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Co-authored-by: Daira Hopwood <daira@jacaranda.org>
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book/src/design/commitment-tree.md
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@ -39,11 +39,11 @@ appended to the tree as a regular leaf.
- For Sprout (and trees composed of the outputs of bit-twiddling hash functions), we use
the all-zeroes array; the probability of a real note having a colliding note commitment
is cryptographically negligible.
- For Sapling (where leaves are u-coordinates of Jubjub points), we use the value $1$
(which is not the u-coordinate of any Jubjub point).
- For Sapling, where leaves are $u$-coordinates of Jubjub points, we use the value $1$
which is not the $u$-coordinate of any Jubjub point.
Orchard note commitments are the x-coordinates of Pallas points; thus we take the same
approach as Sapling, using a value that is not the x-coordinate of any Pallas point as the
Orchard note commitments are the $x$-coordinates of Pallas points; thus we take the same
approach as Sapling, using a value that is not the $x$-coordinate of any Pallas point as the
uncommitted leaf value. It happens that $0$ is the smallest such value for both Pallas and
Vesta, because $0^3 + 5$ is not a square in either $F_p$ or $F_q$: