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I am trying to understand how scrypt works. I am referring to the Algorithm section of scrypt's Wikipedia page. There I find this BlockMix function:

Function BlockMix(B):
    (B0, ... , B2r-1) ← B
    X ← B2r−1
    for i = 0 to 2r − 1 do
        X ← H(X ⊕ Bi)
        Yi ← X
    end for
    Output ← (Y0, Y2, ... , Y2r−2, Y1, Y3, ... , Y2r−1)

Now, as far as my understanding goes, this means: expand an r-bytes block into its single bytes, namely, B0, ..., B2r-1. Set X to the last byte, and propagate some perturbation by updating X with H(X ⊕ Bi). Finally return the output bytes, somehow shuffled (first the even, then the odds).

What I don't understand is the meaning of that H function. It's nowhere specified what it is. I guess it is a function that inputs one byte and outputs one byte. Is that a commonly known function? H usually stands for hash. Should I just pick any random bijection between the numbers in [0, 255]?

Anyone answering my question might as well consider to add this information to the Wikipedia page, to help the next reader.

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  • $\begingroup$ In the original paper by Percival (tarsnap.com/scrypt/scrypt.pdf) BlockMix(.) is parameterised by a function H which is a hash function (modelled, later, as a random oracle). $\endgroup$ – Occams_Trimmer Jan 19 '17 at 15:08
  • $\begingroup$ Ok, that helps. So maybe here blockmix is the implementation of an efficient hash function? $\endgroup$ – Matteo Monti Jan 19 '17 at 15:19
  • $\begingroup$ I stand corrected: the function ROMix_H(.,.) is the "ideal" sequential memory-hard function (MHF) that comes with a security proof under the assumption that H is a random oracle. Since ROMix_H does not fare well in practice, [Per] introduced (as you point out) a "custom" hash function (HF) called BLOCKMix_{H,r}(.) where H is a HF "which is fast while not possessing excess internal parallelism" ([Per] recommends Salsa20/8). But the drawback is that the resulting MHF (SMix_r(B,N):=ROMix_{BLOCKMix_{H,r}}(B,N)) is not provably memory-hard. I hope this helps. $\endgroup$ – Occams_Trimmer Jan 19 '17 at 15:55
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I'll sum up the comments: according to the original paper, $H$ is any hash function which, ideally, uses limited parallelism$^1$, with Salsa20/8 being a candidate.

Footnote 1: In order to make the resulting memory-hard function less susceptible to attacks (which make an essential use of parallelism).

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