mirror of https://github.com/zcash/zips.git
Minor fixes
This commit is contained in:
Jack Grigg
Daira Hopwood
parent
1af5d1a076
commit
9b87a3ef00
45
zip-0221.rst
45
zip-0221.rst
|
|
@ -95,9 +95,10 @@ and represent this numbering in a flat list:
|
|||
| Altitude | 0 | 0 | 1 | 0 | 0 | 1 | 2 | 0 | 0 | 1 | 0 | 0 | 1 | 2 | 3 | 0 | 0 | 1 | 0 |
|
||||
+----------+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
|
||||
|
||||
This allows us to easily jump to the right sibling of a node by adding ``2^(h+1) - 1`` to
|
||||
its position, and its left child by subtracting ``2^h``. This allows us to efficiently
|
||||
find the subtree roots ("peaks") of the mountains.
|
||||
Let :math:`h` be the altitude of a given node. We can easily jump to the node's right
|
||||
sibling (if it has one) by adding :math:`2^{h+1} - 1` to its position, and its left child
|
||||
(if it has one) by subtracting :math:`2^h`. This allows us to efficiently find the subtree
|
||||
roots ("peaks") of the mountains.
|
||||
|
||||
Once we have the positions of the mountain peaks, we "bag" them using the following
|
||||
algorithm:
|
||||
|
|
@ -138,8 +139,8 @@ leafset, sparse Merkle trees, and Zcash's incremental note commitment trees).
|
|||
Motivation
|
||||
==========
|
||||
|
||||
MMR proofs are used in the FlyClient protocol to reduce the proof size needed for light
|
||||
clients to verify
|
||||
MMR proofs are used in the FlyClient protocol [#FlyClient]_, to reduce the proof size
|
||||
needed for light clients to verify:
|
||||
|
||||
- the validity of a block chain received from a full node, and
|
||||
- the inclusion of a block :math:`B` in that chain, and
|
||||
|
|
@ -193,8 +194,10 @@ Each MMR node is defined as follows:
|
|||
|
||||
* This hash is encoded in internal byte order, and does NOT use the BLAKE2b-256
|
||||
personalization string described above.
|
||||
* For clarity, the ``hashSubtreeCommitment`` field of leaf ``n-1`` is *precisely equal*
|
||||
to the ``hashPrevBlock`` field of header ``n``.
|
||||
* For clarity, the ``hashSubtreeCommitment`` field of leaf :math:`n-1` is *precisely
|
||||
equal* to the ``hashPrevBlock`` field in the header of the block at height
|
||||
:math:`x+n`, where :math:`x` is the block height of the most recent network
|
||||
upgrade.
|
||||
|
||||
Internal or root node
|
||||
* Both child nodes are serialized.
|
||||
|
|
@ -227,7 +230,7 @@ Each MMR node is defined as follows:
|
|||
|
||||
Serialized as ``nTime`` (``uint32``).
|
||||
|
||||
4. ``nEarliestTarget``
|
||||
4. ``nEarliestTargetBits``
|
||||
|
||||
Leaf node
|
||||
The header's ``nBits`` field.
|
||||
|
|
@ -237,7 +240,7 @@ Each MMR node is defined as follows:
|
|||
|
||||
Serialized as ``nBits`` (``uint32``).
|
||||
|
||||
5. ``nLatestTarget``
|
||||
5. ``nLatestTargetBits``
|
||||
|
||||
Leaf node
|
||||
The header's ``nBits`` field.
|
||||
|
|
@ -343,8 +346,8 @@ Tree nodes and hashing (pseudocode)
|
|||
hashSubtreeCommitment: bytes
|
||||
nEarliestTimestamp: int
|
||||
nLatestTimestamp: int
|
||||
nEarliestTarget: int
|
||||
nLatestTarget: int
|
||||
nEarliestTargetBits: int
|
||||
nLatestTargetBits: int
|
||||
hashEarliestSaplingRoot: bytes # left child's sapling root
|
||||
hashLatestSaplingRoot: bytes # right child's sapling root
|
||||
nSubTreeTotalWork: int # total difficulty accumulated within each subtree
|
||||
|
|
@ -361,8 +364,8 @@ Tree nodes and hashing (pseudocode)
|
|||
hashSubtreeCommitment=block.header_hash,
|
||||
nEarliestTimestamp=block.timestamp,
|
||||
nLatestTimestamp=block.timestamp,
|
||||
nEarliestTarget=block.nBits,
|
||||
nLatestTarget=block.nBits,
|
||||
nEarliestTargetBits=block.nBits,
|
||||
nLatestTargetBits=block.nBits,
|
||||
hashEarliestSaplingRoot=block.sapling_root,
|
||||
hashLatestSaplingRoot=block.sapling_root,
|
||||
nSubTreeTotalWork=calculate_work(block.nBits),
|
||||
|
|
@ -376,8 +379,8 @@ Tree nodes and hashing (pseudocode)
|
|||
self.hashSubtreeCommitment
|
||||
+ serialize_uint32(self.nEarliestTimestamp)
|
||||
+ serialize_uint32(self.nLatestTimestamp)
|
||||
+ serialize_uint32(self.nEarliestTarget)
|
||||
+ serialize_uint32(self.nLatestTarget)
|
||||
+ serialize_uint32(self.nEarliestTargetBits)
|
||||
+ serialize_uint32(self.nLatestTargetBits)
|
||||
+ hashEarliestSaplingRoot
|
||||
+ hashLatestSaplingRoot
|
||||
+ serialize_uint256(self.nSubTreeTotalWork)
|
||||
|
|
@ -395,8 +398,8 @@ Tree nodes and hashing (pseudocode)
|
|||
hashSubtreeCommitment=H(left_child.serialize() + right_child.serialize()),
|
||||
nEarliestTimestamp=left_child.nEarliestTimestamp,
|
||||
nLatestTimestamp=right_child.nLatestTimestamp,
|
||||
nEarliestTarget=left_child.nEarliestTarget,
|
||||
nLatestTarget=right_child.nLatestTarget,
|
||||
nEarliestTargetBits=left_child.nEarliestTargetBits,
|
||||
nLatestTargetBits=right_child.nLatestTargetBits,
|
||||
hashEarliestSaplingRoot=left_child.sapling_root,
|
||||
hashLatestSaplingRoot=right_child.sapling_root,
|
||||
nSubTreeTotalWork=left_child.nSubTreeTotalWork + right_child.nSubTreeTotalWork,
|
||||
|
|
@ -422,6 +425,7 @@ With each new block :math:`B_n`, we append a new MMR leaf node corresponding to
|
|||
|
||||
# Get number of leaves.
|
||||
leaves = latest_height - (earliest_height - 1)
|
||||
assert(leaves > 0)
|
||||
|
||||
# Check if the number of leaves is a power of two.
|
||||
if (leaves & (leaves - 1)) == 0:
|
||||
|
|
@ -564,8 +568,8 @@ paper.
|
|||
|
||||
- ``nEarliestTimestamp``
|
||||
- ``nLatestTimestamp``
|
||||
- ``nEarliestTarget``
|
||||
- ``nLatestTarget``
|
||||
- ``nEarliestTargetBits``
|
||||
- ``nLatestTargetBits``
|
||||
- ``nEarliestHeight``
|
||||
- ``nLatestHeight``
|
||||
- ``nSubTreeTotalWork``
|
||||
|
|
@ -697,7 +701,6 @@ closely in chain models with rapidly adjusting difficulty.
|
|||
Additional Reading
|
||||
==================
|
||||
|
||||
- `Bitcoin difficulty calculation <https://en.bitcoin.it/wiki/Difficulty>`_
|
||||
- `Flyclient enabled geth fork by FlyClient authors <https://github.com/mahdiz/flyeth>`_
|
||||
- `ECIP-1055: Succinct PoW Using Merkle Mountain Ranges <https://github.com/etclabscore/ECIPs/pull/11/files?short_path=44c106e#diff-44c106ea0ef54fab09596596934d3d15>`_
|
||||
- `Grin project MMR implementation in Rust <https://github.com/mimblewimble/grin/tree/milestone/2.0.0/core/src/core>`_
|
||||
|
|
@ -706,7 +709,7 @@ Additional Reading
|
|||
- `Mimblewimble MMR docs <https://github.com/mimblewimble/grin/blob/master/doc/mmr.md>`_
|
||||
- `MMR Python implementation <https://github.com/proofchains/python-proofmarshal/blob/master/proofmarshal/mmr.py>`_
|
||||
- `Tari MMR documentation <https://docs.rs/merklemountainrange/0.0.1/src/merklemountainrange/lib.rs.html#23-183>`_
|
||||
- `Zcash Protocol Specification, Version 2018.0-beta-37 [Overwinter+Sapling] <https://github.com/zcash/zips/blob/master/protocol/protocol.pdf>`_
|
||||
- `Zcash Protocol Specification, Version 2020.1.1 [Overwinter+Sapling+Blossom] or later <https://zips.z.cash/protocol/protocol.pdf>`_
|
||||
- `opentimestamps-server Merkle Mountain Range documentation <https://github.com/opentimestamps/opentimestamps-server/blob/master/doc/merkle-mountain-range.md>`_
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue