construct/include/ircd/m

Matrix Protocol

Introduction

The authoritative place for learning about matrix is at matrix.org but it may be worthwhile to spend a moment and consider this introduction which explains things by distilling the formal core of the protocol before introducing all of the networking and communicative accoutrements...

Identity

The Matrix-ID or mxid is a universally unique plain-text string allowing an entity to be addressed internet-wide which is fundamental to the matrix federation in contrast to the traditional IRC server/network. An example of an mxid: "@user:host" where host is a public DNS name, user is a party to host, and the '@' character is replaced to convey type information. The character, called a sigil, is defined to be '!' for room_id identifiers, '$' for event_id identifiers, '#' for room aliases, and '@' for users.

Event

The fundamental primitive of this protocol is the event object. This object contains some set of key/value pairs and the protocol defines a list of such keys which are meaningful to the protocol. Other keys which are not meaningful to the protocol can be included directly in the event object but there are no guarantees for if and how a party will pass these keys. To dive right in, here's the list of recognized keys for an event:

auth_events
content
depth
event_id
hashes
membership
origin
origin_server_ts
prev_events
prev_state
redacts
room_id
sender
signatures
state_key
type

In the event structure, the value for sender and room_id and event_id are all an mxid of the appropriate type.

The event object is also the only fundamental primitive of the protocol; in other words: everything is an event. All information is conveyed in events, and governed by rules for proper values behind these keys. The rest of the protocol specification describes an abstract state machine which has its state updated by an event, in addition to providing a standard means for communication of events between parties over the internet. That's it.

Timeline

The data tape of the matrix machine consists of a singly-linked list of event objects with each referencing the event_id of its preceding parents somewhere in the prev_ keys; this is called the timeline. Each event is signed by its creator and affirms all referenced events preceding it. This is a very similar structure to that used by software like Git, and Bitcoin. It allows looking back into the past from any point.

State

The state consists of a subset of events which are accumulated according to a few rules when playing the tape through the machine. Events which are selected as state will overwrite a matching previously selected state event and thus reduce the number of events in this set to far less than the entire timeline. The state is then used to satisfy queries for deciding valid transitions for the machine. This is like the "work tree" in Git when positioned at some commit.

• Events with a state_key are considered state.

• The identity of a state event is the concatenation of the room_id value with the type value with the state_key value. Thus an event with the same room_id, type, state_key replaces an older event in state.

• Some state_key values are empty strings "". This is a convention for singleton state events, like an m.room.create event. The state_key is used to represent a set, like with m.room.member events, where the value of the state_key is a user mxid.

Room

The room structure encapsulates an instance of the matrix machine. A room is a container of event objects in the form of a timeline. The query complexity for information in a room timeline is as follows:

• Ephemeral (non-state) events in the timeline have a linear lookup time: the timeline must be iterated in sequence to find a satisfying message.

• State events in the timeline have a logarithmic lookup: the implementation is expected to maintain a map of the type,state_key values for events present in the timeline.

The matrix protocol specifies certain event types which are recognized to affect the behavior of the room; here is a list of some types:

m.room.name
m.room.create
m.room.topic
m.room.avatar
m.room.aliases
m.room.canonical_alias
m.room.join_rules
m.room.power_levels
m.room.member
m.room.message
...

Some of these events are state events and some are ephemeral (these will be detailed later). All m.room.* namespaced events govern the functionality of the room. Rooms may contain events of any type, but we don't invent new m.room.* type events ourselves. This project tends to create events in the namespace ircd.* These events should not alter the room's functionality for a client with knowledge of only the published m.room.* events wouldn't understand.

Server

Matrix rooms are intended to be distributed entities that are replicated by all participating servers. It is important to make this clear by contrasting it with a common assumption that rooms are "hosted" by some entity. For example when one sees an mxid such as !matrix:matrix.org it is incorrect to assume that matrix.org is "hosting" this room or that it plays any critical role in its operation.

Servers are simply obliged to adhere to the rules of the protocol. There is no cryptographic guarantee that rules will be followed (e.g. zkSNARK), and no central server to query as an authority. Servers should disregard violations of the protocol as the room unfolds from the point of its creation.

The notion of hosting does exist for room aliases. In the above example the room mxid !matrix:matrix.org may be referred to by #matrix:matrix.org. As an analogy, if one considers the room mxid to be an IP address then the alias is like a domain name pointing to the IP address. The example alias is hosted by matrix.org under their authority and may be directed to any room mxid. The alias is not useful when its host is not available, but the room itself is still available from all other servers.

Communication

Servers communicate by broadcasting events to all other servers joined to the room. When a server wishes to broadcast a message, it constructs an event which references all previous events in the timeline which have not yet been referenced. This forms a directed acyclic graph of events, or DAG.

The conversation of messages moves in one direction: past to future. Messages only reference other messages which have a lower degree of separation indicated by the depth from the first message in the graph (where type was m.room.create).

• The monotonic increase in depth contributes to an intuitive "light cone" read coherence. Knowledge of any piece of information (like an event) offers strongly ordered knowledge of all known information which preceded it at that point.

• Write consistency is relaxed. Multiple messages may be issued at the same depth from independent actors and multiple reference trees may form independent of others. This provides the scalar for performance in a large distributed internet system.

DAG

The DAG is a tool which aids with the presentation of a coherent conversation for the room in lieu of the relaxed write consistency as previously mentioned. In this section we will analyze various examples of DAG's and how certain cases are approached by our implementation.

          [M00]
            |
          [M01]

Above: a very simple DAG: message M01 references M00; this means M00 is in the light-cone of M01. In other words, when one obtains M01 one obtains M00 along with it (M01 brings M00 and everything behind it at that point). This is the theoretical causality offered by the DAG, which is considered one of the stronger types of orderings in the various schemes known to distributed system academics.

            [M00]
              |
            [M01]
              |
            [M02]

Above: The normal addition of M02. Now M01 and M00 are "brought by" M02.

            [M00]--o
              |    |
            [M01]  |
              |    |
            [M02]--o

Above: Example of a redundant reference. Note that this is a valid configuration in the matrix protocol and implementations; we do not reject M02 as ill-formed though our implementation prefers to avoid generating such references if possible, it may still do so legitimately. We consider this redundant because:

1. M00 is already reachable through the reference to M01; the reference around M01 reveals no new information in the light-cone which wasn't already known.

2. Since M02 absolutely happens-after M01 and the same holds true for M01 and M00: distinguishing which is the legitimate reference and which is unnecessary is clear.

Redundant references may still be produced for legitimate reasons:

1. Voluntary DAG gaps: For huge rooms as well as long periods of downtime an implementation may not have a complete message graph. In this case it may not know (or care) why there is a gap in the room's DAG, and it simply "bridges" the gap for its own satisfaction to create a unified graph even though such an action is gratuitious to others.

2. Involuntary DAG gaps: In a federated system comprised of many implementations there is a non-zero proability that eventually some message will be accepted or rejected differently. That is a problem for an essentially linked-list data format: the inability to traverse through one event relegates everything on the other side of it inaccessible. A redundant reference may be used to "route around" a malformed event which is considered essential for some and redundant by others.

            [M00]
              |
            [M01]
           /     \
      [M02]       [M02]

Above: When two servers transmit at the same time. This is where the DAG shines by relaxing write-consistency for a large scale distributed system: two actors can issue messages at the same time without explicit synchronization. There is no magic here (yet), and as one would assume, two simultaneous messages as illustrated may still be conflicting.

            [M00]
              |
            [M01]
           /     \
     [M02A]       [M02B]
           \     /
            [M03]

Above: The M03 message "sees" both M02 messages and makes two references.

            [M00]
              |
            [M01]
          /   |   \

   [M02]    [M02]    [M02]

          \   |   /
            [M03]
              |
            [M04]
              |

Below: when three servers transmit, and then a fourth server transmits having only received two out of the three transmissions in the previous round.

            [M00]
              |
            [M01]
          /   |   \

   [M02]    [M02]    [M02]

       \        \     /
        \        [M03]

           \     /
            [M04]
              |
            [M05]
              |

Coherence

Keen observers may have realized by now this system is not fully coherent. To be coherent, a system must leverage entry consistency and/or release consistency. Translated to this system:

• Entry is the point where an event is created containing references to all previous events. Entry consistency would mean that the knowledge of all those references is revealed from all parties to the issuer such that the issuer would not be issuing a conflicting event.

• Release is the act of broadcasting that event to other servers. Release consistency would mean that the integration of the newly issued event does not conflict at the point of acceptance by each and every party.

This system appears to strive for eventual consistency. To be pedantic, that is not a third lemma supplementing the above: it's a higher order composite (like mutual exclusion, or other algorithms). What this system wants to achieve is a byzantine tolerance which can be continuously corrected as more information is learned. This is a tolerance, not a prevention, because the relaxed write consistency is of extreme practical importance.

For eventual consistency to be coherent, the "seeds" of a correction have to be planted early on before any fault. When the fault occurs, all deviations can be corrected toward some single coherent state as each party learns more information. Once all parties learn all information from the system, there is no possibility for incoherence. The caveat is that some parties may need to roll back certain decisions they made without complete information.

Consider the following: Alice is a room founder and has one other member Bob who is an op. Alice outranks Bob. Consider the following scenario:

1. Charlie joins the room. Now the room has three members. Everyone is still in full agreement.

2. GNAA ddos's Alice so she can't reach the internet but she can still use her server on her LAN.

3. Alice likes Charlie so she gives him +e or some ban immunity.

4. Bob doesn't like Charlie so he bans him.

Now there is a classic byzantine fault. The internet sees a room with two members Alice and Bob again while Alice sees a room with three: Alice, Bob and Charlie.

5. GNAA stops the ddos.

This fault now has to be resolved. This is called "state conflict resolution" and the matrix specification does not know how to do this. What is currently specified is that Alice and Bob can only perform actions that are valid with the knowledge they had when they performed them. In fact, that was true in this scenario.

Intuitively, Alice needs to dominate the resolution because Alice outranks Bob. Charlie must not be banned and the room must continue with three members. Exactly how to roll back the ban and reinstate Charlie may seem obvious but there are practicalities to consider: Perhaps Alice is ddosed for something like a year straight and Charlie has entirely given up on socializing over the internet. A seemingly random and irrelevant correction will be in store for the room and the effects might be far more complicated.

Implementation

Model

This system embraces the fact that "everything is an event." It then follows that everything is a room. We use rooms for both communication and storage of everything.

There is only one† backend database and it stores events. For example: there is no "user accounts database" holding all of the user data for the server- instead there is an !accounts room. To use these rooms as efficient databases we categorize a piece of data with an event type and key it with the event state_key and the value is the event content. Iteration of these events is also possible. This is now a sufficient key-value store as good as any other approach; better though, since such a databasing room retains all features and distributed capabilities of any other room. We then focus our efforts to optimize the behavior of a room, to the benefit of all rooms, and all things.

† Under special circumstances other databases may exist but they are purely slave to the events database: i.e one could rm -rf a slave database and it would be rebuilt from the events database. These databases only exist if an event is truly inappropriate and doesn't fit the model even by a stretch. An example of this is the search-terms database which specializes in indexing individual words to the events where they are found so content searches can be efficient.

Technique

The Matrix room, as described earlier, is a state machine underwritten by timelines of events in a directed acyclic graph with eventual consistency. To operate effectively, the state machine must respond to queries about the state of the room at the point of any event in the past. This is similar to a git reset to some specific commit where one can browse the work tree as it appeared at that commit.

Was X a member of room Y when event Z happened?

The naive approach is to trace the graph from the event backward collecting all of the state events to then satisfy the query. Sequences of specific state event types can be held by implementations to hasten such a trace. Alternatively, a complete list of all state events can be created for each modification to the state to avoid the reference chasing of a trace at the cost of space.

Our approach is more efficient. We create a b-tree to represent the complete state to satisfy any query in logarithmic time. When the state is updated, only one path in the tree is modified and the root is stored with that event. This structure is actually immutable: the previous versions of the affected nodes are not discarded allowing past configurations of the tree to be represented. We further benefit from the fact that each node is referenced by the hash of its content for efficient reuse, as well as our database being well compressed.

Flow

This is a single-writer/multiple-reader approach. The "core" is the only writer. The write itself is just the saving of an event. This serves as a transaction advancing the state of the machine with effects visible to all future transactions and external actors.

The core takes the pattern of evaluate + exclude -> write commitment -> release sequence. The single writer approach means that we resolve all incoherence using exclusion or reordering or rejection on entry and before any writing and release of the event. Many ircd::ctx's can orbit the inner core resolving their evaluation with the tightest exclusion occurring around the write at the inner core. This also gives us the benefit of a total serialization at this point.

   :::::::
   |||||||      <-- evaluation + rejection
     \|/        <-- evaluation + exclusion / reordering
      !
      *         <-- actor serialized core write commitment
   //|||\\
 //|// \\|\\
:::::::::::::   <-- release sequence propagation cone

The entire core commitment process relative to an event riding through it on an ircd::ctx has a duration tolerable for something like a REST interface, so the response to the user can wait for the commitment to succeed or fail and properly inform them after.

The core process is then optimized by the following facts:

* The resource exclusion zone around most matrix events is either
  small or non-existent because of its relaxed write consistency.

* Writes in this implementation will not delay.

"Core dilation" is a phenomenon which occurs when large numbers of events which have relaxed dependence are processed concurrently because none of them acquire any exclusivity which impede the others.

   :::::::
   |||||||
   |||||||   <-- Core dilation; flow shape optimized for volume.
   |||||||
   /|||||\
  ///|||\\\
 //|/|||\|\\
:::::::::::::

Close up of the charybdis's write head when tight to one schwarzschild-radius of matrix room surface which propagates only one event through at a time. Vertical tracks are contexts on their journey through each evaluation and exclusion step to the core.

Input Events                                            Phase
::::::::::::::::::::::::::::::::::::::::::::::::::::::  validation / dupcheck
||||||||||||||||||||||||||||||||||||||||||||||||||||||  identity/key resolution
||||||||||||||||||||||||||||||||||||||||||||||||||||||  verification
|||| ||||||||||||||| ||||||||||||||| |||||||||||||||||  head resolution
--|--|----|-|---|--|--|---|---|---|---------|---|---|-  graph resolutions
----------|-|---|---------|-------|-----------------|-  module evaluations
 \          |   |         |       |                  /  post-commit prefetching
   ==       ==============|       |               ==    Lowest velocity locks
      \                   |       |             /
        ==                |       |          ==         Mid velocity locks
           \              |       |        /
             ==           |      /      ==              High velocity locks
                \         |     /     /
                  ==      =====/=  ==                   Highest velocity lock
                     \       /   /
                      \__   / __/
                         _ | _
                           !                            Write commitment

Above, two contexts are illustrated as contending for the highest velocity lock. The highest velocity lock is not held for significant time.

                           *                            Singularity
                         [   ]
           /-------------[---]-------------\
        /                :   :                \         Federation send
     /         /---------[---]---------\         \
             /           :   :           \              Client sync
    out    /      /------[---]------\      \   out
         /       /       :   :       \       \
       /   out  /        |   |        \  out   \
               /   out   /   \   out   \
                        /     \
                        return
                     | result to |
                     | evaluator |
                     -------------

Above, a close-up of the release sequence. The new event is being "viewed" by each consumer context separated by the horizontal lines representing a context switch from the perspective of the event travelling down. Each consumer performs its task for how to propagate the commissioned event.

Scaling

Scaling beyond the limit of a single CPU core can be done with multiple instances of IRCd which form a cluster of independent actors. This cluster can extend to other machines on the network too. The independent actors leverage the weak write consistency and strong ordering of the matrix protocol to scale the same way the federation scales.

Interference pattern of two IRCd'en:

  ::::::::::::::::::::::::::::::::::::
  --------\:::::::/--\:::::::/--------
           |||||||    |||||||
             \|/        \|/
              !          !
              *          *
           //|||\\    //|||\\
         //|// \\|\\//|// \\|\\
        /|/|/|\|\|\/|/|/|\|\|\|\