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ch-brontide: add initial draft of the brontide chapter
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= Brontide: Lightning's Encrypted Message Transport
== Intro
Unlike the vanilla Bitcoin P2P network, every node in the Lightning Network is
identified by a unique public key which serves as it identity. By default, this
public key is used to end-to-end encrypt _all_ communication within the
network. Encryption by default at the lowest level of the protocol ensures that
all messages are authenticated, are immune to man-in-the-middle attacks,
snooping by 3rd parties, and ensures privacy at the fundamental transport
level. In this chapter, we'll learn about the encryption protocol used by the
Lightning network in detail. Upon completion of this chapter, the reader will
be familiar with the state of the art in encrypted messaging protocols, as well
as the various properties such a protocol provides to the network. It's worth
mentioning that the core of the encrypted message transport is _agonstic_ to
its usage within the context of the Lightning Network. As a result, the
custom encrypted message transport Lightning uses, commonly referred to as
"Brontide" (more on that later) can be dropped into any context that requires
encrypted communication between two parties.
== The Channel Graph as Decentralized Public Key Infrastructure
As we learned in the chapter on multi-hop forwarding, very node has a long-term
identity that is used as the identifier for a vertex during path finding and
also used in the asymmetric cryptographic operations related to the creation of
onion encrypted routing packets. This public key, which serves as a node's
long-term identity is included in the DNS bootstrapping response, as well as
embedded within the Channel Graph. As a result, before a node attempts to
connect out to another node on the P2P network, it already knows the public key
of the node it wishes to connect to.
Additionally, if the node being connected to already h a series of public
channels within the graph, then the connecting node is able to further verify
the sanctity of the identity of the node. As the entire channel graph is fully
authenticated, one can view it as a sort of decentralized public key
infrastructure: in order to register a key, a public channel in the Bitcoin
blockchain must be opened, once a node no longer has any public channels, then
they've effectively been removed from the PKI.
As Lightning is a decentralized network, it's imperative that no one central
party is designated the power to provision a public key identity within the
network. In place of a central party, the Lightning Network uses the Bitcoin
blockchain as a sybil mitigation mechanism, as gaining an identity on the
network has a tangible cost: the fee needed to create a channel in the
blockchain, as well as the opportunity cost of the capital allocated to their
channels. In the process of essentially rolling a domain specific PKI, the
Lightning network is able to significantly simply its encrypted transport
protocol as it doesn't need to deal with all the complexities that come along
with TLS, the Transport Layer Security protocol.
== Why Not TLS?
Readers familiar with the TLS system may be wondering at this point: why wasn't
TLS used in spite of the drawbacks of the existing PKI system? It is indeed a
fact that "self signed certificates" can be used to effectively sidestep the
existing global PKI system by simply asserting to the identity of a given
public key amongst a set of peers. However, even with the existing PKI system
out of the way, TLS has several drawbacks that prompted the creators of the LN
to instead opt for a more compact custom encryption protocol.
To start with, TLS is a protocol that has been around for several decades and
as a result has evolved over time as new advances have been made in the space
of transport encryption. However, overtime this evolution has caused the
protocol to balloon in size and complexity. Over the past few decades several
vulnerabilities in TLS has been discovered, and patched with each evolution
further increasing the complexity of the protocol. As a result of the age of
the protocol several versions and iterations exist, meaning a client needs to
understand many of the prior iterations of the protocol in order to communicate
with a large portion of the public internet further increasing implementation
complexity.
In the past several memory safety vulnerabilities have been discovered in
widely used implementations of SSL/TLS. Packaging such a protocol within every
Lightning node would serve to increase the attack surface of nodes exposed to
to the public peer to peer network. In order to increase the security of the
network as a whole, and minimize exploitable attack surface, the creators of
the LN instead opted to adopt the Noise Protocol Framework. Noise as a protocol
internalizes several of the security and privacy lessons learned over time due
to continual scrutiny of the TLS protocol over decades. In a way, the existence
of Noise allows the community to effective "start over", with a more compact,
simplified protocol that retains all the added benefits of TLS.
== The Noise Protocol Framework
The Noise Protocol Framework is a modern, extensible, and flexible message
encryption protocol designed by the creators of the Signal protocol. The Signal
protocol is one of the most widely used message encryption protocols in the
world. It's used by both Signal and Whatsapp, which cumulatively are used by
over a billion people around the world. The Noise framework is the result of
decades of evolution both within academia as well as industry of message
encryption protocols. Lightning uses the Noise protocol framework to implement
a _message oriented_ encryption protocol used by all nodes to communicate with
each other.
A communication session using Noise has two distinct phases: the handshake
phase, and the messaging phase. Before two parties can communicate with each
other, they first need to arrive at a shared secret known only to them which
will be used to encrypt and authenticate messages sent to each other. A flavor
of an authenticated key agreement is used to arrive at a final shared key
between the tow parties. In the context of the Noise protocol, this
authenticated key agreement is referred to as a "handshake". Once that
handshake has been completed, both nodes can now being to send each other
encrypted messages. Each time peers need to connect, or reconnect to each
other, a fresh iteration of the handshake protocol is executed ensuring that
forward secrecy (leaking the key of a prior transcript doesn't compromise any
future transcripts) is achieved.
As the Noise protocol allows a protocol designer to drop choose from several
cryptographic primitives such as symmetric encryption and public key
cryptography, its customary that each flavor of the Noise protocol is referred
to by a unique name. In the spirit of "Noise", each flavor of the protocol
selects a name derived from some sort of "noise". In the context of the
Lightning Network, the flavor of Noise use will be referred to from here on as
"Brontide". A brontide is a low billowing noise, similar to what one would hear
during a thunderstorm when very far away.
=== Noise Protocol Handshakes
The Noise protocol is extremely flexible in that it advertises several
handshakes, each with different security and privacy properties for a would be
protocol implementer to select from. A deep exploration of each of the
handshakes, and their various trade-offs is out of the scope of this chapter.
With that said, the Lighting Network uses a specific handshake referred to as
`Noise_XK`. The unique property provided by this handshake is "identity
hiding": in order for a node to initiate a connection with another node, it
must first know it's public key. Mechanically, this means that the public key
of the responder is actually never transmitted during the context of the
handshake. Instead, a clever series of Elliptic-Curve Diffie-Hellman (ECDH) and
Message Authentication Code (MAC) checks are used to authenticate the
responder.
=== Handshake Notation & Protocol Flow
Each handshakes typically consist of several steps. At each step some
(possibly) encrypted material is sent to the opposite party, an ECDH (or
several) are performed, with the result of the handshake being "mixed" into a
protocol "transcript". This transcript serves to authenticate each step of the
protocol and helps thwart a flavor of main-man-in-the-middle attacks. At the
end of the handshake, two keys `ck` and `k` are produced which are used to
encrypt messages (`k`) as well as rotate keys (`ck`) throughout the lifetime of
the session.
In the context of a handshake, `s` is usually a long-term static public key.
Within Brontide, the public key crypto system used is an elliptic curve one,
instantiated with the `secp256k1` curve which is used elsewhere in Bitcoin.
Several ephemeral keys are generated throughout the handshake. We use `e` to
refer to a new ephemeral key. ECDH operations between two keys are notated as
the concatenation of two keys. As an example, `ee` represents an ECDH operation
between two ephemeral keys.
== Brontide: Lightning's P2P Encryption
=== High-Level Overview
Using the notation laid out earlier, we can succinctly describe the `Noise_XK`
as follows:
```
Noise_XK(s, rs):
<- rs
...
-> e, e(rs)
<- e, ee
-> s, se
```
The protocol begins with the "pre-transmission" of the responder's static key
(`rs)` to the initiator. Before executing the handshake, the initiator is to
generate its own static key (`s`). During each step of the handshake, all
material sent across the wire, as well as the keys sent/used are incrementally
hashed into a "handshake digest", `h`. This digest is never sent across the
wire during the handshake, and is instead used as the "Associated Data" when an
AEAD (authenticated encryption w/ associated data) is sent across the wire.
Associated data allows an encryption protocol to authenticate additional
information along side a cipher text packet. In other domains, the AD may be a
domain name, or plaintext portion of the packet.
The existence of `h` ensures that if a portion of a transmitted handshake
message is replaced, then the other side will notice. At each step, a MAC
digest is checked. If the MAC check succeeds, then the receiving party knows
that the handshake has been successful up until that point. Otherwise if a MAC
check ever fails, then the handshake process has failed, and the connection
should be terminated.
Brontide also adds a new piece of data to each handshake message: a protocol
version. The initial protocol version is `0`. At the time of writing, no new
protocol versions has been created. As a result, if a peer receives a version
other than `0`, then they should reject the handshake initiation attempt.
As far as cryptographic primitives, `SHA-256` is used as the hash function of
choice, `secp256k1` as the elliptic curve, and `ChaChaPoly-130` as the AEAD
(symmetric encryption) construction.
Each variant of the Noise protocol has a unique ASCII string used to uniquely
refer to it. In order to ensure that two parties are using the same protocol
variant, the ASCII string is hashed into a digest, which is used to initialize
the starting handshake state. In the context of Brontide, the ASCII string
describing the protocol is: `Noise_XK_secp256k1_ChaChaPoly_SHA256`.
=== Brontide: A Handshake in Three Acts
The handshake portion of Brontide can be see prated into three distinct "acts".
The entire handshake takes 1.5 round trips between the initiator and responder.
At each act, a single message is sent between both parties. The handshake
message is a _fixed_ sized payload prefixed by the protocol version.
The Noise protocol uses an object oriented inspired notation to describe the
protocol at each step. During set up of the handshake state, each side will
initialize the following "variables":
* `ck`: the **chaining key**. This value is the accumulated hash of all
previous ECDH outputs. At the end of the handshake, `ck` is used to derive
the encryption keys for Lightning messages.
* `h`: the **handshake hash**. This value is the accumulated hash of _all_
handshake data that has been sent and received so far during the handshake
process.
* `temp_k1`, `temp_k2`, `temp_k3`: the **intermediate keys**. These are used to
encrypt and decrypt the zero-length AEAD payloads at the end of each handshake
message.
* `e`: a party's **ephemeral keypair**. For each session, a node MUST generate a
new ephemeral key with strong cryptographic randomness.
* `s`: a party's **static keypair** (`ls` for local, `rs` for remote)
Given this handshake+messaging session state, we'll then define a series of
functions that will operate on the handshake and messaging state. When
describing the handshake protocol, we'll use these variables in a manner
similar to pseudo-code in order to reduce the verbosity of the explanation of
each step in the protocol. We'll define the _functional_ primitives of the
handshake as:
* `ECDH(k, rk)`: performs an Elliptic-Curve Diffie-Hellman operation using
`k`, which is a valid `secp256k1` private key, and `rk`, which is a valid public key
* The returned value is the SHA256 of the compressed format of the
generated point.
* `HKDF(salt,ikm)`: a function defined in `RFC 5869`<sup>[3](#reference-3)</sup>,
evaluated with a zero-length `info` field
* All invocations of `HKDF` implicitly return 64 bytes of
cryptographic randomness using the extract-and-expand component of the
`HKDF`.
* `encryptWithAD(k, n, ad, plaintext)`: outputs `encrypt(k, n, ad, plaintext)`
* Where `encrypt` is an evaluation of `ChaCha20-Poly1305` (IETF variant)
with the passed arguments, with nonce `n` encoded as 32 zero bits,
followed by a *little-endian* 64-bit value. Note: this follows the Noise
Protocol convention, rather than our normal endian.
* `decryptWithAD(k, n, ad, ciphertext)`: outputs `decrypt(k, n, ad, ciphertext)`
* Where `decrypt` is an evaluation of `ChaCha20-Poly1305` (IETF variant)
with the passed arguments, with nonce `n` encoded as 32 zero bits,
followed by a *little-endian* 64-bit value.
* `generateKey()`: generates and returns a fresh `secp256k1` keypair
* Where the object returned by `generateKey` has two attributes:
* `.pub`, which returns an abstract object representing the public key
* `.priv`, which represents the private key used to generate the
public key
* Where the object also has a single method:
* `.serializeCompressed()`
* `a || b` denotes the concatenation of two byte strings `a` and `b`
==== Handshake Session State Initialization
Before starting the handshake process, both sides need to initialize the
starting state that they'll use to advance the handshake process. To start,
both sides need to construct the initial handshake digest `h` which will be
used as the initial handshake digest.
1. `h = SHA-256(protocolName)`
* where `protocolName = "Noise_XK_secp256k1_ChaChaPoly_SHA256"` encoded as
an ASCII string
2. `ck = h`
3. `h = SHA-256(h || prologue)`
* where `prologue` is the ASCII string: `lightning`
In addition to the protocol name, we also add in an extra "prologue" that is
used to further bind the protocol context to the Lightning network.
To conclude the initialization step, both sides mix the responder's public key
into the handshake digest. As this digest is used as the associated data with a
zero-length ciphertext (only the MAC) is sent, this ensures that the initiator
does indeed know the public key of the responder.
* The initiating node mixes in the responding node's static public key
serialized in Bitcoin's compressed format:
* `h = SHA-256(h || rs.pub.serializeCompressed())`
* The responding node mixes in their local static public key serialized in
Bitcoin's compressed format:
* `h = SHA-256(h || ls.pub.serializeCompressed())`
==== Handshake Acts
After the initial handshake initialization, we can begin the actual execution
of the handshake process. The Brontide handshake is compromised of a series of
three messages sent between the initiator and responder, hence referred to as
"acts". As each act is a single message sent between the parties, a handshake
is completed in a total of 1.5 round trips (0.5 for each act).
The first act completes the initial portion of the incremental Triple Diffie
Hellman key exchange (using a new ephemeral key generated by the initiator),
and also ensures that the initiator actually knows the long-term public key of
the responder. During the second act, the responder transmits the thermal key
they wish to use for the session to the initiator, and one again incrementally
mixes this new key into the Triple DH handshake. During the third and final
act, the initiator transmits their long-term static public key to the
responder, and executes the final DH operation to mix that into the final
resulting shared secret.
===== Act One
```
-> e, es
```
Act One is sent from initiator to responder. During Act One, the initiator
attempts to satisfy an implicit challenge by the responder. To complete this
challenge, the initiator must know the static public key of the responder.
The handshake message is _exactly_ 50 bytes: 1 byte for the handshake
version, 33 bytes for the compressed ephemeral public key of the initiator,
and 16 bytes for the `poly1305` tag.
**Sender Actions:**
1. `e = generateKey()`
2. `h = SHA-256(h || e.pub.serializeCompressed())`
* The newly generated ephemeral key is accumulated into the running
handshake digest.
3. `es = ECDH(e.priv, rs)`
* The initiator performs an ECDH between its newly generated ephemeral
key and the remote node's static public key.
4. `ck, temp_k1 = HKDF(ck, es)`
* A new temporary encryption key is generated, which is
used to generate the authenticating MAC.
5. `c = encryptWithAD(temp_k1, 0, h, zero)`
* where `zero` is a zero-length plaintext
6. `h = SHA-256(h || c)`
* Finally, the generated ciphertext is accumulated into the authenticating
handshake digest.
7. Send `m = 0 || e.pub.serializeCompressed() || c` to the responder over the network buffer.
**Receiver Actions:**
1. Read _exactly_ 50 bytes from the network buffer.
2. Parse the read message (`m`) into `v`, `re`, and `c`:
* where `v` is the _first_ byte of `m`, `re` is the next 33
bytes of `m`, and `c` is the last 16 bytes of `m`
* The raw bytes of the remote party's ephemeral public key (`re`) are to be
deserialized into a point on the curve using affine coordinates as encoded
by the key's serialized composed format.
3. If `v` is an unrecognized handshake version, then the responder MUST
abort the connection attempt.
4. `h = SHA-256(h || re.serializeCompressed())`
* The responder accumulates the initiator's ephemeral key into the authenticating
handshake digest.
5. `es = ECDH(s.priv, re)`
* The responder performs an ECDH between its static private key and the
initiator's ephemeral public key.
6. `ck, temp_k1 = HKDF(ck, es)`
* A new temporary encryption key is generated, which will
shortly be used to check the authenticating MAC.
7. `p = decryptWithAD(temp_k1, 0, h, c)`
* If the MAC check in this operation fails, then the initiator does _not_
know the responder's static public key. If this is the case, then the
responder MUST terminate the connection without any further messages.
8. `h = SHA-256(h || c)`
* The received ciphertext is mixed into the handshake digest. This step serves
to ensure the payload wasn't modified by a MITM.
===== Act Two
```
<- e, ee
```
Act Two is sent from the responder to the initiator. Act Two will _only_
take place if Act One was successful. Act One was successful if the
responder was able to properly decrypt and check the MAC of the tag sent at
the end of Act One.
The handshake is _exactly_ 50 bytes: 1 byte for the handshake version, 33
bytes for the compressed ephemeral public key of the responder, and 16 bytes
for the `poly1305` tag.
**Sender Actions:**
1. `e = generateKey()`
2. `h = SHA-256(h || e.pub.serializeCompressed())`
* The newly generated ephemeral key is accumulated into the running
handshake digest.
3. `ee = ECDH(e.priv, re)`
* where `re` is the ephemeral key of the initiator, which was received
during Act One
4. `ck, temp_k2 = HKDF(ck, ee)`
* A new temporary encryption key is generated, which is
used to generate the authenticating MAC.
5. `c = encryptWithAD(temp_k2, 0, h, zero)`
* where `zero` is a zero-length plaintext
6. `h = SHA-256(h || c)`
* Finally, the generated ciphertext is accumulated into the authenticating
handshake digest.
7. Send `m = 0 || e.pub.serializeCompressed() || c` to the initiator over the network buffer.
**Receiver Actions:**
1. Read _exactly_ 50 bytes from the network buffer.
2. Parse the read message (`m`) into `v`, `re`, and `c`:
* where `v` is the _first_ byte of `m`, `re` is the next 33
bytes of `m`, and `c` is the last 16 bytes of `m`.
3. If `v` is an unrecognized handshake version, then the responder MUST
abort the connection attempt.
4. `h = SHA-256(h || re.serializeCompressed())`
5. `ee = ECDH(e.priv, re)`
* where `re` is the responder's ephemeral public key
* The raw bytes of the remote party's ephemeral public key (`re`) are to be
deserialized into a point on the curve using affine coordinates as encoded
by the key's serialized composed format.
6. `ck, temp_k2 = HKDF(ck, ee)`
* A new temporary encryption key is generated, which is
used to generate the authenticating MAC.
7. `p = decryptWithAD(temp_k2, 0, h, c)`
* If the MAC check in this operation fails, then the initiator MUST
terminate the connection without any further messages.
8. `h = SHA-256(h || c)`
* The received ciphertext is mixed into the handshake digest. This step serves
to ensure the payload wasn't modified by a MITM.
===== Act Three
```
-> s, se
```
Act Three is the final phase in the authenticated key agreement described in
this section. This act is sent from the initiator to the responder as a
concluding step. Act Three is executed _if and only if_ Act Two was successful.
During Act Three, the initiator transports its static public key to the
responder encrypted with _strong_ forward secrecy, using the accumulated `HKDF`
derived secret key at this point of the handshake.
The handshake is _exactly_ 66 bytes: 1 byte for the handshake version, 33
bytes for the static public key encrypted with the `ChaCha20` stream
cipher, 16 bytes for the encrypted public key's tag generated via the AEAD
construction, and 16 bytes for a final authenticating tag.
**Sender Actions:**
1. `c = encryptWithAD(temp_k2, 1, h, s.pub.serializeCompressed())`
* where `s` is the static public key of the initiator
2. `h = SHA-256(h || c)`
3. `se = ECDH(s.priv, re)`
* where `re` is the ephemeral public key of the responder
4. `ck, temp_k3 = HKDF(ck, se)`
* The final intermediate shared secret is mixed into the running chaining key.
5. `t = encryptWithAD(temp_k3, 0, h, zero)`
* where `zero` is a zero-length plaintext
6. `sk, rk = HKDF(ck, zero)`
* where `zero` is a zero-length plaintext,
`sk` is the key to be used by the initiator to encrypt messages to the
responder,
and `rk` is the key to be used by the initiator to decrypt messages sent by
the responder
* The final encryption keys, to be used for sending and
receiving messages for the duration of the session, are generated.
7. `rn = 0, sn = 0`
* The sending and receiving nonces are initialized to 0.
8. Send `m = 0 || c || t` over the network buffer.
**Receiver Actions:**
1. Read _exactly_ 66 bytes from the network buffer.
2. Parse the read message (`m`) into `v`, `c`, and `t`:
* where `v` is the _first_ byte of `m`, `c` is the next 49
bytes of `m`, and `t` is the last 16 bytes of `m`
3. If `v` is an unrecognized handshake version, then the responder MUST
abort the connection attempt.
4. `rs = decryptWithAD(temp_k2, 1, h, c)`
* At this point, the responder has recovered the static public key of the
initiator.
5. `h = SHA-256(h || c)`
6. `se = ECDH(e.priv, rs)`
* where `e` is the responder's original ephemeral key
7. `ck, temp_k3 = HKDF(ck, se)`
8. `p = decryptWithAD(temp_k3, 0, h, t)`
* If the MAC check in this operation fails, then the responder MUST
terminate the connection without any further messages.
9. `rk, sk = HKDF(ck, zero)`
* where `zero` is a zero-length plaintext,
`rk` is the key to be used by the responder to decrypt the messages sent
by the initiator,
and `sk` is the key to be used by the responder to encrypt messages to
the initiator
* The final encryption keys, to be used for sending and
receiving messages for the duration of the session, are generated.
10. `rn = 0, sn = 0`
* The sending and receiving nonces are initialized to 0.
==== Transport Message Encryption
At the conclusion of Act Three, both sides have derived the encryption keys, which
will be used to encrypt and decrypt messages for the remainder of the
session.
The actual Lightning protocol messages are encapsulated within AEAD ciphertexts.
Each message is prefixed with another AEAD ciphertext, which encodes the total
length of the following Lightning message (not including its MAC).
The *maximum* size of _any_ Lightning message MUST NOT exceed `65535` bytes. A
maximum size of `65535` simplifies testing, makes memory management easier, and
helps mitigate memory-exhaustion attacks.
In order to make traffic analysis more difficult, the length prefix for all
encrypted Lightning messages is also encrypted. Additionally a 16-byte
`Poly-1305` tag is added to the encrypted length prefix in order to ensure that
the packet length hasn't been modified when in-flight and also to avoid
creating a decryption oracle.
The structure of packets on the wire resembles the following:
```
+-------------------------------
|2-byte encrypted message length|
+-------------------------------
| 16-byte MAC of the encrypted |
| message length |
+-------------------------------
| |
| |
| encrypted Lightning |
| message |
| |
+-------------------------------
| 16-byte MAC of the |
| Lightning message |
+-------------------------------
```
The prefixed message length is encoded as a 2-byte big-endian integer, for a
total maximum packet length of `2 + 16 + 65535 + 16` = `65569` bytes.
===== Encrypting and Sending Messages
In order to encrypt and send a Lightning message (`m`) to the network stream,
given a sending key (`sk`) and a nonce (`sn`), the following steps are
completed:
1. Let `l = len(m)`.
* where `len` obtains the length in bytes of the Lightning message
2. Serialize `l` into 2 bytes encoded as a big-endian integer.
3. Encrypt `l` (using `ChaChaPoly-1305`, `sn`, and `sk`), to obtain `lc`
(18 bytes)
* The nonce `sn` is encoded as a 96-bit little-endian number. As the
decoded nonce is 64 bits, the 96-bit nonce is encoded as: 32 bits
of leading 0s followed by a 64-bit value.
* The nonce `sn` MUST be incremented after this step.
* A zero-length byte slice is to be passed as the AD (associated data).
4. Finally, encrypt the message itself (`m`) using the same procedure used to
encrypt the length prefix. Let encrypted ciphertext be known as `c`.
* The nonce `sn` MUST be incremented after this step.
5. Send `lc || c` over the network buffer.
===== Receiving and Decrypting Messages
In order to decrypt the _next_ message in the network stream, the following
steps are completed:
1. Read _exactly_ 18 bytes from the network buffer.
2. Let the encrypted length prefix be known as `lc`.
3. Decrypt `lc` (using `ChaCha20-Poly1305`, `rn`, and `rk`), to obtain the size of
the encrypted packet `l`.
* A zero-length byte slice is to be passed as the AD (associated data).
* The nonce `rn` MUST be incremented after this step.
4. Read _exactly_ `l+16` bytes from the network buffer, and let the bytes be
known as `c`.
5. Decrypt `c` (using `ChaCha20-Poly1305`, `rn`, and `rk`), to obtain decrypted
plaintext packet `p`.
* The nonce `rn` MUST be incremented after this step.
==== Lightning Message Key Rotation
Changing keys regularly and forgetting previous keys is useful to prevent the
decryption of old messages, in the case of later key leakage (i.e. backwards
secrecy).
Key rotation is performed for _each_ key (`sk` and `rk`) _individually_. A key
is to be rotated after a party encrypts or decrypts 1000 times with it (i.e.
every 500 messages). This can be properly accounted for by rotating the key
once the nonce dedicated to it exceeds 1000.
Key rotation for a key `k` is performed according to the following steps:
1. Let `ck` be the chaining key obtained at the end of Act Three.
2. `ck', k' = HKDF(ck, k)`
3. Reset the nonce for the key to `n = 0`.
4. `k = k'`
5. `ck = ck'`