damgård hash $H(S\mathbin\|\mathtt{00})\mathbin\|H(S\mathbin\|\mathtt{01})\mathbin\|H(S\mathbin\|\mathtt{02})\mathbin\|H(S\mathbin\|\mathtt{03})\mathbin\|\ldots$ (minimum entropy, potentialy down to the hash size) and $H(\mathtt{00}\mathbin\|S)\mathbin\|H(\mathtt{01}\mathbin\|S)\mathbin\|H(\mathtt{02}\mathbin\|S)\mathbin\|H(\mathtt{03}\mathbin\|S)\mathbin\|\ldots$ (maximum entropy, near the output width). $\endgroup$ Commented Oct 19, 2022 at 5:44
  • $\begingroup$ And about H(H(F) || 00) || H(H(F) || 01) || H(H(F) || 02) || H(H(F) || 03) || .. ? How does it compare to H(00||S) || H(01||S) || H(02||S) || H(03||S) || ... ? -- If I use H(00||S) || H(01||S) || H(02||S) || H(03||S) || ... instead of H(S||00) || H(S||01) || H(S||02) || H(S||03) || ..., the answer to my question would be "yes"? $\endgroup$ Commented Nov 23, 2022 at 23:18