[[routing_on_a_network_of_payment_channels]]
== Routing on a Network of Payment channels
In this section you will finally understand how payment channels can be connected to a network of payment channels via what we call routing.
When we say routing, we refer to the series of interactions across the network that allow a payment to _flow_ from point A to point B.
This differs from _path finding_ which was covered earlier as this refers to the _active_ process of sending payments, while path finding can be seen as a re-processing step.
An important rule of thumb to remember is that it's possible for a path to exist between Alice and Bob, yet there may be a lack of an active _route_ at any given point.
On concrete eaxmple of such a scenario can be illustrated by assuming that all the nodes connecting Alice and Bob are currently off-line. 
In this case, one can examine the _payment graph_ to construct a path for a payment, but the payment cannot be sent as an _active route_ does not exist.

The innovation of routed payment channels, allows our gamer Gloria to receive funds from her viewers without being required to maintain a separate channel with every of her viewers who want to tip her.
As long as there exists a path of well funded payment channels from a fan to Gloria she will be able to receive money.
Despite the fact that the nodes along the path forward the money to Gloria they are not able to steal the money and run with it.
Similarly, they cannot lose money while participating in the routing process assuming all time-locks along the route are constructed properly relative to the current on-chain fee market.k
They are however entitled to charge a routing fee for their service.
In particular due to the use of onion routing, intermediary nodes are only explicitly aware of who came before them in the route, and the node that'll continue to forward the payment after them.

This process of connecting a series of payment channels with end-to-end security, and the existence of incentives for nodes to _forward_ payments, is considered one of the key innovations of the Lightning Network.
In this chapter, we'll dive into the mechanism of routing in the Lightning Network, detailing the precise manner in-which payments flow through the network.
First, we'll cover the concept of a conditional chained end to end secure payment, most commonly known by the name of the first known working construct: the Hash Time Locked Transaction (HTLC).
Having learned _how_ payments can be transmitted through the network, we'll then cover the concept of source routing, and the privacy preserving variant (onion routing) used in the network today.
Finally, we'll explore the exact mechanism of _payment forwarding_ and how the _structure_ (edges, fees, time-locks, etc) of the route is determined by the sender is transmitted to each individual node along the route.


=== Creating a Network of payment channels

Before we dive into the concept of a conditional chained end to end secure payment, let's walk through a simple motivating example.
Let us assume after Alice bought her coffee at Bob's coffee shop using a direction channel, she began to watch the live stream of our gamer Gloria who accepts donations via the Lightning Network from her viewers.
Alice and Gloria do not have a _direct_ channel connecting them, and don't wish to create one as they'd like to minimize the total number of channels they have open.
However, they do in fact have an _indirect path_ via the network of connected payment channels that comprises the Lightning Network.
The structure of our mini-network is as follows.
Bob has an open channel with his the software developer Wei who helps him with technical issues of the point of sale system he uses in his coffee shop.
Wei is actually the owner of a large software company which also develops the game that Gloria plays so that she had opened a channel with the company to pay for the game's license, access to the server, and in game items.
If we draw out this series of payment channels, it's possible to manually trace a _path_ from Alice to Gloria that uses Bob and Wei as supporting intermediary routing nodes.
Alice can then craft a _route_ from this outlined path, and use it to send a tip of a few thousand satoshis to Gloria, with the payment being _forwarded_ by Bob and Wei.

[[routing-network]]
.The network of payment channels of our friends can be seen here:
image:images/routing-network.png[]

The main challenge is to do this in a way that prevents Bob and Wei from stealing the money that Alice wants to be delivered to Gloria.
To understand how the Lightning Network protects the payment packages that are being routed through the network we compare the situation of indirect payments with physical payments with gold coins in the offline world.
Let us assume Alice wanted to give 10 gold coins to Gloria and decides to ask Bob and Wei for help.
How could Alice make sure that Bob and Alice does not run with the gold coins after receiving them?
In the physical world, traditional legal contracts contracts may be used to safely transmit this cascade of payments.

Alice could negotiate a contract with Bob which reads:

_I (Alice) will give you (Bob) 10 golden coins if you pass them on to Wei_

While this contract is nice in the abstract, in the real world, Alice runs the risk that Bob might just breach the contract and hope to not get caught by law enforcement.
Even if Bob got caught by law enforcement, Alice faces the risk that he might be bankrupt, rendering her unable to actually claim those 10 golden coins.
Assuming these issues are magically solved it, it's still unclear how to leverage such a contract to achieve our desired outcome: the coins ultimately being delivered to Gloria.

Thus we improve our contract:

_I (Alice) will reimburse you (Bob) with 10 golden coins if you can proof to me (for example via a receipt) that you already have delivered 10 golden coins to Wei_

Now you might ask yourself why should Bob sign such a contract as Bob now has the risk of _not_ getting reimbursed?
Typically, in economic systems, participants must be properly compensated for contractual risk (whatever that may be), otherwise, they wouldn't agreed to said contract.
Even putting aside the risk, Bob must _already_ have 10 gold coins to send to Gloria, otherwise, he wouldn't be able to participate in the contract.
Therefore Bob must deal with the opportunity cost of allocating his capital to this contract, in addition to the counter party risk that would arise if Alice doesn't hold up her end.
Adjusting things slightly to compensate Bob, Alice could offer a routing fee of Golden coin to Bob, and another to Wei who bares similar costs.
Thus we alter the contract yet again, to factor in this new information:

_I (Alice) will reimburse you (Bob) with 12 golden coins if you can proof to me (for example via a receipt) that you already have delivered 11 golden coins to Wei_

Alice now promises Bob 12 golden coins.
10 to be delivered to Gloria and two for the fees.
She promises 12 to Bob if he shows proof that he has forwarded 11.
The difference of 1 golden coin is the fee that Bob will earn for helping out with this particular payment process.

As there is still the issue of trust and that even law enforcement does not protect Alice and Bob from malicious behavior they decide to add an escrow service.
To resolve this issue, all parties opt to add in a 3rd party escrow service.
This escrow service serves as our "ideal functionality", which will later be replaced by a more trust-minimized mechanism.

Of course Alice and Bob both have to trust this escrow service.
Having such an escrow Alice could already provide the 12 golden coins to that service which would only release them to Bob if Bob shows the proof of delivering 11 golden coins to Wei.

Using a bit of cryptography, it's actually possible for this proof to be contingent on a secret that only Gloria knows, which itself is included in the contract by including the sha256 hash of the secret in the contract.
We call this hash of the receipt's secret, a payment hash, with the secret that "unlocks" the payment contracting, being known as the payment secret.

As Gloria, wants to ensure that no one else can guess this secret, in practice it's chosen to be a _very, very_ large number (typically encoded using 256 bits!).
For simplicity, let's assume that Gloria's secret is actually just: `*Glorias secret*`.
In order to "commit" to this secret, she computes the `sha256` hash which when encoded in hex, can be displayed as: `*f23c83babfb0e5f001c5030cf2a06626f8a940af939c1c35bd4526e90f9759f5*`.
You can verify this by typing `echo -n "Glorias secret" | sha256sum` to your Linux command line shell.

As Alice wants to send 10 golden coins to Gloria she is told by Gloria to use this payment hash to receive a proof of payment.
Alice now sets up a contract that reads:

_I (Alice) will reimburse you (Bob) with 12 golden coins if you can show me a valid message - we call it preimage - that hashes to `*f23c83babfb0e5f001c5030cf2a06626f8a940af939c1c35bd4526e90f9759f5*`. You can acquire this message by setting up a similar Contract with Wei who has to set up a similar contract with Gloria. In order to assure you that you will get reimbursed I will provide the 12 Golden coins to an trusted escrow before you set up your next contract._

After Bob and Alice agree to the contract and Bob receives the message from the escrow that Alice has deposited the 12 golden coins Bob negotiates a very similar contract with Wei.
Note that due to the service fees he will only forward 11 golden coins to Wei and demand from Wei who also wants to earn a fee of 1 golden coin to show proof that 10 golden coins have been delivered to Gloria.

_I (Bob) will reimburse you (Wei) with 11 golden coins if you can show me a valid message - we call it preimage - that hashes to `*f23c83babfb0e5f001c5030cf2a06626f8a940af939c1c35bd4526e90f9759f5*`. You can acquire this message by setting up a similar contract with Gloria. In order to assure you that you will get reimbursed I will provide the 11 Golden coins to an trusted escrow before you set up your next contract._


As Wei gets message from the escrow that Bob has deposited the 10 golden coins Wei sets up a similar contract with Gloria:

_I (Wei) will reimburse you (Gloria) with 10 golden coins if you can show me a valid message - we call it preimage - that hashes to `*f23c83babfb0e5f001c5030cf2a06626f8a940af939c1c35bd4526e90f9759f5*`. In order to assure you that you will get reimbursed after revealing the secret I will provide the 10 Golden coins to an trusted escrow._

After Gloria learns that the coins were deposited from the escrow, she reveals the secret preimage to Wei.
As she was the one that originally committed to the secret in the form of a payment hash, she must know the secret, as otherwise there's no way she can be paid.
Therefore, Alice provides the secret to Wei and the escrow service.
Wei takes the preimage as a proof of payment and shows it to Bob.
The escrow service releases the money so that Wei is reimbursed.
Now Bob repeats the process by fulfilling the contract between Alice and him with the help of the secret preimage.

With such a chain of contracts Bob and Wei were not able to run with the money as an escrow was used to prevent this.
However if Gloria or anyone along this chain does not release the secret preimage, since everyone has already send golden coins to their escrow service but will never get reimbursed.
So while no one can steal money from Alice everyone can still lose money.
This is obviously not desirable.
Luckily, this can be resolved by adding a deadline to the contract.
With this new deadline, the contract has to be fulfilled in time, or it expires, with the escrow refunding the money to the party that made the original deposit.
We call this deadline a "time lock "as the deposit is locked with the escrow service for a certain amount of time and then released if no proof of payment was provided.

In order to factor this in, the Contract between Alice and Bob is once again amended with a new clause:

_Bob has 24 hours to show the secret after the contract was signed. If the time has passed Alice will get her deposit back from the escrow service and the contract becomes invalid._

Bob of course now has to make sure to receive the proof of payment before 24 hours is up.
If he would receive this proof after 24 hours, the contract between him and Alice would already be nullified and Bob would not get reimbursed.
After he signed the contract with Alice he creates a new (altered) original contract between him and Wei that reads:

_Wei has 22 hours to show the secret after the contract was signed. If the time has passed Bob will get his deposit back from the escrow service and the contract becomes invalid._

As you have guessed Wei is now incentivised create a _new_ (altered) contract with Gloria:

_Gloria has 20 hours to show the secret after the contract was signed. If the time has passed Wei will get his deposit back from the escrow service and the contract becomes invalid._

With such a chain of contracts we can be sure that after 24 hours of setting up the first contract that the payment was either successfully delivered from Alice via Bob and Wei to Gloria or that the payment has failed and was not conducted at all.
Either the contract failed or succeeded, there's no middle ground. 
In the context of the Lightning Network, we call this "all or nothing" property "atomicity".

As long as the escrow is trustworthy and faithfully performs its duty, then no party will have their coins stolen in the process.
The pre-condition to this _route_ working at all, is that all parties in the path already needed to have enough money to satisfy the required series of deposits.
While this seems like a minor detail we will see in this chapter, this requirement is actually one of the harder issues for Lightning Network nodes.
As parties are required to deposit the funds used for the payment in escrow, they aren't able to use this money for anything else while the contract is active.
However, as discussed earlier, they're compensated for this opportunity cost in the forms of earned routing fees when they successfully forward the payment.

In the next section, we'll dive into the details of the "HTLC", exploring the properties that allow it to implement the concept of a conditional chained end to end secure payment _without_ involving the 3rd party escrow.
You'll see how the Bitcoin network can be seen as a stand-in for a trusted third party to ensure proper HTLC contract execution. 
After that, we'll explore how a user is able to use an HTLC to "route" a payment through the network securely.
In the Lightning Network today, we use a technique called source-based onion routing, though it's also possible to route payment with alternative techniques.
Finally, we'll dive into the precise details concerning the exact mechanics of forward, settle ling, and cancelling HTLCs in the network.

= Hash Time Locked Contracts as a Conditional Chained End to End Secure Payment =

Our example in the prior section using "golden coins", was intended to lay same base intuition which we'll leverage in this section to explain how HTLCs work in practice.
HTLC is actually an acronym that stands for "Hash Time-Locked Contracts". 
A HTLC is a _specific_ instantiation of a Conditional Chained End to End Secure Payment (CCESP, don't use this acronym?).
As we'll see in the later chapters, given a set of adequate cryptographic constructs, many other instantiations are possible as well.

Before we dive into the specifics of HTLCs, it may be helpful to first build intuition on an abstraction over this concrete concept.
First, let's unpack what it means for something to be a conditional chained end to end secure payment:

== Conditional End to End Secure Payments by Construction ==

=== Conditional Payments ===

A payment can be said to be conditional, if the completion of the payment relies on the completion of a certain event. 
In the golden coins example, this "condition" was the reveal of a hash pre-image. 
We could feasibly substitute this hash pre-image reveal for any other construct with "hardness" properties. Namely: it should be infeasible for a party that doesn't know the proper "solution" of the condition to satisfy it, the "description" of the condition shouldn't give away any information about the true "solution", and once a solution has been chosen and a description created from it, it shouldn't be possible to "alter" that solution and have it still be a valid condition for the description. 

The payment should _only_ be able to be redeemed if a valid solution is revealed. Critical, all conditions need to be timed in order to allow the construct to return the funds back to the sender if a solution to this condition isn't revealed.
The combination of the condition, and a timeout on the condition gives the payment a trait we commonly refer to as atomicity: either the payment happens, or the receiver if refunded the funds.

=== Conditional Chained Payment ===

Building upon our conditional payment, it may be possible to *chain* this payment, allowing it to involve the payer, the payee, and possibly several intermediaries. 
Each intermediary, is able to present a _slightly_ modified version of the condition (without invalidating it all together), and so in an iterated manner until the conditional payment reaches the payee.
Once it reaches the payee, then the payment should be able to be _iteratively_ resolved, starting at the payee all the way back to the payer. 

Each chaining creates an "incoming" and "outgoing" conditional payment.
A node receives a conditional payment from a party (incoming condition), and then extends the conditional payment to the next party in the chain (outgoing condition).
The payment is extended in from payer to payee, but settled from payee to payer, as each of the intermediaries gain the solution to the outgoing condition, and use that (possibly augmenting it) to satisfy the incoming solution.

Typically the payer rewards the intermediaries by sending slightly more than the payment amount, in order to allow the intermediaries to send out less with their outgoing payment than what they received from the incoming payment.
The difference between these two payment values makes up the "forwarding fee" collected by the intermediary.

=== Conditional Chained End to End Secure Payment === 

With our final addition, we'll achieve "end to end security".
By this we mean that: no intermediaries are able to "claim" the payment without first obtaining the solution from someone further down from them in the chain.
Additionally, we also require that the amount the payer intended to send is fully received by the payee.
Finally, we require that non of the intermediaries are able to "contaminate" the payment beyond giving incorrect directions to the party that directly follows them.
In other words, the intermediary shouldn't be able to materially affect the propagation of the payment several hops away from it.

== Hash Time Locked Contracts ==

In this section, we'll construct a conditional chained end to end payment known as the HTLC. 
At each step we'll add a new component, then examine it in light of our original definition to ensure all requirements and security properties are reached.

First, the "condition". For an HTLC, the condition is typically the reveal of a hash pre-image that matches a particular hash.
This hash is typically referred to as the "payment hash", with the pre-image being called the "payment pre-image".
If the name didn't give too much away, for an HTLC, we'll use a _cryptographically secure_ hash function as one part of our condition.
By using a cryptographic hash function, we ensure that it's infeasible for another party to "guess" the solution of our condition, it's easy for anyone to verify the solution, and there's only one "solution" to the condition.

In order to implement the "refund" functionality, we rely on the "absolute time lock" functionality of Bitcoin script.

With all that said, a basic Bitcoin script implementing a hash time-locked contract would look something like the following:
```
OP_SIZE 32 OP_EQUAL

OP_IF
    OP_HASH160 <ripemd(payHash)> OP_EQUALVERIFY
    <receiver key>
OP_ELSE
   OP_CHECKLOCKTIMEVERIFY <timeout>
   OP_DROP
   <sender key>

OP_CHECKSIGVERIFY
```

Alice can present this script to Bob in order to kick off the conditional payment.
For the chained aspect, Alice needs to be able to communicate the proper payment details to each hop in the route.
Recall that each hop will specify a forwarding fee rate, as well as other parameters that express their forwarding policy.
In addition to this forwarding rate, Alice also needs to be conceded about what time locks to use.
Each node in the hop needs some time to be able to settle the outgoing, then incoming payment on-chain in the worst case.
As a result, when constructing the final route, we need to give each node some buffer time, we call this before time, the "time lock delta".
Factoring in this time-lock delta, the time-lock of the outgoing HTLC will decrease as the route progresses, as the outgoing HTLC will expire before the incoming HTLC.
This set of decrementing time-locks is critical to the operation of the system, as it ensure out atomicity property for each hop, assuming they're able to get into the chain in time.

In the next section, we'll go into the exact mechanism of how Alice is able to deliver forwarding details to each hop in the route.
In addition, we'll dive further into proper time-lock construction, as incorrect time-lock set up can violate our atomicity property and lead to a loss of funds.

=== HTLC Packet Forwarding: Source Based Onion Routing

# TODO(roasbeef): onion routing in the abstract first

So far you have learnt that payment channels can be connected to a network which can be utilized to send payment from one participant to another one through a path of payment channels.
You have seen that with the use of HTLCs the intermediary nodes along the path are not able to steal any funds that they are supposed to forward and also how a node can set up and settle an HTLC.
With this bare foundation laid, the following questions may have come across you mind:

- Who chooses the path for a candidate route?
- How is a path selected as a candidate to attempt to route the HTLC for a payment?
- How much information do nodes know about the total path?
- How exactly does a payment flow through the network at each node?

In the network today, the sender is the one that selects the route and decides nearly all the details of the resulting route.

As for how path finding is done, there is no single approach that all nodes in the network use.  
Instead, answer to the second question has a very large solution space, meaning there are several algorithms and neuritics used in the network today.
Most commonly, a variation of Dijkstra's algorithm is used which takes into account additional Lightning Network details such as fees and time-locks.
Remember from earlier that a path turns into a route which is used to trigger a payment attempt.
As several conditions need to be satisfied for the HTLC to be completely extended, the sender may need to try several routes until one succeeds.
However, the user of the wallet typically will not be aware of these failed path finding attempts, just as when we load a web-page on the Internet, we don't learn of any TCP packet retransmissions.

In the early days of the network, a payment could only utilize a single channel in its final route.
With the rise of Multi-Path Payments, the sender is able to split the amount into smaller pieces, and use distinct strategies to route all the payment chunks.
This splitting behavior is similar to IP packet fragmentation on the IP layer: each node expresses its Maximum Payment Unit, with the sender using this as a guide to adequately split all payments.
In later chapters, we'll discuss further details of payment splitting and combination once we get to advanced path finding.

At a high level, each node in the route is only _explicitly_ told: how to validate the incoming HTLC packet (remember all details need to be correct for a payment to flow!), who the next hop in the route is, and how to modify the incoming HTLC packet into a valid outgoing HTLC packet to forward to the next node.
Combined with the fact that intermediate forwarding nodes aren't explicitly given the sender and receiver of a payment, nodes are given the _least_ amount of information they need to successfully forward a payment.
In addition to these privacy enhancing attributes, intermediate nodes aren't able to arbitrarily modify an HTLC packet, as all information is encrypted and cryptically authenticated with integrity checks carried out at each hop to ensure contents haven't been modified.
Readers familiar with onion routing may have realized that we'll be using some clever cryptographic technique application to achieve all thees traits.
We call this series of clever application of cryptographic techniques: sourced based onion routing!

Source based routing (the non-cryptographic portion of onion routing), is distinct from how packets are typically transmitted on the IP layer.
On the Internet today, packet switching is widely used to transmit data across the Internet.
Packet switching typically explicitly indicates the sender and receiver of a given packet.
Intermediate routing nodes then attempt to deliver the packet on a best effort basis, with great freedom with to exactly _how_ they select the next node in the route.
However, the lack of encryption, end-to-end integrity checks, and arbitrary choice of routes may this a poor system to use in a _payment network_.

Source routing instead has the sender select the route entirely (which all we'll learn later is important due to fees and timelocks).
The onion routing layers then gives the sender nearly completely control of the route, and allows the sender to only tell the intermediate nodes what they need to successfully forward a payment.
Onion routing is used in several popular protocols on the Internet, with the most notable of them being Tor.
In the Lightning Network, we use a specific onion routing _packet_ format called Sphinx, with some special modifications made in order to make it more suited to the unique constraints of the Lightning Network.

[NOTE]
====
While the Lightning Network also uses an onion routing scheme it is actually very different to the onion routing scheme that is used in the TOR network.
Aside from the distinct cryptographic techniques they use, the biggest difference is that TOR is being used for arbitrary data to be exchanged between two participants where on the Lightning Network the main use case is to pay people and transfer data that encodes monetary value.
In the Lightning Network, we're only concerned with transmitting the details that are needed for a successful payment.
On the Lightning Network there is no analogy to the exit nodes of the Tor Network as there's no need to "exit" the network: all payments flow within the network. 
Although, in an idea model only a precise amount of information is leaked by a route, in practice several "side channels' exist, that may allow an adversary to deduce more information about a route.
As an example, information about CTLV deltas, or the set of possible routes in the network may give away additional information about a given route.
Similar to Tor, onion routing in the Lightning Network isn't secure against a global passive adversary (one that can monitor all links and information flows in the network).
Today in the network, every node in the route sees the same payment hash, meaning that if two nodes are "compromised" more details of the route are leaked.
On the TOR network nodes can theoretically be connected via a full graph as every node could create an encrypted connection with every other node on top of the Internet Protocol almost instantaneously and at no cost. 
On the Lightning Network payments can only flow along existing payment channels. 
Removing and adding of those channels is a slow and expensive process as it requires onchain bitcoin transactions.
On the Lightning Network nodes might not be able to forward a payment package because they do not own enough funds on their side of the payment channel. 
On the other hand there are hardly any plausible reasons other then its wish to act maliciously why a TOR node might not be able to forward an onion.
Last but not least the Lightning Network can actually run on Tor to use it as a message transport layer.
This means that all connections of a node with its peers and the resulting communication will by obfuscated once more through the TOR network.
====

Lets stick to our example in which Alice still wants to tip Gloria and has decided to use the path via Bob and Wei.
We note that there might have been alternative paths from Alice to Gloria but for now we will just assume it is this path that Alice has decided to use.
In order to kick off the transfer, Alice needs to send a special message to Bob to kick off the multi-hop transfer.
You'll learn about the specific structure of this message in later chapters, but for now we'll call it an "HTLC Add" message.
Aside from the amount, the payment hash, and the time-lock, this message also contains an opaque field use to store encrypted forwarding information.
Today in the network, this field is 1366 bytes, as that's the _fixed_ size length of the onion packet. #TODO(roasbeef): explain security properties earlier
This onion contains all the information about the path that Alice intends to use to send the payment to Gloria.
However Bob who receives the onion cannot read all the information about the path as most of the onion is hidden from him through a sequence of encryptions.
The name onion comes from the analogy to an onion that consists of several layers. In our case every layer corresponds to one round of encryption.
Each round of encryption uses different encryption keys.
They are chosen by Alice in a way that only the rightful recipient of an onion can peel of (decrypt) the top layer of the onion.

For example after Bob received the onion from Alice he will be able to decrypt the first layer and he will only see the information that he is supposed to forward the onion to Wei by setting up an HTLC with Wei.
The HTLC with Wei should use the same Payment Hash as the receiving HTLC from Alice.
The amount of the forwarded HTLC was specified in Bob decrypted layer of the onion.
It will be slightly smaller than the amount of his incoming HTLC from Alice.
The difference of these two amounts has to be at least as big as to cover the routing fees that Bob's node announced earlier on the gossip protocol.

In order to set up the HTLC Bob will modify the onion a little bit in a deterministic manner.
He removes the information that he could read from it and passes it along to Wei.

Wei in turn is only able to see that he is supposed to forward the package to Gloria.
Wei knows he received the onion from Bob but has no clue that it was actually Alice who initiated the onion in the first place.
In this way every participant is only able to peel of one layer of the onion by decrypting it.
Each participant will only learn the information it has to learn to fulfill the routing request.
For example Bob will explicitly be told that Alice offered him an HTLC and sent him an onion and that he is supposed to offer an HTLC to Wei and forward a slightly modified onion.
Bob isn't explicitly told if Alice is the originator of this payment as she could also just have forwarded the payment to him.
Due to the layered encryption he cannot see the inside of Wei's, and Gloria's layer.
The only thing Bob is told explicitly is that he was involved in a path that involved Alice, him and Wei.

While the Onion is decrypted layer by layer while it travels along the path from Alice via Bob and Wei to Gloria it is created from the inside layer to the outside layers via several rounds of encryption.
Being created from the inside means that the construction starts with the Onion Package that Gloria is supposed to receive in plain text.
Let us now look at the construction of the Onion that Alice has to follow and at the exact information that is being put inside each layer of the onion.


Today the network uses a modification of the Sphinx mix-net packet format which structurally, has four components: 

1. A version byte to allow future structural changes to the packet format.
2. The header consisting of a public key that can be used by the recipient to produce the shared secret for decrypting the outer layer and to derive the public key that has to be put in the header of the modified onion for the next recipient.
3. The payload itself which contains encrypted forwarding information.
4. An HMAC tag which serves to allow nodes to check the authenticity and integrity of the entire packet. The HMAC tag also convers the _payment hash_ of the HTLC the packet is encoded in, which provides an economic disincentive against replayed packets, as the same payment hash _must_ be used.

For now we will ignore how the public keys are derived and exchanged and focus on the payload of the onion.
Only the payload is actually encrypted and will be peeled of layer by layer.
The payload consists of a sequence of a sequence of per hop data.
This data can come in two formats the legacy one and the Type Length Value (TLV) Format.
The TLV format is very flexible as new keys/values can be added in a forwards and backwards compatible manner.
For example, with the new TLV format, the sender can actually included the preimage in the payload for the last hop.
This is nice as it allow a payer to initiate a payment without the necessity to ask the payer for an invoice and payment hash first.
We will this feature called key send in a different chapter.

Before a node starts to forward an HTLC, they should _verify_ the field of the onion against the incoming HTLC.
A node should reject an incoming HTLC packet if any of the following conditions are violated:

  * The HMAC fails to validate.
  * Any of the channel policy forwarding constraints are violated. See chapter xxx for more details on the various forwarding policies a node can express.
  * The HTLC expires "too soon" based on the HTLCs absolute expiry height, and the current absolute block height.
  * The HTLC expiry is "too long".
  * The target channel doesn't have enough incoming bandwidth to carry the HTLC.
  * The implicit fee (the difference between the outgoing and incoming HTLCs) doesn't mach a ndoe's forwarding policy.
  * The outgoing HTLC's time lock delta doesn't factor a node's `cltv_delta` properly.

A node needs three pieces of information to forward the package:

1. The short channel id of the next channel along which it is supposed to forward the onion by setting up an HTLC with the same payment hash.
2. The amount that it is supposed to be forwarded and thus being used in the HTLC.
3. Timelock information encoded to a `outgoing_cltv_delta` is the last piece of information that is needed as HTLCs are hashed time locked contracts.

As we learned in chapter xxx, describes _where_ in the chain a channel was first confirmed using three identifiers: the block height, the transaction index within the block, and the output index within the transaction.
To make them easier to handle, we'll compress these three attributes into a single integer, which we'll use as the `short_channel_id_ throughout the rest of our examples and graphics.

[[routing-onion-1]]
.`per_hop` payload of Glorias onion and the encrypted
image:images/routing-onion-1.png[]

We can see that Alice has created some per hop data for David.
The short channel id is set to 0, which is a special reserved value which signals that the receiver of the payload is the final node in the route. 
The amount to forward is set to 3000.
On the incoming HTLCs David should have seen that exact amount. 
David can use these values to further verify the incoming packet was crafted as intended, usually this amount is intended to say how many satoshis should be forwarded.
The final CLTV delta itself should be set to the absolute expiry of the incoming HTLC.

These data fields consist of 20 Bytes.
The Lightning Network protocol actually allows to store 65 Bytes of data the Onion for every hope.

Throughout our examples, we'll assume the new modern TLV paylaod format is used.
This format differs from the legacy format in that there's no fixed structure, instead a series of key-value pairs are used to communicate forwarding information.

- 1 Byte Realm which signals nodes how to decode the following 32 Bytes.
- 20 bytes for the base routing information
- 32 Byte of a Hashed Message Authentication code.

In the next diagram we can see how the per hop payload for David looks like.

[[routing-onion-2]]
.`per_hop` payload of Glorias onion and the encrypted
image:images/routing-onion-2.png[]

On important feature to protect the privacy is to make sure that onions are always of equal length independent of their position along the payment path.
The onion should always remain a fixed-sized packet throughout the entire route, in order to avoid leaking any path length information.
This trait is important from the perspective of packet indistinguishably: a short route should "look" the same as a long route.
If a packet got shorter each time a node processed it, then other nodes would easily be able to deduce their "position" in the route.
Note that with the TLV format, based on the information given to each node, the individual payload size may vary, but the packet still remains a fixed size throughout the entire route.

After Alice has set all the data she needs to encrypt the onion payload.
For this she derives a shared secret between Davids public node key and the private secret that she generated for David.
This process is also well known as an Elliptic Curve Diffie Hellmann key exchange and a standard technique in cryptography and Bitcoin.

[[routing-onion-3]]
.`per_hop` payload of Glorias onion and the encrypted
image:images/routing-onion-3.png[]

You can see that Alice put the encrypted payload inside the full Onion Package which contains a the public keys from the secret key that she used to derive the shared secret.
Full onion package also has a version byte in the beginning and an HMAC for the entire Onion.
When David receives the Onion package he will extract the public key from the unencrypted part of the onion package.
The property of the Elliptic Curve Diffie Hellmann key exchange is that if he multiplies this public key with his private node key he will get the same shared secret as a result as Alice did.
However others cannot derive the same shared secret as they neither know Alice's nor David's private key.

[NOTE]
====
Let `(d,D)` be the secret and Public key of David and let G be the generator point of the elliptic curve so that `D = d*G`.
Similarly let `(ek_d, EPK_D)` the ephemeral keys that Alice has generated for David such that the Public ephemeral Key `EPK_D = ek_d*G`.
Alice computed the shared secret as ss_`d =  ek_d*D`.
Using the definition of public keys this is the same as `ek_d*(d*G)=(ek_d*d)*G`.
Since multiplication with the generator point is a group homomorphism we can apply the law of associativity.
And because the secrets are just numbers modulo some prime we can change the order of the multiplication resulting in `ss_d = (d*ek_d)*G`.
With the same argument as before we apply the law of associativity and apply the definition of public keys resulting in `(d*ek_d)*G = d*(ek_d*G) = d*EPK_D`.
We just saw why `ek_d*D = d*EPK_D = ss_d` and why Alice and Davide will be able to derive the same shared secret if Alice puts the ephemeral public key inside the onion.
====

After the encrypted Onion for David is created Alice will create the next outer layer by creating the onion for Wei.

She truncates 65 Bytes from the end of the encrypted onion and prepends the truncated onion with 65 Byte per Hop data for Wei.
The per hop data follows the same structure as the per hop data for David.
Thus she starts with the Realm Byte that she will set to 0 again.
Then comes the short channel id.
This is set to 452 as Wei is supposed to use that channel to forward the onion.
She sets the amount to 3000 satoshi as this is the amount that David is supposed to receive.
Finally she uses the CLTV delta that was announced for this channel on the gossip protocol and that Wei should use for the HTLC when he forwards the Onion.
Again 12 Bytes of zeros are padded and an HMAC is computed.
Note that she did not have to compute filler this time as she already has too much data with the encrypted inner onion.
That is why the inner onion had to be truncated at the end.
This is the plain text version of Weis Onion payload and can be seen in the following diagram:

[[routing-onion-4]]
.`per_hop` payload of Glorias onion and the encrypted
image:images/routing-onion-4.png[]

We emphasize that Wei has no chance to decrypt the inner part of the onion.
However the information for Wei should also be protected from others.
Thus Alice conducts another ECDH.
This time with Wei's public key and and ephemeral keypair that she has generated particularly for Wei.
She uses the shared secret to encrypt the onion payload.
She would be able to construct the entire onion for Wei - which actually Bob does while he forwards the onion.
The Onion that Wei would receive can be seen in the following diagram:

[[routing-onion-5]]
.`per_hop` payload of Glorias onion and the encrypted
image:images/routing-onion-5.png[]

Note that in the entire onion there will be Wei's ephemeral public key.
David ephemeral public key is not stored anywhere in the onion.
Neither in the header, nor in the payload data.
However we have seen that David needed to have this key in the header of the Onion that he received.
Luckily the ephemeral keys that Alice used for the ECDH with David can be derived from the ephemeral key that she used for Wei.
Thus after Wei decrypts his layer he can use the shared secret and his ephemeral public key to derive the ephemeral public key that David is supposed to use and store it in the header of the Onion that he forwards to David.
The exact progress to generate the ephemeral keys for every hope will be explained at the very end of the chapter.
Similarly it is important to recognize that Alice removed data from the end of Davids onion payload to create space for the per hop data in Wei's onion.
Thus when Wei has received his onion and removed his routing hints and per hop data the onion would be to short and he somehow needs to be able to append the 65 Bytes of filled junk data in a way that the HMACs will still be valid.
This process is of filler generation as well as the process of deriving the ephemeral keys is described in the end of this chapter.
What is important to know is that every hope can derive the Ephemeral Public key that is necessary for the next hop and that the onions save space by always storing only one ephemeral key instead of all the keys for all the hops.


Finally after Alice has computed the encrypted version for Wei she will use the exact same process to compute the encrypted version for Bob.
For Bobs onion she actually computes the header and provides the ephemeral public key herself.
Note how Wei was still supposed to forward 3000 satoshis but How Bob was supposed to forward a different amount.
The difference is the routing fee for Wei.
Bob on the other hand will only forward the onion if the difference between the mount to forward and the HTLC that Alice sets up while transferring the Onion to him is large enough to cover for the fees that he would like to earn.

[NOTE]
====
We have not discussed the exact cryptographic algorithms and schemes that are being used to compute the ciphertext from the plain text.
Also we have not discussed how the HMACs are being computed at every step and how everything fits together while the Onions are always being truncated and modified on the outer layer.
If everything until here made perfect sense to you and you want to learn about those details we believe that you have all the necessary tools at hand to read BOLT 04 which is why we decided not to include all those technical details here in the book.
BOLT 04 is the open source specification of the onion routing scheme that is being used on the Lightning Network and a perfect resource for the missing details.
====

TODO: everything from here on will most likely change and could even be redundant.

Onions are being constructed from the inside to the outside.
As the inside of the onion is decrypted last it has to correspond to the recipient which in our case is Gloria.
As every layer of the Onion is encrypted by Alice in such a way that only the respective recipient can decrypt their layer Alice needs to come up with a sequence of encryption keys that she will use for each and every hop.
The main concept that is being used is the shared secret computation via an elliptic Curve Diffie Hellmann Key exchange (ECDH) between Alice and each of the hops.
However for the recipients to be able to to compute their shared secret they have to know a public key which they can use.
If Alice used the same private key for the computation of each of the shared secrets Alice would have to send the same public key with the onion.

the different payments could be linked together by an attacker that is why

Every layer of the onion has 32 Bytes of `per_hop` data.
This data is split into 4 data fields

- The 8 Byte `short_channel_id` indicates on which channel the onion should be forwarded next
- The 8 Bytes `amt_to_forward` is a 64 Bit unsigned integer that encodes an amount in millisatoshi and indicates the amount that is supposed to be forwarded
- The 4 Bytes `cltv_delta` is a 32 Bit unsigned integer that is used for the time locks in the HTLCs.
- Finally there are 12 Byte left for padding and future versions and updates of the onion package format.






[[routing-onion-6]]
.`per_hop` payload of Glorias onion and the encrypted
image:images/routing-onion-6.png[]


Interestingly enough Alice can construct the onion with different encryption keys for Bob, Wei and Gloria without the necessity to establish a peer connection with them.
She only needs a public key from each participant which is the public `node_id` of the lightning node and known to Alice.
As other nodes she has learnt about the existence of public payment channels and the public `node_id` of other participants via the gossip protocol which we described in its own chapter.
In order to have a different encryption key for every layer Alice produces a shared secret with each hop using the public `node_id` of each node and conduct an Elliptic Curve Diffie Hellmann Key exchange (ECDH).

She starts by generating a temporary session key.
This key will also be called the ephemeral key.
This private key multiplied with the generator Point of the Elliptic curve that is being used in Bitcoin produces a public key.
This happens in the same way how the nodes public key is generated from the secret private key of the node.
Alice could use this session keys to conduct the Diffie Hellmann key exchange if she would send the public key with the onion.
However she wishes to use a different session key to conduct the Diffie Hellmann key exchange with each of the nodes along the path.
**TODO**: WHY?!
Yet she does not want to add a public key (which consumes quite some space) into every layer of the onion.
Luckily there is a nice deterministic way in which she can derive different sessions keys for every hop and execute the Diffie Hellmann and allow the hops to use their shared secret to derive the next session public key.
Lets explore this in detail with the following example:


[Note]
====
Of course the Lightning Network protocol could have been designed in a way that Alice will only use her node's key to conduct the ECDH with every nodes public key.
However she would have to put her public key in the header of the onion.
This is necessary for nodes to be able to execute an ECDH and produce the same shared secret that Alice used for the respective layer of the Onion.
However with that information nodes would know that Alice was the originator of the payment lifting the anonymity of the payer by design.
====

===== CLTV expiry and deltas

==== Pitfalls with source based Routing and HTLCs

In the first part of the routing chapter you have learnt that payments securely flow through the network via a path of HTLCs.
You saw how a single HTLC is negotiated between two peer and added to the commitment transaction of each peer.
In the second part you have seen how the necessary information for setting up HTLCs along a path of hops are being transfered via onions from the source to the sender.
A mechanism that protects the privacy of payer and payee.
However there are quite some challenges and things that can go not as expected.
This is why we we want to discuss how errors are being handled and what users and developers should take into consideration.

Most importantly it is absolutely necessary that you understand that once your node sent out an onion on your behalf (most likely because you wanted to pay someone) Everything that happens to the onion is now out of your control.

* You cannot force nodes to forward the onion immediately.
* You cannot force nodes to send back an error if they cannot forward the onion because of missing liquidity or other reasons.
* You cannot be sure that the recipient has the preimage to the payment hash or releases it as soon as the HTLCs of the correct amount arrived.

By setting up an HTLC - which you do by sending out an onion - you have committed to settle the HTLCs in exchange for the preimage if the preimage arrives before the absolute timelock of the HTLC.
This can be very frustrating from a use experience point of view.
You want to quickly pay a person but the payment path that your node choose has CLTV deltas that quickly add up to several 100 blocks which is a couple of days.
This means now that if nodes on the path misbehave - on purpose or maybe just because they have a downtime which your node didn't know about - you will have to wait even though you don't see a preimage.
You must not send out another onion along a different path because there is a risk that both payments will settle eventually.
While our user experience is that most payments find a path and settle in far less than 10 seconds the Lightning Network protocol cannot and does not give any service level agreement that within this time payments will settle or fail.

[NOTE]
====
There are ideas out that might solve this issue to some degree by allowing the payer to abort a payment. You can find more about that under the terms `cancelable payments` or `stuckless payments`. However the proposals that exist only reverse the problem as now the sender can misbehave and the recipient looses control. Another solution is to use many paths in a multipath payment and include some redundancy and ignore the problem that a path takes longer to complete.
====

Despite these principle problems there are plausible situations in which the routing process fails and in which honest nodes can and should react.
This is why the onion protocol has the ability to send back errors.
Some - but not all - of the reasons for errors could be:

* A node has not enough liquidity to set up the next HTLC
* The next payment channel does not exist anymore as it might have been closed while the onion was routed to node that was supposed to forward the onion along the channel.
* While the channel might still be open - as the funding transaction was never spent - it might happen that the other peer is offline. This of course prevents the node to forward the onion.
* The key exchanges of the sender might have been wrong so the decryption of the onion or the HMCAs do not match. (also because someone tried to tamper with the onion)
* The recipient might not have issued an invoice and does not know the payment details.
* The amount of the final HTLC is too low and the recipient does not want to release the preimage.

If errors like those occur a node should send back a reply onion.
The reply onion will be encrypted at each hop with the same shared secrets that have been used to construct the onion or decrypt a layer.
These shared keys are all known to the originator of the payment.
The onion innermost onion contains the error message and an HMAC for the error message.
The process makes sure that the sender of the onion and recipient of the reply can be sure that the error really originated from the node that the error messages says.
Another important step in the process of handling errors is to abort the routing process.
We discussed that the sender of a payment cannot just remove the HTLC on the channel along which the sender sent the payment.
Recall for example the situation in which Alice sent and onion to Bob who set up an HTLC with Wei.
If Alice wanted to remove the HTLC with Bob this would put a financial risk on Bob.
He fears that his HTLC with Wei still might be fulfilled meaning that he could not claim the reimbursement from Alice.
Thus Bob would never agree to remove the HTLC with Alice unless he already has removed his HTLC with Wei.
If however the HTLC between Alice and Bob are set up and the HTLC between Bob and Wei are set up but Wei encounters problems with forwarding the onion it is perfectly Wei has more options than Alice.
While sending back the error Onion to Bob Wei could ask him to remove the HTLC.
Bob has no risk in removing the HTLC with Wei and Wei also has no risk as there is no downstream HTLC.
Removing an HTLC is happening very similar to adding HTLCs.
Due to the just presented argument only peers who have accepted an offered HTLC can initiate the removal of HTLCs.
In the case of errors peers signals that they wish to remove the HTLC by sending an `update_fail_htlc` or `update_fail_malformed_htlc` message.
These messages contain the id of an HTLC that should be removed in the next version of the commit transaction.
In the same handshake like process that was used to exchange `commitment_signed` and `revoke_and_ack` messages the new state and thus pair of commitment signatures has to be negotiated and agreed upon.
This also means while the balance of a channel that was involved in a failed routing process will not have changed at the end it will have negotiated two new commitment transactions.
Despite having the same balance it must not got back to the previous commitment transaction which did not include the HTLC as this commitment transaction was revoked.
If it was used to force close the channel the channel partner would have the ability to create a penalty transaction and get all the funds.

==== Settling HTLCs
In the last section you you understood the error cases that can happen with onion routing via the chain of HTLCs.
You have learnt how HTLCs are removed if there is an error.
Of course HTLCs also need to be removed and the balance needs to be updated if the chain of HTLCs was successfully set up to the destination and the preimage is being released.
Not surprisingly this process is initiated with anther lightning message called `update_fulfill_htlc`.
You will remember that HTLCs are set up and supposed to be removed with a new balance for the recipient in exchange for a secret `preimage`.
Recalling the complex protocol with `commitment_signed` and `revoke_and_ack` messages you might wonder how to make this exchange `preimage` for new state atomic.
The cool thing is it doesn't have to be.
Once a channel partner with an accepted incoming HTLC knows the preimage can savely just pass it to the channel partner.
That is why the `update_fulfill_htlc` message contains only the `channel_id` the `id` of the HTLC and the `preimage`.
You might wonder that channel partner could now refuse to sign a new channel state by sending `commitment_siged` and `revoke_and_ack` messages.
This is not a problem though.
In that case the recipient of the offered HTLC can just go on chain by force closing the channel.
Once that has happened the preimage can be used to claim the HTLC output.

==== Some Considerations for routing nodes
Accepting and HTLC removes funds from a peer that the peer cannot utilize unless the HTLC is removed due to success or failure.
Similarly forwarding an HTLC binds some funds from your nodes payment channel until the HTLC is being removed again.
As we explained in the very beginning of the chapter engaging into the forwarding process of HTLCs does neither yield a direct risk to loose funds nor does it gain the chance to gain funds.
However the funds in jeopardy could be locked for some time.
In the worst case the routing process needs to be resolved on chain as the payment channel was forced close due to some other circumstances.
In that case outstanding HTLCs produce additional onchain food print and costs.
Thus there are two small economic risks involved with the participation in the routing process.

. Higher onchain fees in case of forced channel closes due to the higher footprint of HTLCs
. Opportunity costs of locked funds. While the HTLC is active the funds cannot be used otherwise.

In economics and financial mathematics the idea to pay another person that takes a risk is widely spread and seems reasonable.
Owners of routing nodes might want to monitor the routing behavior and opportunities and compare them to the onchain costs and the opportunity costs in order to compute their own routing fees that they wish to charge to accept and forward HTLCs.

Also one should notice that HTLCs are outputs in the commitment transaction.
Lightning network protocol allows users to pay a single satoshi.
However it is impossible to set up HTLCs for this amount.
The reason is that the corresponding outputs in the commitment transaction would be below the dust limit.
Such cases are solved in practice with the following trick:
Instead of setting up an HTLC the amount is taken from the output of the sender but not added to the output of the recipient.
Thus the HTLCs which are below the dust limit can understood as additional fees in the commitment transaction.
Most Lightning Nodes support the configuration of minimum accepted HTLC values.
Operators have to consider if they want to risk overpaying fees or loosing funds in the forced channel close cases because the commitment transactions have been added to the fees.


Explain fee and time-lock considerations
The “HTLC Switch” analogy compared to regular network switch
Circuit map concept, how to handle forwarding
Pipeline styles for HTLCs
Error handling and encryption for HTLCs



Explain “one little trick” of DH re-randomization
Explain how we keep the packet size fixed, what’s MAC’d, etc
Introduce the new modern payload format which uses TLV
