Update nullifier explanation to include Extract_P.

Signed-off-by: Daira Hopwood <daira@jacaranda.org>
This commit is contained in:
Daira Hopwood 2021-04-21 18:25:18 +01:00
parent b88e77dd56
commit f5bab61f81
1 changed files with 7 additions and 1 deletions

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@ -2,7 +2,7 @@
The nullifier design we use for Orchard is
$$\mathsf{nf} = [F_{\mathsf{nk}}(\rho) + \psi \pmod{p}] \mathcal{G} + \mathsf{cm},$$
$$\mathsf{nf} = \mathsf{Extract}_{\mathbb{P}}\big([F_{\mathsf{nk}}(\rho) + \psi \pmod{p}] \mathcal{G} + \mathsf{cm}\big),$$
where:
@ -15,6 +15,7 @@ where:
is derived from both $\rho$ and a sender-selected random value $\mathsf{rseed}$:
$$\psi = KDF^\psi(\rho, \mathsf{rseed}).$$
- $\mathcal{G}$ is a fixed independent base.
- $\mathsf{Extract}_{\mathbb{P}}$ extracts the $x$-coordinate of a Pallas curve point.
This gives a note structure of
@ -95,6 +96,11 @@ $\color{red}{\textsf{⚠ Caution}}$: be skeptical of the claims in this table ab
problem(s) each security property depends on. They may not be accurate and are definitely
not fully rigorous.
The entries in this table omit the application of $\mathsf{Extract}_{\mathbb{P}}$,
which is an optimization to halve the nullifier length. That optimization requires its
own security analysis, but because it is a deterministic mapping, only Faerie Resistance
could be affected by it.
$$
\begin{array}{|c|l|c|c|c|c|c|}
\hline