734 lines
22 KiB
Rust
734 lines
22 KiB
Rust
//! Common types and utilities used in incremental Merkle tree implementations.
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use either::Either;
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use std::cmp::Ordering;
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use std::convert::{TryFrom, TryInto};
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use std::num::TryFromIntError;
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use std::ops::{Add, AddAssign, Range, Sub};
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pub mod frontier;
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#[cfg(feature = "legacy-api")]
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pub mod witness;
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#[cfg(feature = "test-dependencies")]
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pub mod testing;
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/// A type for metadata that is used to determine when and how a leaf can be pruned from a tree.
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#[derive(Clone, Copy, Debug, PartialEq, Eq, PartialOrd, Ord)]
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pub enum Retention<C> {
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Ephemeral,
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Checkpoint { id: C, is_marked: bool },
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Marked,
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}
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impl<C> Retention<C> {
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pub fn is_checkpoint(&self) -> bool {
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matches!(self, Retention::Checkpoint { .. })
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}
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pub fn is_marked(&self) -> bool {
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match self {
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Retention::Ephemeral => false,
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Retention::Checkpoint { is_marked, .. } => *is_marked,
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Retention::Marked => true,
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}
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}
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pub fn map<'a, D, F: Fn(&'a C) -> D>(&'a self, f: F) -> Retention<D> {
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match self {
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Retention::Ephemeral => Retention::Ephemeral,
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Retention::Checkpoint { id, is_marked } => Retention::Checkpoint {
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id: f(id),
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is_marked: *is_marked,
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},
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Retention::Marked => Retention::Marked,
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}
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}
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}
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#[derive(Copy, Clone, Debug, PartialEq, Eq)]
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pub enum Source {
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/// The sibling to the address can be derived from the incremental frontier
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/// at the contained ommer index
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Past(usize),
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/// The sibling to the address must be obtained from values discovered by
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/// the addition of more nodes to the tree
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Future,
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}
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#[must_use = "iterators are lazy and do nothing unless consumed"]
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struct WitnessAddrsIter {
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root_level: Level,
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current: Address,
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ommer_count: usize,
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}
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impl Iterator for WitnessAddrsIter {
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type Item = (Address, Source);
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fn next(&mut self) -> Option<(Address, Source)> {
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if self.current.level() < self.root_level {
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let current = self.current;
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let source = if current.is_right_child() {
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Source::Past(self.ommer_count)
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} else {
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Source::Future
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};
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self.current = current.parent();
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if matches!(source, Source::Past(_)) {
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self.ommer_count += 1;
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}
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Some((current.sibling(), source))
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} else {
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None
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}
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}
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}
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/// A type representing the position of a leaf in a Merkle tree.
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#[derive(Copy, Clone, Debug, PartialEq, Eq, PartialOrd, Ord, Hash)]
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#[repr(transparent)]
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pub struct Position(usize);
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impl Position {
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/// Return whether the position is odd-valued.
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pub fn is_odd(&self) -> bool {
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self.0 & 0x1 == 1
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}
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/// Returns the minimum possible level of the root of a binary tree containing at least
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/// `self + 1` nodes.
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pub fn root_level(&self) -> Level {
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Level((usize::BITS - self.0.leading_zeros()) as u8)
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}
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/// Returns the number of cousins and/or ommers required to construct an authentication
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/// path to the root of a merkle tree that has `self + 1` nodes.
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pub fn past_ommer_count(&self) -> usize {
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(0..self.root_level().0)
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.filter(|i| (self.0 >> i) & 0x1 == 1)
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.count()
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}
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/// Returns whether the binary tree having `self` as the position of the rightmost leaf
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/// contains a perfect balanced tree with a root at level `root_level` that contains the
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/// aforesaid leaf.
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pub fn is_complete_subtree(&self, root_level: Level) -> bool {
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!(0..(root_level.0)).any(|l| self.0 & (1 << l) == 0)
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}
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/// Returns an iterator over the addresses of nodes required to create a witness for this
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/// position, beginning with the sibling of the leaf at this position and ending with the
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/// sibling of the ancestor of the leaf at this position that is required to compute a root at
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/// the specified level.
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pub fn witness_addrs(&self, root_level: Level) -> impl Iterator<Item = (Address, Source)> {
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WitnessAddrsIter {
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root_level,
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current: Address::from(*self),
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ommer_count: 0,
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}
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}
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}
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impl From<Position> for usize {
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fn from(p: Position) -> usize {
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p.0
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}
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}
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impl From<Position> for u64 {
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fn from(p: Position) -> Self {
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p.0 as u64
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}
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}
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impl Add<usize> for Position {
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type Output = Position;
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fn add(self, other: usize) -> Self {
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Position(self.0 + other)
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}
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}
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impl AddAssign<usize> for Position {
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fn add_assign(&mut self, other: usize) {
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self.0 += other
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}
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}
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impl Sub<usize> for Position {
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type Output = Position;
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fn sub(self, other: usize) -> Self {
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if self.0 < other {
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panic!("position underflow");
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}
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Position(self.0 - other)
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}
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}
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impl From<usize> for Position {
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fn from(sz: usize) -> Self {
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Self(sz)
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}
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}
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impl TryFrom<u64> for Position {
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type Error = TryFromIntError;
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fn try_from(sz: u64) -> Result<Self, Self::Error> {
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<usize>::try_from(sz).map(Self)
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}
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}
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/// A type-safe wrapper for indexing into "levels" of a binary tree, such that
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/// nodes at level `0` are leaves, nodes at level `1` are parents of nodes at
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/// level `0`, and so forth. This type is capable of representing levels in
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/// trees containing up to 2^255 leaves.
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#[derive(Copy, Clone, Debug, PartialEq, Eq, PartialOrd, Ord, Hash)]
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#[repr(transparent)]
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pub struct Level(u8);
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impl Level {
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// TODO: replace with an instance for `Step<Level>` once `step_trait`
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// is stabilized
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pub fn iter_to(self, other: Level) -> impl Iterator<Item = Self> {
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(self.0..other.0).map(Level)
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}
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}
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impl Add<u8> for Level {
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type Output = Self;
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fn add(self, value: u8) -> Self {
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Self(self.0 + value)
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}
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}
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impl From<u8> for Level {
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fn from(value: u8) -> Self {
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Self(value)
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}
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}
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impl From<Level> for u8 {
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fn from(level: Level) -> u8 {
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level.0
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}
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}
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impl From<Level> for usize {
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fn from(level: Level) -> usize {
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level.0 as usize
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}
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}
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impl TryFrom<usize> for Level {
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type Error = TryFromIntError;
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fn try_from(sz: usize) -> Result<Self, Self::Error> {
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<u8>::try_from(sz).map(Self)
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}
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}
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impl Sub<u8> for Level {
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type Output = Self;
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fn sub(self, value: u8) -> Self {
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if self.0 < value {
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panic!("underflow")
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}
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Self(self.0 - value)
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}
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}
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/// The address of an internal node of the Merkle tree.
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/// When `level == 0`, the index has the same value as the
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/// position.
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#[derive(Copy, Clone, Debug, PartialEq, Eq, PartialOrd, Ord, Hash)]
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pub struct Address {
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level: Level,
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index: usize,
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}
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impl Address {
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/// Construct a new address from its constituent parts.
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pub fn from_parts(level: Level, index: usize) -> Self {
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Address { level, index }
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}
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/// Returns the address at the given level that contains the specified leaf position.
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pub fn above_position(level: Level, position: Position) -> Self {
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Address {
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level,
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index: position.0 >> level.0,
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}
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}
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/// Returns the level of the root of the tree having its root at this address.
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pub fn level(&self) -> Level {
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self.level
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}
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/// Returns the index of the address.
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///
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/// The index of an address is defined as the number of subtrees with their roots
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/// at the address's level that appear to the left of this address in a binary
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/// tree of arbitrary height > level * 2 + 1.
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pub fn index(&self) -> usize {
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self.index
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}
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/// The address of the node one level higher than this in a binary tree that contains
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/// this address as either its left or right child.
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pub fn parent(&self) -> Address {
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Address {
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level: self.level + 1,
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index: self.index >> 1,
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}
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}
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/// Returns the address that shares the same parent as this address.
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pub fn sibling(&self) -> Address {
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Address {
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level: self.level,
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index: self.index ^ 1,
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}
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}
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/// Returns the immediate children of this address.
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pub fn children(&self) -> Option<(Address, Address)> {
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if self.level == Level::from(0) {
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None
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} else {
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let left = Address {
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level: self.level - 1,
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index: self.index << 1,
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};
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let right = Address {
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level: self.level - 1,
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index: (self.index << 1) + 1,
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};
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Some((left, right))
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}
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}
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/// Returns whether this address is an ancestor of the specified address.
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pub fn is_ancestor_of(&self, addr: &Self) -> bool {
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self.level > addr.level && { addr.index >> (self.level.0 - addr.level.0) == self.index }
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}
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/// Returns whether this address is an ancestor of, or is equal to,
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/// the specified address.
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pub fn contains(&self, addr: &Self) -> bool {
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self == addr || self.is_ancestor_of(addr)
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}
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/// Returns the minimum value among the range of leaf positions that are contained within the
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/// tree with its root at this address.
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pub fn position_range_start(&self) -> Position {
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(self.index << self.level.0).try_into().unwrap()
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}
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/// Returns the (exclusive) end of the range of leaf positions that are contained within the
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/// tree with its root at this address.
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pub fn position_range_end(&self) -> Position {
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((self.index + 1) << self.level.0).try_into().unwrap()
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}
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/// Returns the maximum value among the range of leaf positions that are contained within the
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/// tree with its root at this address.
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pub fn max_position(&self) -> Position {
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self.position_range_end() - 1
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}
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/// Returns the end-exclusive range of leaf positions that are contained within the tree with
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/// its root at this address.
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pub fn position_range(&self) -> Range<Position> {
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Range {
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start: self.position_range_start(),
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end: self.position_range_end(),
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}
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}
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/// Returns either the ancestor of this address at the given level (if the level is greater
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/// than or equal to that of this address) or the range of indices of root addresses of
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/// subtrees with roots at the given level contained within the tree with its root at this
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/// address otherwise.
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pub fn context(&self, level: Level) -> Either<Address, Range<usize>> {
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if level >= self.level {
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Either::Left(Address {
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level,
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index: self.index >> (level.0 - self.level.0),
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})
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} else {
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let shift = self.level.0 - level.0;
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Either::Right(Range {
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start: self.index << shift,
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end: (self.index + 1) << shift,
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})
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}
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}
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/// Returns whether the tree with this root address contains the given leaf position, or if not
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/// whether an address at the same level with a greater or lesser index will contain the
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/// specified leaf position.
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pub fn position_cmp(&self, pos: Position) -> Ordering {
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let range = self.position_range();
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if range.start > pos {
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Ordering::Greater
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} else if range.end <= pos {
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Ordering::Less
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} else {
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Ordering::Equal
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}
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}
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/// Returns whether this address is the right-hand child of its parent
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pub fn is_right_child(&self) -> bool {
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self.index & 0x1 == 1
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}
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pub fn current_incomplete(&self) -> Address {
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// find the first zero bit in the index, searching from the least significant bit
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let mut index = self.index;
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for level in self.level.0.. {
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if index & 0x1 == 1 {
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index >>= 1;
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} else {
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return Address {
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level: Level(level),
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index,
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};
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}
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}
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unreachable!("The loop will always terminate via return in at most 64 iterations.")
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}
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pub fn next_incomplete_parent(&self) -> Address {
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if self.is_right_child() {
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self.current_incomplete()
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} else {
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let complete = Address {
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level: self.level,
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index: self.index + 1,
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};
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complete.current_incomplete()
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}
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}
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/// Increments this address's index by 1 and returns the resulting address.
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pub fn next_at_level(&self) -> Address {
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Address {
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level: self.level,
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index: self.index + 1,
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}
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}
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}
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impl From<Position> for Address {
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fn from(p: Position) -> Self {
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Address {
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level: 0.into(),
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index: p.into(),
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}
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}
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}
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impl<'a> From<&'a Position> for Address {
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fn from(p: &'a Position) -> Self {
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Address {
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level: 0.into(),
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index: (*p).into(),
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}
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}
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}
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impl From<Address> for Option<Position> {
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fn from(addr: Address) -> Self {
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if addr.level == 0.into() {
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Some(addr.index.into())
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} else {
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None
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}
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}
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}
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impl<'a> From<&'a Address> for Option<Position> {
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fn from(addr: &'a Address) -> Self {
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if addr.level == 0.into() {
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Some(addr.index.into())
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} else {
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None
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}
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}
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}
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/// A path from a position in a particular commitment tree to the root of that tree.
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#[derive(Clone, Debug, PartialEq, Eq)]
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pub struct MerklePath<H, const DEPTH: u8> {
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path_elems: Vec<H>,
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position: Position,
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}
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impl<H, const DEPTH: u8> MerklePath<H, DEPTH> {
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/// Constructs a Merkle path directly from a path and position.
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#[allow(clippy::result_unit_err)]
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pub fn from_parts(path_elems: Vec<H>, position: Position) -> Result<Self, ()> {
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if path_elems.len() == usize::from(DEPTH) {
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Ok(MerklePath {
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path_elems,
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position,
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})
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} else {
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Err(())
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}
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}
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pub fn path_elems(&self) -> &[H] {
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&self.path_elems
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}
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pub fn position(&self) -> Position {
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self.position
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}
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}
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impl<H: Hashable, const DEPTH: u8> MerklePath<H, DEPTH> {
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/// Returns the root of the tree corresponding to this path applied to `leaf`.
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pub fn root(&self, leaf: H) -> H {
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self.path_elems
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.iter()
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.zip(0u8..)
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.fold(leaf, |root, (h, i)| {
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if (self.position.0 >> i) & 0x1 == 0 {
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H::combine(i.into(), &root, h)
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} else {
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H::combine(i.into(), h, &root)
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}
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})
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}
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}
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|
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/// A trait describing the operations that make a type suitable for use as
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/// a leaf or node value in a merkle tree.
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pub trait Hashable: Sized + core::fmt::Debug {
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fn empty_leaf() -> Self;
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fn combine(level: Level, a: &Self, b: &Self) -> Self;
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fn empty_root(level: Level) -> Self {
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Level::from(0)
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.iter_to(level)
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.fold(Self::empty_leaf(), |v, lvl| Self::combine(lvl, &v, &v))
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}
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}
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#[cfg(test)]
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pub(crate) mod tests {
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use crate::MerklePath;
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use super::{Address, Level, Position, Source};
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use core::ops::Range;
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use either::Either;
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|
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#[test]
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fn position_is_complete_subtree() {
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assert!(Position(0).is_complete_subtree(Level(0)));
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assert!(Position(1).is_complete_subtree(Level(1)));
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assert!(!Position(2).is_complete_subtree(Level(1)));
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assert!(!Position(2).is_complete_subtree(Level(2)));
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assert!(Position(3).is_complete_subtree(Level(2)));
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assert!(!Position(4).is_complete_subtree(Level(2)));
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assert!(Position(7).is_complete_subtree(Level(3)));
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assert!(Position(u32::MAX as usize).is_complete_subtree(Level(32)));
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}
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|
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#[test]
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fn position_past_ommer_count() {
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assert_eq!(0, Position(0).past_ommer_count());
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assert_eq!(1, Position(1).past_ommer_count());
|
|
assert_eq!(1, Position(2).past_ommer_count());
|
|
assert_eq!(2, Position(3).past_ommer_count());
|
|
assert_eq!(1, Position(4).past_ommer_count());
|
|
assert_eq!(3, Position(7).past_ommer_count());
|
|
assert_eq!(1, Position(8).past_ommer_count());
|
|
}
|
|
|
|
#[test]
|
|
fn position_root_level() {
|
|
assert_eq!(Level(0), Position(0).root_level());
|
|
assert_eq!(Level(1), Position(1).root_level());
|
|
assert_eq!(Level(2), Position(2).root_level());
|
|
assert_eq!(Level(2), Position(3).root_level());
|
|
assert_eq!(Level(3), Position(4).root_level());
|
|
assert_eq!(Level(3), Position(7).root_level());
|
|
assert_eq!(Level(4), Position(8).root_level());
|
|
}
|
|
|
|
#[test]
|
|
fn position_witness_addrs() {
|
|
use Source::*;
|
|
let path_elem = |l, i, s| (Address::from_parts(Level::from(l), i), s);
|
|
assert_eq!(
|
|
vec![path_elem(0, 1, Future), path_elem(1, 1, Future)],
|
|
Position::from(0)
|
|
.witness_addrs(Level::from(2))
|
|
.collect::<Vec<_>>()
|
|
);
|
|
assert_eq!(
|
|
vec![path_elem(0, 3, Future), path_elem(1, 0, Past(0))],
|
|
Position::from(2)
|
|
.witness_addrs(Level::from(2))
|
|
.collect::<Vec<_>>()
|
|
);
|
|
assert_eq!(
|
|
vec![
|
|
path_elem(0, 2, Past(0)),
|
|
path_elem(1, 0, Past(1)),
|
|
path_elem(2, 1, Future)
|
|
],
|
|
Position::from(3)
|
|
.witness_addrs(Level::from(3))
|
|
.collect::<Vec<_>>()
|
|
);
|
|
assert_eq!(
|
|
vec![
|
|
path_elem(0, 5, Future),
|
|
path_elem(1, 3, Future),
|
|
path_elem(2, 0, Past(0)),
|
|
path_elem(3, 1, Future)
|
|
],
|
|
Position::from(4)
|
|
.witness_addrs(Level::from(4))
|
|
.collect::<Vec<_>>()
|
|
);
|
|
assert_eq!(
|
|
vec![
|
|
path_elem(0, 7, Future),
|
|
path_elem(1, 2, Past(0)),
|
|
path_elem(2, 0, Past(1)),
|
|
path_elem(3, 1, Future)
|
|
],
|
|
Position::from(6)
|
|
.witness_addrs(Level::from(4))
|
|
.collect::<Vec<_>>()
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn address_current_incomplete() {
|
|
let addr = |l, i| Address::from_parts(Level(l), i);
|
|
assert_eq!(addr(0, 0), addr(0, 0).current_incomplete());
|
|
assert_eq!(addr(1, 0), addr(0, 1).current_incomplete());
|
|
assert_eq!(addr(0, 2), addr(0, 2).current_incomplete());
|
|
assert_eq!(addr(2, 0), addr(0, 3).current_incomplete());
|
|
}
|
|
|
|
#[test]
|
|
fn address_next_incomplete_parent() {
|
|
let addr = |l, i| Address::from_parts(Level(l), i);
|
|
assert_eq!(addr(1, 0), addr(0, 0).next_incomplete_parent());
|
|
assert_eq!(addr(1, 0), addr(0, 1).next_incomplete_parent());
|
|
assert_eq!(addr(2, 0), addr(0, 2).next_incomplete_parent());
|
|
assert_eq!(addr(2, 0), addr(0, 3).next_incomplete_parent());
|
|
assert_eq!(addr(3, 0), addr(2, 0).next_incomplete_parent());
|
|
assert_eq!(addr(1, 2), addr(0, 4).next_incomplete_parent());
|
|
assert_eq!(addr(3, 0), addr(1, 2).next_incomplete_parent());
|
|
}
|
|
|
|
#[test]
|
|
fn addr_is_ancestor() {
|
|
let l0 = Level(0);
|
|
let l1 = Level(1);
|
|
assert!(Address::from_parts(l1, 0).is_ancestor_of(&Address::from_parts(l0, 0)));
|
|
assert!(Address::from_parts(l1, 0).is_ancestor_of(&Address::from_parts(l0, 1)));
|
|
assert!(!Address::from_parts(l1, 0).is_ancestor_of(&Address::from_parts(l0, 2)));
|
|
}
|
|
|
|
#[test]
|
|
fn addr_position_range() {
|
|
assert_eq!(
|
|
Address::from_parts(Level(0), 0).position_range(),
|
|
Range {
|
|
start: Position(0),
|
|
end: Position(1)
|
|
}
|
|
);
|
|
assert_eq!(
|
|
Address::from_parts(Level(1), 0).position_range(),
|
|
Range {
|
|
start: Position(0),
|
|
end: Position(2)
|
|
}
|
|
);
|
|
assert_eq!(
|
|
Address::from_parts(Level(2), 1).position_range(),
|
|
Range {
|
|
start: Position(4),
|
|
end: Position(8)
|
|
}
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn addr_above_position() {
|
|
assert_eq!(
|
|
Address::above_position(Level(3), Position(9)),
|
|
Address::from_parts(Level(3), 1)
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn addr_children() {
|
|
assert_eq!(Address::from_parts(Level(0), 1).children(), None);
|
|
|
|
assert_eq!(
|
|
Address::from_parts(Level(3), 1).children(),
|
|
Some((
|
|
Address::from_parts(Level(2), 2),
|
|
Address::from_parts(Level(2), 3),
|
|
))
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn addr_is_ancestor_of() {
|
|
assert!(Address::from_parts(Level(3), 1).is_ancestor_of(&Address::from_parts(Level(2), 2)));
|
|
assert!(Address::from_parts(Level(3), 1).is_ancestor_of(&Address::from_parts(Level(1), 7)));
|
|
assert!(!Address::from_parts(Level(3), 1).is_ancestor_of(&Address::from_parts(Level(1), 8)));
|
|
}
|
|
|
|
#[test]
|
|
fn addr_context() {
|
|
assert_eq!(
|
|
Address::from_parts(Level(3), 1).context(Level(0)),
|
|
Either::Right(Range { start: 8, end: 16 })
|
|
);
|
|
|
|
assert_eq!(
|
|
Address::from_parts(Level(3), 4).context(Level(5)),
|
|
Either::Left(Address::from_parts(Level(5), 1))
|
|
);
|
|
}
|
|
|
|
#[test]
|
|
fn merkle_path_root() {
|
|
let path: MerklePath<String, 3> = MerklePath::from_parts(
|
|
vec!["a".to_string(), "cd".to_string(), "efgh".to_string()],
|
|
Position(1),
|
|
)
|
|
.unwrap();
|
|
|
|
assert_eq!(path.root("b".to_string()), "abcdefgh".to_string());
|
|
|
|
let path: MerklePath<String, 3> = MerklePath::from_parts(
|
|
vec!["d".to_string(), "ab".to_string(), "efgh".to_string()],
|
|
Position(2),
|
|
)
|
|
.unwrap();
|
|
|
|
assert_eq!(path.root("c".to_string()), "abcdefgh".to_string());
|
|
}
|
|
}
|