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Adding explicit assumption for canonical encodings for the Asset Base. (
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zcash#33)

This addresses [this comment](zcash#680 (comment)).
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vivek-arte authored and daira committed Feb 7, 2024
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Expand Up @@ -90,7 +90,9 @@ where

- :math:`\mathsf{AssetBase}^{\mathsf{Orchard}} : \mathbb{P}*` is the unique element of the Pallas group [#protocol-pallasandvesta]_ that identifies each Asset in the Orchard protocol, defined as the Asset Base in ZIP 227 [#zip-0227]_, a valid non-bottom group element that is not the identity. The byte representation of the Asset Base is defined as :math:`\mathsf{asset\_base} : \mathbb{B}^{[\ell_{\mathbb{P}}]} := \mathsf{repr}_{\mathbb{P}}(\mathsf{AssetBase}^{\mathsf{Orchard}})`.

Specifically, we define the note commitment scheme :math:`\mathsf{NoteCommit^{OrchardZSA}_{rcm}}` as follows:
Note that the above assumes a canonical encoding, which is true for the Pallas group, but may not hold for future shielded protocols.

We define the note commitment scheme :math:`\mathsf{NoteCommit^{OrchardZSA}_{rcm}}` as follows:

.. math:: \mathsf{NoteCommit}^{\mathsf{OrchardZSA}} : \mathsf{NoteCommit}^{\mathsf{Orchard}}.\mathsf{Trapdoor} \times \mathbb{B}^{[\ell_{\mathbb{P}}]} \times \mathbb{B}^{[\ell_{\mathbb{P}}]} \times \{0 .. 2^{\ell_{\mathsf{value}}} - 1\} \times \mathbb{F}_{q_{\mathbb{P}}} \times \mathbb{F}_{q_{\mathbb{P}}} \times \mathbb{P}* \to \mathsf{NoteCommit}^{\mathsf{Orchard}}.\mathsf{Output}

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