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4 changes: 2 additions & 2 deletions zip-0226.html
Original file line number Diff line number Diff line change
Expand Up @@ -293,9 +293,9 @@
<li>The Split Input note could be an already spent note containing the same Asset Base (note that by zeroing the value in the circuit, we prevent double spending).</li>
</ol>
<p>For Split Notes, the nullifier is generated as follows:</p>
<div class="math">\(\mathsf{nf_{old}} = \mathsf{Extract}_{\mathbb{P}} ([(\mathsf{PRF^{nfOrchard}_{nk}} (\text{ρ}^{\mathsf{old}}) + \text{ψ}') \bmod q_{\mathbb{P}}]\,\mathcal{K}^\mathsf{Orchard} + \mathsf{cm^{old}} + \mathcal{L}^\mathsf{Orchard})\)</div>
<div class="math">\(\mathsf{nf_{old}} = \mathsf{Extract}_{\mathbb{P}} ([(\mathsf{PRF^{nfOrchard}_{nk}} (\text{ρ}^{\mathsf{old}}) + \text{ψ}^{\mathsf{nf}}) \bmod q_{\mathbb{P}}]\,\mathcal{K}^\mathsf{Orchard} + \mathsf{cm^{old}} + \mathcal{L}^\mathsf{Orchard})\)</div>
<p>where
<span class="math">\(\text{ψ}'\)</span>
<span class="math">\(\text{ψ}^{\mathsf{nf}}\)</span>
is sampled uniformly at random on
<span class="math">\(\mathbb{F}_{q_{\mathbb{P}}}\!\)</span>
,
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4 changes: 2 additions & 2 deletions zip-0226.rst
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Expand Up @@ -243,9 +243,9 @@ Wallets and other clients have to choose from the following to ensure the Asset

For Split Notes, the nullifier is generated as follows:

.. math:: \mathsf{nf_{old}} = \mathsf{Extract}_{\mathbb{P}} ([(\mathsf{PRF^{nfOrchard}_{nk}} (\text{ρ}^{\mathsf{old}}) + \text{ψ}') \bmod q_{\mathbb{P}}]\,\mathcal{K}^\mathsf{Orchard} + \mathsf{cm^{old}} + \mathcal{L}^\mathsf{Orchard})
.. math:: \mathsf{nf_{old}} = \mathsf{Extract}_{\mathbb{P}} ([(\mathsf{PRF^{nfOrchard}_{nk}} (\text{ρ}^{\mathsf{old}}) + \text{ψ}^{\mathsf{nf}}) \bmod q_{\mathbb{P}}]\,\mathcal{K}^\mathsf{Orchard} + \mathsf{cm^{old}} + \mathcal{L}^\mathsf{Orchard})

where :math:`\text{ψ}'` is sampled uniformly at random on :math:`\mathbb{F}_{q_{\mathbb{P}}}\!`, :math:`\mathcal{K}^{\mathsf{Orchard}}` is the Orchard Nullifier Base as defined in [#protocol-commitmentsandnullifiers]_, and :math:`\mathcal{L}^{\mathsf{Orchard}} := \mathsf{GroupHash^{\mathbb{P}}}(\texttt{"z.cash:Orchard"}, \texttt{"L"})\!`.
where :math:`\text{ψ}^{\mathsf{nf}}` is sampled uniformly at random on :math:`\mathbb{F}_{q_{\mathbb{P}}}\!`, :math:`\mathcal{K}^{\mathsf{Orchard}}` is the Orchard Nullifier Base as defined in [#protocol-commitmentsandnullifiers]_, and :math:`\mathcal{L}^{\mathsf{Orchard}} := \mathsf{GroupHash^{\mathbb{P}}}(\texttt{"z.cash:Orchard"}, \texttt{"L"})\!`.

Rationale for Split Notes
`````````````````````````
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