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Add definition of PRF^nr.
Signed-off-by: Daira Hopwood <daira@jacaranda.org>
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@ -734,6 +734,7 @@ electronic commerce and payment, financial privacy, proof of work, zero knowledg
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\newcommand{\NotePosition}{\mathsf{pos}}
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\newcommand{\NotePosition}{\mathsf{pos}}
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\newcommand{\NotePositionBase}{\mathcal{J}}
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\newcommand{\NotePositionBase}{\mathcal{J}}
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\newcommand{\NullifierRand}{\mathsf{nr}}
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\newcommand{\NullifierRand}{\mathsf{nr}}
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\newcommand{\Hashnr}{H^{\NullifierRand}}
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\newcommand{\Diversifier}{\mathsf{d}}
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\newcommand{\Diversifier}{\mathsf{d}}
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\newcommand{\DiversifierLength}{\mathsf{\ell_{\Diversifier}}}
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\newcommand{\DiversifierLength}{\mathsf{\ell_{\Diversifier}}}
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\newcommand{\DiversifierType}{\byteseq{\DiversifierLength/8}}
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\newcommand{\DiversifierType}{\byteseq{\DiversifierLength/8}}
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@ -4310,6 +4311,30 @@ be necessary.})
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}
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}
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}
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}
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\newsavebox{\nrbox}
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\begin{lrbox}{\nrbox}
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\setsapling
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\begin{bytefield}[bitwidth=0.04em]{512}
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\bitbox{256}{$256$-bit $\reprJ(\AuthProvePublic)$} &
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\bitbox{256}{$256$-bit $\reprJ(\NoteAddressRand)$}
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\end{bytefield}
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\end{lrbox}
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\sapling{
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\introlist
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\vspace{2ex}
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$\PRFnr{}$, described in \crossref{abstractprfs}, is instantiated using the
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$\BlakeTwosGeneric$ \hashFunction defined in \crossref{concreteblake2}:
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Define:
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\begin{formulae}
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\item $\Hashnr(x) := \BlakeTwos{256}(\ascii{ZcashnrL}, x) \bconcat \BlakeTwos{256}(\ascii{ZcashnrH}, x)$.
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\item $\PRFnr{\AuthProvePublic}(\NoteAddressRand) :=
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\LEOStoIP{512}\!\left(\Hashnr\!\left(\Justthebox{\nrbox}\right)\right) \bmod \ParamS{r}$.
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\end{formulae}
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}
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\sapling{
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\sapling{
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\introsection
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\introsection
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\nsubsubsection{\PseudoRandomGenerators} \label{concreteprgs}
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\nsubsubsection{\PseudoRandomGenerators} \label{concreteprgs}
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