MIME-Version: 1.0
From: Jim Posen <jim.posen@gmail.com>
Date: Tue, 27 Mar 2018 16:31:58 -0700
Message-ID: <CADZtCSg7+x-sg-ysgacXobRexOVwT+k9fr6a9S-6xU2w8f8m3A@mail.gmail.com>
To: Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
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Subject: [bitcoin-dev] Optimized Header Sync
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Based on some ideas that were thrown around in this thread (
https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2017-December/015385.html),
I have been working on a P2P extension that will allow faster header sync
mechanisms. The one-sentence summary is that by encoding headers more
efficiently (eg. omitting prev_hash) and downloading evenly spaced
checkpoints throughout history (say every 1,000th) from all peers first, we
could speed up header sync, which would be a huge improvement for light
clients. Here is a draft of the BIP:
https://github.com/jimpo/bips/blob/headers-sync/headersv2.mediawiki. The
full text is below as well.

I'd love to hear any feedback people have.

----------------------------------------------------------

== Abstract ==

This BIP describes a P2P network extension enabling faster, more
reliable methods for syncing the block header chain. New P2P messages
are proposed as more efficient replacements for
<code>getheaders</code> and <code>headers</code> during initial block
download. The proposed header download protocol reduces bandwidth
usage by ~40%-50% and supports downloading headers ranges from
multiple peers in parallel, which is not possible with the current
mechanism. This also enables sync strategies with better resistance to
denial-of-service attacks.

== Motivation ==

Since 2015, optimized Bitcoin clients fetch all block headers before
blocks themselves in order to avoid downloading ones that are not part
of the most work chain. The protocol currently in use for fetching
headers leaves room for further optimization, specifically by
compressing header data and downloading more headers
simulaneously<ref>https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2017-December/015385.html</ref>.
Any savings here should have a large impact given that both full nodes
and light clients must sync the header chain as a first step, and that
the time to validate and index the headers is negligible compared to
the time spent downloading them from the network. Furthermore, some
current implementations of headers syncing rely on preconfigured
checkpoints to discourage attackers attempting to fill up a victim's
disk space with low-work headers. The proposed messages enable sync
strategies that are resilient against these types of attacks. The P2P
messages are designed to be flexible, supporting multiple header sync
strategies and leaving room for future innovations, while also
compact.

== Definitions ==

''double-SHA256'' is a hash algorithm defined by two invocations of
SHA-256: <code>double-SHA256(x) = SHA256(SHA256(x))</code>.

== Specification ==

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in RFC 2119.

=== New Structures ===

==== Compressed Headers ====

Bitcoin headers are serialized by default in 80 bytes as follows:

{| class="wikitable"
! Field Name
! Data Type
! Byte Size
! Description
|-
| version
| int32_t
| 4
| Block version information
|-
| prev_block
| uint256
| 32
| The hash of the previous block
|-
| merkle_root
| uint256
| 32
| The root hash of the transaction Merkle tree
|-
| timestamp
| uint32_t
| 4
| A Unix timestamp of the block creation time, as reported by the miner
|-
| bits
| uint32_t
| 4
| The calculated difficulty target for this block
|-
| nonce
| uint32_t
| 4
| A nonce that is set such that the header's hash matches the difficulty target
|}

When deserializing a correctly-formed sequence of block headers
encoded in this way, it can be noted that:

* The prev_block field should always match the double-SHA256 hash of
the previous header, making it redundant
* According to Bitcoin consensus rules, the bits field only changes
every 2016 blocks
* The version often matches that of a recent ancestor block
* The timestamp is often a small delta from the preceding header's timestamp

To take advantage of these possible savings, this document defines a
variable-sized ''compressed encoding'' of block headers that occur in
a range. Note that no savings are possible when serializing a single
header; it should only be used for vectors of sequential headers. The
full headers are reconstructed using data from previous headers in the
range. The serialization begins with an ''encoding indicator'', which
is a bitfield specifying how each field is serialized. The bits of the
indicator have the following semantics:

{| class="wikitable"
! Bit Index
! Reconstruction
! Description
|-
| 0
| <code>prev_block[i] = DSHA256(header[i-1])</code>
| The prev_block field is ommitted and assigned to the double-SHA256
hash of the previous uncompressed header.
|-
| 1
| <code>nbits[i] = nbits[i-1]</code>
| The nbits field is omitted and matches that of the previous header.
|-
| 2
| <code>timestamp[i] = timestamp[i-1] + value</code>
| The timestamp is replaced by a 2-byte signed short int, representing
an offset from the previous block's timestamp
|-
| 3
|
| Interpreted along with bits 4 & 5.
|-
| 4
|
| Interpreted along with bits 3 & 5.
|-
| 5
| <code>version[i] = version[i - ((bit[3] << 2) + (bit[4] << 1) +
bit[5])]</code>
| Bits 3, 4, and 5 are first interpreted as a 3-bit offset, with bit
index 3 as the most significant and bit index 5 as the least
significant. If the offset is non-zero, the version field is omitted
and assigned to the version of the block at the offset number of
blocks prior.
|-
| 6
|
| Reserved.
|-
| 7
|
| Reserved. May be used in a future encoding version to signal another
indicator byte.
|}

The compressed header format is versioned by a 256-bit unsigned
integer. This document defines version 0.

==== VarInt ====

''VarInt'' is a variable-length unsigned integer encoding that
supports a greater range of numbers than the standard ''CompactSize''.
This encoding was introduced at the database layer in Bitcoin
Core<ref>https://github.com/bitcoin/bitcoin/commit/4d6144f97faf9d2a6c89f41d7d2360f21f0b71e2</ref>
in 2012, but is new to the Bitcoin P2P layer.

This definition is per the code comments in Bitcoin Core written by
Pieter Wuille:

<pre>
Variable-length integers: bytes are a MSB base-128 encoding of the number.
The high bit in each byte signifies whether another digit follows. To make
the encoding is one-to-one, one is subtracted from all but the last digit.
Thus, the byte sequence a[] with length len, where all but the last byte
has bit 128 set, encodes the number:

  (a[len-1] & 0x7F) + sum(i=1..len-1, 128^i*((a[len-i-1] & 0x7F)+1))

Properties:
* Very small (0-127: 1 byte, 128-16511: 2 bytes, 16512-2113663: 3 bytes)
* Every integer has exactly one encoding
* Encoding does not depend on size of original integer type
* No redundancy: every (infinite) byte sequence corresponds to a list
  of encoded integers.

0:         [0x00]  256:        [0x81 0x00]
1:         [0x01]  16383:      [0xFE 0x7F]
127:       [0x7F]  16384:      [0xFF 0x00]
128:  [0x80 0x00]  16511: [0x80 0xFF 0x7F]
255:  [0x80 0x7F]  65535: [0x82 0xFD 0x7F]
2^32:           [0x8E 0xFE 0xFE 0xFF 0x00]
</pre>

==== Checkpoints ====

A ''checkpoint'' is defined for a block as a tuple of its hash and the
chain work:

{| class="wikitable"
! Field Name
! Data Type
! Byte Size
! Description
|-
| block_hash
| uint256
| 32
| The hash of the block
|-
| chain_work
| VarInt
| Variable(1-20)
| A delta between the total work in the chain at the checkpoint block
and a previous checkpoint, determined by context
|}

=== Service Bit ===

This BIP allocates a new service bit:

{| class="wikitable"
|-
| NODE_HEADERS_V2
| <code>1 << ?</code>
| If enabled, the node MUST respond to <code>getcheckpts</code> and
<code>getheaders2</code> queries
|}

=== New Messages ===

==== getcheckpts ====
<code>getcheckpts</code> is used to request block headers at a
specified distance from each other which serve as checkpoints during
parallel header download. The message contains the following fields:

{| class="wikitable"
! Field Name
! Data Type
! Byte Size
! Description
|-
| block_locator
| uint256[]
| Variable
| A vector of block hashes in descending order by height used to
identify the header chain of the requesting node
|-
| interval
| uint32_t
| 4
| The distance in block height between requested block hashes
|}

# Nodes SHOULD NOT send <code>getcheckpts</code> unless the peer has
set the <code>NODE_HEADERS_V2</code> service bit
# The hashes in <code>block_locator</code> MUST be in descending order
by block height
# The block locator SHOULD be generated as it is in
<code>getheaders</code> requests
# The receiving node MUST respond to valid requests with a
<code>checkpts</code> response where the interval is the same as in
the request and the first checkpoint hash matches the first common
block hash in the block locator

==== checkpts ====
<code>checkpts</code> is sent in response to <code>getcheckpts</code>,
listing block hashes at the specified interval. The message contains
the following fields:

{| class="wikitable"
! Field Name
! Data Type
! Byte Size
! Description
|-
| start_height
| uint32_t
| 4
| The height of the first block in the active chain matching the
request's block locator
|-
| end_height
| uint32_t
| 4
| The height of the last block in the active chain
|-
| start_checkpoint
| Checkpoint
| 48
| The checkpoint structure for the block in the active chain at height
start_height
|-
| end_checkpoint
| Checkpoint
| 48
| The checkpoint structure for the block in the active chain at height
end_height
|-
| interval
| uint32_t
| 4
| The distance in block height between checkpoints
|-
| checkpoints_length
| CompactSize
| Variable(1-5)
| The number of checkpoints to follow
|-
| checkpoints
| Checkpoint[]
| checkoints_length * Variable(33-52)
| The checkpoints as specified below
|}

# The interval SHOULD match the field in the <code>getcheckpts</code> request
# The start_checkpoint SHOULD correspond to the first block hash in
the locator from the <code>getcheckpts</code> request that is part of
the active chain
# The end_checkpoint SHOULD correspond to the tip of the node's active chain
# The start_height MOST be set to the block height of the start_checkpoint
# The end_height MOST be set to the block height of the end_checkpoint
# If the interval is zero, the checkpoints vector MUST be empty
# If the interval is non-zero, checkpoints MUST correspond to blocks
on the active chain between the start_checkpoint and the
end_checkpoint (exclusive), where the difference in block height
between each entry and the previous one is equal to the interval
# The checkpoints_length MUST be less than or equal to 2,000
# The node SHOULD include as many checkpoints on its active chain as
are available, up to the limit of 2,000
# The chain_work field in the first checkpoint MUST be the total work
in the chain ending at that block
# The chain_work field in each subsequent checkpoint MUST be the
difference in chain work between that block and the previous
checkpoint
# The chain_work field in each checkpoint MUST be a properly-encoded
VarInt, not exceeding 20 bytes

==== getheaders2 ====
<code>getheaders2</code> is used to request compressed headers for a
range of blocks. The message contains the following fields:

{| class="wikitable"
! Field Name
! Data Type
! Byte Size
! Description
|-
| max_version
| uint8_t
| 1
| The maximum supported encoding version of the headers
|-
| flags
| uint8_t
| 1
| A bitfield of message encoding flags
|-
| start_height
| uint32_t
| 4
| The height of the first block header in the requested range
|-
| end_hash
| uint256
| 32
| The hash of the last block header in the requested range
|}

# Nodes SHOULD NOT send <code>getheaders2</code> unless the peer has
set the <code>NODE_HEADERS_V2</code> service bit
# The height of the block with hash end_hash MUST be greater than or
equal to start_height, and the difference MUST be strictly less than
3,000
# The end_hash SHOULD match one in a previously received
<code>checkpts</code> message, otherwise the receiving node MAY
disconnect
# The 0th bit (least significant order) of the flags field MAY be set
to request the coinbase transaction and merkle branch for the block at
height start_height

==== headers2 ====
<code>headers2</code> is sent in response to <code>getheaders2</code>,
listing the compressed headers in the requested range. The message
contains the following fields:

{| class="wikitable"
! Field Name
! Data Type
! Byte Size
! Description
|-
| version
| uint8_t
| 1
| The encoding version of the headers
|-
| flags
| uint8_t
| 1
| A bitfield of message encoding flags
|-
| start_height
| uint32_t
| 4
| The height of the first block header returned
|-
| headers_length
| CompactSize
| 1-3
| The number of block headers to follow
|-
| headers
| CompressedHeader[]
| Variable
| The compressed block headers
|-
| start_block_coinbase_tx
| CTransaction
| Variable
| The coinbase transaction in the block at start_height
|-
| start_block_coinbase_branch
| uint256[]
| Variable
| A merkle branch linking the coinbase transaction in the block at
start_height to its header
|}

# The version MUST be less than or equal to the max_version field of
the <code>getheaders2</code> request
# Any bits set in the flags field of the <code>getheaders2</code>
request MAY be set in the response field
# Any bits not set in the flags field of the <code>getheaders2</code>
request MUST NOT be set in the response field
# The first header MUST be encoded with a 0-byte indicator (ie. the
header is uncompressed)
# start_height MUST be set to the block height of the first header
# The hash of the last block SHOULD equal the end_hash of the
<code>getheaders2</code> request, ''even if the block is no longer
part of the active chain''
# The length of the headers vector MUST be less than or equal to 3,000
# The headers MUST be sequential in order of height, with each header
a successor of the previous one
# Each header SHOULD be optimally compressed
# The start_block_coinbase_tx should be the serialized coinbase
transaction in the block corresponding to the first header
# The start_block_coinbase_branch should be a vector of
right-hand-side hashes in the merkle branch linking the coinbase
transaction to the first header, in order from bottom of the tree to
top
# If the 0th bit (least significant order) of the flags field is
unset, the start_block_coinbase_tx and start_block_coinbase_branch
fields MUST be omitted

=== Sync Strategies ===

The general header sync protocol for clients now is to first request
checkpoints from all peers with <code>getcheckpts</code>, then decide
which peers to fetch ranges of headers from and download them with
<code>getheaders2</code>.

==== Forward Sequential Syncing ====

Similar to the current sync protocol, a client may choose one peer to
download headers from, then fetch them in forward sequential order.
Once this peer is out of headers, the client performs the same routine
with any peers offering more headers.

With this strategy, the client is able to fully validate the block
headers in order and abort if the peer serves an invalid one. On the
other hand, the peer may be able to serve a longer, lower-work chain
than the global active chain, wasting the client's time, memory, and
storage space.

==== Parallel Header Download ====

In order to increase the throughput of header downloads, a node may
download multiple header ranges in parallel from all peers serving the
same checkpoints, then validate them in sequential order.

==== Random Sampling Proof-of-Work  ====

Similar the FlyClient<ref>https://www.youtube.com/watch?time_continue=8400&v=BPNs9EVxWrA</ref>
header download protocol, clients can select the peer claiming the
greatest total work chain and use random sampling to efficiently
determine if the peer is likely to be reporting its chain work
honestly.

The client treats the checkpoint message as a commitment to chain work
of intermediate ranges of headers, the client then randomly samples
ranges of headers weighted by total work to determine whether the
total chain work is valid before downloading all headers. To defend
against malicious peers attempting to reuse earlier headers later in
the chain to fake greater total work, the client should check the
block height in the coinbase transaction for all headers after the BIP
34 activation height. If the peer is found to be dishonest, they can
be banned before the client downloads too many headers, otherwise the
client chooses this as the primary sync peer for forward sequential
sync or parallel download.

== Rationale ==

* '''Why include the coinbase transaction in the headers messages?'''
The primary reason is that after BIP
34<ref>https://github.com/bitcoin/bips/blob/master/bip-0034.mediawiki</ref>
activation at block height 227,835, coinbase transactions constitute
cryptographic commitments to a block's height in the chain, which
mitigates certain attacks during header sync. Furthermore, the
<code>getheaders2</code> message can be used as a simple way of
requesting a coinbase transaction for a single header, which may be
independently useful.

* '''Why not omit nBits entirely?''' The compression is designed to
permit full decompression of all headers in a <code>headers2</code>
message ''without'' requiring any other chain context. This is
desirable so that proofs of work may be validated for arbitrary header
ranges. While nBits can be computed knowing previous headers, this
requires block headers that may not be sent in the same message.

== Compatibility ==

This is backwards compatible, as it defines new P2P messages which are
available if a service bit is signaled. There are no changes to
consensus rules.

== Acknowledgements ==

Thanks to Gregory Maxwell for suggestions on the compressed header
encoding and the DOS-resistant sync strategies. Thanks to Suhas
Daftuar for helpful discussions.

Credit for the VarInt encoding goes to Pieter Wuille.

--000000000000193c7705686d4c09
Content-Type: text/html; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable

<div dir=3D"ltr">Based on some ideas that were thrown around in this thread=
 (<a href=3D"https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2017-D=
ecember/015385.html">https://lists.linuxfoundation.org/pipermail/bitcoin-de=
v/2017-December/015385.html</a>), I have been working on a P2P extension th=
at will allow faster header sync mechanisms. The one-sentence summary is th=
at by encoding headers more efficiently (eg. omitting prev_hash) and downlo=
ading evenly spaced checkpoints throughout history (say every 1,000th) from=
 all peers first, we could speed up header sync, which would be a huge impr=
ovement for light clients.=C2=A0Here is a draft of the BIP:=C2=A0<a href=3D=
"https://github.com/jimpo/bips/blob/headers-sync/headersv2.mediawiki">https=
://github.com/jimpo/bips/blob/headers-sync/headersv2.mediawiki</a>. The ful=
l text is below as well.<div><div><br></div><div>I&#39;d love to hear any f=
eedback people have.</div></div><div><br></div><div>-----------------------=
-----------------------------------</div><div><br></div><div><pre style=3D"=
color:rgb(0,0,0);font-style:normal;font-variant-ligatures:normal;font-varia=
nt-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-=
indent:0px;text-transform:none;word-spacing:0px;text-decoration-style:initi=
al;text-decoration-color:initial;word-wrap:break-word;white-space:pre-wrap"=
>=3D=3D Abstract =3D=3D

This BIP describes a P2P network extension enabling faster, more reliable m=
ethods for syncing the block header chain. New P2P messages are proposed as=
 more efficient replacements for &lt;code&gt;getheaders&lt;/code&gt; and &l=
t;code&gt;headers&lt;/code&gt; during initial block download. The proposed =
header download protocol reduces bandwidth usage by ~40%-50% and supports d=
ownloading headers ranges from multiple peers in parallel, which is not pos=
sible with the current mechanism. This also enables sync strategies with be=
tter resistance to denial-of-service attacks.

=3D=3D Motivation =3D=3D

Since 2015, optimized Bitcoin clients fetch all block headers before blocks=
 themselves in order to avoid downloading ones that are not part of the mos=
t work chain. The protocol currently in use for fetching headers leaves roo=
m for further optimization, specifically by compressing header data and dow=
nloading more headers simulaneously&lt;ref&gt;<a href=3D"https://lists.linu=
xfoundation.org/pipermail/bitcoin-dev/2017-December/015385.html">https://li=
sts.linuxfoundation.org/pipermail/bitcoin-dev/2017-December/015385.html</a>=
&lt;/ref&gt;. Any savings here should have a large impact given that both f=
ull nodes and light clients must sync the header chain as a first step, and=
 that the time to validate and index the headers is negligible compared to =
the time spent downloading them from the network. Furthermore, some current=
 implementations of headers syncing rely on preconfigured checkpoints to di=
scourage attackers attempting to fill up a victim&#39;s disk space with low=
-work headers. The proposed messages enable sync strategies that are resili=
ent against these types of attacks. The P2P messages are designed to be fle=
xible, supporting multiple header sync strategies and leaving room for futu=
re innovations, while also compact.

=3D=3D Definitions =3D=3D

&#39;&#39;double-SHA256&#39;&#39; is a hash algorithm defined by two invoca=
tions of SHA-256: &lt;code&gt;double-SHA256(x) =3D SHA256(SHA256(x))&lt;/co=
de&gt;.

=3D=3D Specification =3D=3D

The key words &quot;MUST&quot;, &quot;MUST NOT&quot;, &quot;REQUIRED&quot;,=
 &quot;SHALL&quot;, &quot;SHALL NOT&quot;, &quot;SHOULD&quot;, &quot;SHOULD=
 NOT&quot;, &quot;RECOMMENDED&quot;, &quot;MAY&quot;, and &quot;OPTIONAL&qu=
ot; in this document are to be interpreted as described in RFC 2119.

=3D=3D=3D New Structures =3D=3D=3D

=3D=3D=3D=3D Compressed Headers =3D=3D=3D=3D

Bitcoin headers are serialized by default in 80 bytes as follows:

{| class=3D&quot;wikitable&quot;
! Field Name
! Data Type
! Byte Size
! Description
|-
| version
| int32_t
| 4
| Block version information
|-
| prev_block
| uint256
| 32
| The hash of the previous block
|-
| merkle_root
| uint256
| 32
| The root hash of the transaction Merkle tree
|-
| timestamp
| uint32_t
| 4
| A Unix timestamp of the block creation time, as reported by the miner
|-
| bits
| uint32_t
| 4
| The calculated difficulty target for this block
|-
| nonce
| uint32_t
| 4
| A nonce that is set such that the header&#39;s hash matches the difficult=
y target
|}

When deserializing a correctly-formed sequence of block headers encoded in =
this way, it can be noted that:

* The prev_block field should always match the double-SHA256 hash of the pr=
evious header, making it redundant
* According to Bitcoin consensus rules, the bits field only changes every 2=
016 blocks
* The version often matches that of a recent ancestor block
* The timestamp is often a small delta from the preceding header&#39;s time=
stamp

To take advantage of these possible savings, this document defines a variab=
le-sized &#39;&#39;compressed encoding&#39;&#39; of block headers that occu=
r in a range. Note that no savings are possible when serializing a single h=
eader; it should only be used for vectors of sequential headers. The full h=
eaders are reconstructed using data from previous headers in the range. The=
 serialization begins with an &#39;&#39;encoding indicator&#39;&#39;, which=
 is a bitfield specifying how each field is serialized. The bits of the ind=
icator have the following semantics:

{| class=3D&quot;wikitable&quot;
! Bit Index
! Reconstruction
! Description
|-
| 0
| &lt;code&gt;prev_block[i] =3D DSHA256(header[i-1])&lt;/code&gt;
| The prev_block field is ommitted and assigned to the double-SHA256 hash o=
f the previous uncompressed header.
|-
| 1
| &lt;code&gt;nbits[i] =3D nbits[i-1]&lt;/code&gt;
| The nbits field is omitted and matches that of the previous header.
|-
| 2
| &lt;code&gt;timestamp[i] =3D timestamp[i-1] + value&lt;/code&gt;
| The timestamp is replaced by a 2-byte signed short int, representing an o=
ffset from the previous block&#39;s timestamp
|-
| 3
|
| Interpreted along with bits 4 &amp; 5.
|-
| 4
|
| Interpreted along with bits 3 &amp; 5.
|-
| 5
| &lt;code&gt;version[i] =3D version[i - ((bit[3] &lt;&lt; 2) + (bit[4] &lt=
;&lt; 1) + bit[5])]&lt;/code&gt;
| Bits 3, 4, and 5 are first interpreted as a 3-bit offset, with bit index =
3 as the most significant and bit index 5 as the least significant. If the =
offset is non-zero, the version field is omitted and assigned to the versio=
n of the block at the offset number of blocks prior.
|-
| 6
|
| Reserved.
|-
| 7
|
| Reserved. May be used in a future encoding version to signal another indi=
cator byte.
|}

The compressed header format is versioned by a 256-bit unsigned integer. Th=
is document defines version 0.

=3D=3D=3D=3D VarInt =3D=3D=3D=3D

&#39;&#39;VarInt&#39;&#39; is a variable-length unsigned integer encoding t=
hat supports a greater range of numbers than the standard &#39;&#39;Compact=
Size&#39;&#39;. This encoding was introduced at the database layer in Bitco=
in Core&lt;ref&gt;<a href=3D"https://github.com/bitcoin/bitcoin/commit/4d61=
44f97faf9d2a6c89f41d7d2360f21f0b71e2">https://github.com/bitcoin/bitcoin/co=
mmit/4d6144f97faf9d2a6c89f41d7d2360f21f0b71e2</a>&lt;/ref&gt; in 2012, but =
is new to the Bitcoin P2P layer.

This definition is per the code comments in Bitcoin Core written by Pieter =
Wuille:

&lt;pre&gt;
Variable-length integers: bytes are a MSB base-128 encoding of the number.
The high bit in each byte signifies whether another digit follows. To make
the encoding is one-to-one, one is subtracted from all but the last digit.
Thus, the byte sequence a[] with length len, where all but the last byte
has bit 128 set, encodes the number:

  (a[len-1] &amp; 0x7F) + sum(i=3D1..len-1, 128^i*((a[len-i-1] &amp; 0x7F)+=
1))

Properties:
* Very small (0-127: 1 byte, 128-16511: 2 bytes, 16512-2113663: 3 bytes)
* Every integer has exactly one encoding
* Encoding does not depend on size of original integer type
* No redundancy: every (infinite) byte sequence corresponds to a list
  of encoded integers.

0:         [0x00]  256:        [0x81 0x00]
1:         [0x01]  16383:      [0xFE 0x7F]
127:       [0x7F]  16384:      [0xFF 0x00]
128:  [0x80 0x00]  16511: [0x80 0xFF 0x7F]
255:  [0x80 0x7F]  65535: [0x82 0xFD 0x7F]
2^32:           [0x8E 0xFE 0xFE 0xFF 0x00]
&lt;/pre&gt;

=3D=3D=3D=3D Checkpoints =3D=3D=3D=3D

A &#39;&#39;checkpoint&#39;&#39; is defined for a block as a tuple of its h=
ash and the chain work:

{| class=3D&quot;wikitable&quot;
! Field Name
! Data Type
! Byte Size
! Description
|-
| block_hash
| uint256
| 32
| The hash of the block
|-
| chain_work
| VarInt
| Variable(1-20)
| A delta between the total work in the chain at the checkpoint block and a=
 previous checkpoint, determined by context
|}

=3D=3D=3D Service Bit =3D=3D=3D

This BIP allocates a new service bit:

{| class=3D&quot;wikitable&quot;
|-
| NODE_HEADERS_V2
| &lt;code&gt;1 &lt;&lt; ?&lt;/code&gt;
| If enabled, the node MUST respond to &lt;code&gt;getcheckpts&lt;/code&gt;=
 and &lt;code&gt;getheaders2&lt;/code&gt; queries
|}

=3D=3D=3D New Messages =3D=3D=3D

=3D=3D=3D=3D getcheckpts =3D=3D=3D=3D
&lt;code&gt;getcheckpts&lt;/code&gt; is used to request block headers at a =
specified distance from each other which serve as checkpoints during parall=
el header download. The message contains the following fields:

{| class=3D&quot;wikitable&quot;
! Field Name
! Data Type
! Byte Size
! Description
|-
| block_locator
| uint256[]
| Variable
| A vector of block hashes in descending order by height used to identify t=
he header chain of the requesting node
|-
| interval
| uint32_t
| 4
| The distance in block height between requested block hashes
|}

# Nodes SHOULD NOT send &lt;code&gt;getcheckpts&lt;/code&gt; unless the pee=
r has set the &lt;code&gt;NODE_HEADERS_V2&lt;/code&gt; service bit
# The hashes in &lt;code&gt;block_locator&lt;/code&gt; MUST be in descendin=
g order by block height
# The block locator SHOULD be generated as it is in &lt;code&gt;getheaders&=
lt;/code&gt; requests
# The receiving node MUST respond to valid requests with a &lt;code&gt;chec=
kpts&lt;/code&gt; response where the interval is the same as in the request=
 and the first checkpoint hash matches the first common block hash in the b=
lock locator

=3D=3D=3D=3D checkpts =3D=3D=3D=3D
&lt;code&gt;checkpts&lt;/code&gt; is sent in response to &lt;code&gt;getche=
ckpts&lt;/code&gt;, listing block hashes at the specified interval. The mes=
sage contains the following fields:

{| class=3D&quot;wikitable&quot;
! Field Name
! Data Type
! Byte Size
! Description
|-
| start_height
| uint32_t
| 4
| The height of the first block in the active chain matching the request=
9;s block locator
|-
| end_height
| uint32_t
| 4
| The height of the last block in the active chain
|-
| start_checkpoint
| Checkpoint
| 48
| The checkpoint structure for the block in the active chain at height star=
t_height
|-
| end_checkpoint
| Checkpoint
| 48
| The checkpoint structure for the block in the active chain at height end_=
height
|-
| interval
| uint32_t
| 4
| The distance in block height between checkpoints
|-
| checkpoints_length
| CompactSize
| Variable(1-5)
| The number of checkpoints to follow
|-
| checkpoints
| Checkpoint[]
| checkoints_length * Variable(33-52)
| The checkpoints as specified below
|}

# The interval SHOULD match the field in the &lt;code&gt;getcheckpts&lt;/co=
de&gt; request
# The start_checkpoint SHOULD correspond to the first block hash in the loc=
ator from the &lt;code&gt;getcheckpts&lt;/code&gt; request that is part of =
the active chain
# The end_checkpoint SHOULD correspond to the tip of the node&#39;s active =
chain
# The start_height MOST be set to the block height of the start_checkpoint
# The end_height MOST be set to the block height of the end_checkpoint
# If the interval is zero, the checkpoints vector MUST be empty
# If the interval is non-zero, checkpoints MUST correspond to blocks on the=
 active chain between the start_checkpoint and the end_checkpoint (exclusiv=
e), where the difference in block height between each entry and the previou=
s one is equal to the interval
# The checkpoints_length MUST be less than or equal to 2,000
# The node SHOULD include as many checkpoints on its active chain as are av=
ailable, up to the limit of 2,000
# The chain_work field in the first checkpoint MUST be the total work in th=
e chain ending at that block
# The chain_work field in each subsequent checkpoint MUST be the difference=
 in chain work between that block and the previous checkpoint
# The chain_work field in each checkpoint MUST be a properly-encoded VarInt=
, not exceeding 20 bytes

=3D=3D=3D=3D getheaders2 =3D=3D=3D=3D
&lt;code&gt;getheaders2&lt;/code&gt; is used to request compressed headers =
for a range of blocks. The message contains the following fields:

{| class=3D&quot;wikitable&quot;
! Field Name
! Data Type
! Byte Size
! Description
|-
| max_version
| uint8_t
| 1
| The maximum supported encoding version of the headers
|-
| flags
| uint8_t
| 1
| A bitfield of message encoding flags
|-
| start_height
| uint32_t
| 4
| The height of the first block header in the requested range
|-
| end_hash
| uint256
| 32
| The hash of the last block header in the requested range
|}

# Nodes SHOULD NOT send &lt;code&gt;getheaders2&lt;/code&gt; unless the pee=
r has set the &lt;code&gt;NODE_HEADERS_V2&lt;/code&gt; service bit
# The height of the block with hash end_hash MUST be greater than or equal =
to start_height, and the difference MUST be strictly less than 3,000
# The end_hash SHOULD match one in a previously received &lt;code&gt;checkp=
ts&lt;/code&gt; message, otherwise the receiving node MAY disconnect
# The 0th bit (least significant order) of the flags field MAY be set to re=
quest the coinbase transaction and merkle branch for the block at height st=
art_height

=3D=3D=3D=3D headers2 =3D=3D=3D=3D
&lt;code&gt;headers2&lt;/code&gt; is sent in response to &lt;code&gt;gethea=
ders2&lt;/code&gt;, listing the compressed headers in the requested range. =
The message contains the following fields:

{| class=3D&quot;wikitable&quot;
! Field Name
! Data Type
! Byte Size
! Description
|-
| version
| uint8_t
| 1
| The encoding version of the headers
|-
| flags
| uint8_t
| 1
| A bitfield of message encoding flags
|-
| start_height
| uint32_t
| 4
| The height of the first block header returned
|-
| headers_length
| CompactSize
| 1-3
| The number of block headers to follow
|-
| headers
| CompressedHeader[]
| Variable
| The compressed block headers
|-
| start_block_coinbase_tx
| CTransaction
| Variable
| The coinbase transaction in the block at start_height
|-
| start_block_coinbase_branch
| uint256[]
| Variable
| A merkle branch linking the coinbase transaction in the block at start_he=
ight to its header
|}

# The version MUST be less than or equal to the max_version field of the &l=
t;code&gt;getheaders2&lt;/code&gt; request
# Any bits set in the flags field of the &lt;code&gt;getheaders2&lt;/code&g=
t; request MAY be set in the response field
# Any bits not set in the flags field of the &lt;code&gt;getheaders2&lt;/co=
de&gt; request MUST NOT be set in the response field
# The first header MUST be encoded with a 0-byte indicator (ie. the header =
is uncompressed)
# start_height MUST be set to the block height of the first header
# The hash of the last block SHOULD equal the end_hash of the &lt;code&gt;g=
etheaders2&lt;/code&gt; request, &#39;&#39;even if the block is no longer p=
art of the active chain&#39;&#39;
# The length of the headers vector MUST be less than or equal to 3,000
# The headers MUST be sequential in order of height, with each header a suc=
cessor of the previous one
# Each header SHOULD be optimally compressed
# The start_block_coinbase_tx should be the serialized coinbase transaction=
 in the block corresponding to the first header
# The start_block_coinbase_branch should be a vector of right-hand-side has=
hes in the merkle branch linking the coinbase transaction to the first head=
er, in order from bottom of the tree to top
# If the 0th bit (least significant order) of the flags field is unset, the=
 start_block_coinbase_tx and start_block_coinbase_branch fields MUST be omi=
tted

=3D=3D=3D Sync Strategies =3D=3D=3D

The general header sync protocol for clients now is to first request checkp=
oints from all peers with &lt;code&gt;getcheckpts&lt;/code&gt;, then decide=
 which peers to fetch ranges of headers from and download them with &lt;cod=
e&gt;getheaders2&lt;/code&gt;.

=3D=3D=3D=3D Forward Sequential Syncing =3D=3D=3D=3D

Similar to the current sync protocol, a client may choose one peer to downl=
oad headers from, then fetch them in forward sequential order. Once this pe=
er is out of headers, the client performs the same routine with any peers o=
ffering more headers.

With this strategy, the client is able to fully validate the block headers =
in order and abort if the peer serves an invalid one. On the other hand, th=
e peer may be able to serve a longer, lower-work chain than the global acti=
ve chain, wasting the client&#39;s time, memory, and storage space.

=3D=3D=3D=3D Parallel Header Download =3D=3D=3D=3D

In order to increase the throughput of header downloads, a node may downloa=
d multiple header ranges in parallel from all peers serving the same checkp=
oints, then validate them in sequential order.

=3D=3D=3D=3D Random Sampling Proof-of-Work  =3D=3D=3D=3D

Similar the FlyClient&lt;ref&gt;<a href=3D"https://www.youtube.com/watch?ti=
me_continue=3D8400&amp;v=3DBPNs9EVxWrA">https://www.youtube.com/watch?time_=
continue=3D8400&amp;v=3DBPNs9EVxWrA</a>&lt;/ref&gt; header download protoco=
l, clients can select the peer claiming the greatest total work chain and u=
se random sampling to efficiently determine if the peer is likely to be rep=
orting its chain work honestly.

The client treats the checkpoint message as a commitment to chain work of i=
ntermediate ranges of headers, the client then randomly samples ranges of h=
eaders weighted by total work to determine whether the total chain work is =
valid before downloading all headers. To defend against malicious peers att=
empting to reuse earlier headers later in the chain to fake greater total w=
ork, the client should check the block height in the coinbase transaction f=
or all headers after the BIP 34 activation height. If the peer is found to =
be dishonest, they can be banned before the client downloads too many heade=
rs, otherwise the client chooses this as the primary sync peer for forward =
sequential sync or parallel download.

=3D=3D Rationale =3D=3D

* &#39;&#39;&#39;Why include the coinbase transaction in the headers messag=
es?&#39;&#39;&#39; The primary reason is that after BIP 34&lt;ref&gt;<a hre=
f=3D"https://github.com/bitcoin/bips/blob/master/bip-0034.mediawiki">https:=
//github.com/bitcoin/bips/blob/master/bip-0034.mediawiki</a>&lt;/ref&gt; ac=
tivation at block height 227,835, coinbase transactions constitute cryptogr=
aphic commitments to a block&#39;s height in the chain, which mitigates cer=
tain attacks during header sync. Furthermore, the &lt;code&gt;getheaders2&l=
t;/code&gt; message can be used as a simple way of requesting a coinbase tr=
ansaction for a single header, which may be independently useful.

* &#39;&#39;&#39;Why not omit nBits entirely?&#39;&#39;&#39; The compressio=
n is designed to permit full decompression of all headers in a &lt;code&gt;=
headers2&lt;/code&gt; message &#39;&#39;without&#39;&#39; requiring any oth=
er chain context. This is desirable so that proofs of work may be validated=
 for arbitrary header ranges. While nBits can be computed knowing previous =
headers, this requires block headers that may not be sent in the same messa=
ge.

=3D=3D Compatibility =3D=3D

This is backwards compatible, as it defines new P2P messages which are avai=
lable if a service bit is signaled. There are no changes to consensus rules=
.

=3D=3D Acknowledgements =3D=3D

Thanks to Gregory Maxwell for suggestions on the compressed header encoding=
 and the DOS-resistant sync strategies. Thanks to Suhas Daftuar for helpful=
 discussions.

Credit for the VarInt encoding goes to Pieter Wuille.</pre></div></div>

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