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Some points towards an answer: Why HMAC-SHA3? HMAC and its security proofs have been devised for Merkle-Damgård hashes, and SHA3 is not one. HMAC-SHA256 would be fine (Updated per comment: the Keccak submission does endorse its use with HMAC, using a block size parameters of 576 (resp. 832, 1088, 1152) bits for the hash with output of 512 (resp 384, 256, ...

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The way the iterations work is that it roughly increases your security (in bits) by $\log_2(iterations)$. So you would still need $\frac{\log{2}}{\log{97}}\cdot (256 - \log_2(10000)) \approx 37$ characters in your password to have 256-bits of security. Think of it this way, if you have $2^{256}$ possible keys, that is an astronomically large number. Much ...

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Probably because a simple cascade would only be stronger against some attacks, while opening the door to more implementation bugs. While bcrypt and scrypt are (password based) key-derivation functions, much of what is in the answers to this question about combining hash functions applies here. Different constructions give preimage resistance and PRF-ness, ...

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