# SETI — Peer to peer set intersections

The SETI service implements efficient set intersection between two peers over a CADET tunnel. Elements of a set consist of an element type and arbitrary binary data. The size of an element’s data is limited to around 62 KB.

## Intersection Sets

Sets created by a local client can be modified (by adding additional elements) and reused for multiple operations. If elements are to be removed, a fresh set must be created by the client.

## Set Intersection Modifications

Even when set operations are active, one can add elements to a set. However, these changes will only be visible to operations that have been created after the changes have taken place. That is, every set operation only sees a snapshot of the set from the time the operation was started. This mechanism is not implemented by copying the whole set, but by attaching generation information to each element and operation.

## Set Intersection Operations

Set operations can be started in two ways: Either by accepting an operation request from a remote peer, or by requesting a set operation from a remote peer. Set operations are uniquely identified by the involved peers, an application id and the operation type.

The client is notified of incoming set operations by set listeners. A set listener listens for incoming operations of a specific operation type and application id. Once notified of an incoming set request, the client can accept the set request (providing a local set for the operation) or reject it.

## Intersection Result Elements

The SET service has two result modes that determine how an operation’s result set is delivered to the client:

- Return intersection. All elements of set resulting from the set intersection are returned to the client.

- Removed Elements. Only elements that are in the local peer’s initial set but not in the intersection are returned.

libgnunetseti libgnunetseti ————-

### Intersection Set API

New sets are created with `GNUNET_SETI_create`. Only the local peer’s configuration (as each set has its own client connection) must be provided. The set exists until either the client calls `GNUNET_SET_destroy` or the client’s connection to the service is disrupted. In the latter case, the client is notified by the return value of functions dealing with sets. This return value must always be checked.

Elements are added with `GNUNET_SET_add_element`.

### Intersection Listeners

Listeners are created with `GNUNET_SET_listen`. Each time time a remote peer suggests a set operation with an application id and operation type matching a listener, the listener’s callback is invoked. The client then must synchronously call either `GNUNET_SET_accept` or `GNUNET_SET_reject`. Note that the operation will not be started until the client calls `GNUNET_SET_commit` (see Section "Supplying a Set").

### Intersection Operations

Operations to be initiated by the local peer are created with `GNUNET_SET_prepare`. Note that the operation will not be started until the client calls `GNUNET_SET_commit` (see Section "Supplying a Set").

### Supplying a Set for Intersection

To create symmetry between the two ways of starting a set operation (accepting and initiating it), the operation handles returned by `GNUNET_SET_accept` and `GNUNET_SET_prepare` do not yet have a set to operate on, thus they can not do any work yet.

The client must call `GNUNET_SET_commit` to specify a set to use for an operation. `GNUNET_SET_commit` may only be called once per set operation.

### The Intersection Result Callback

Clients must specify both a result mode and a result callback with `GNUNET_SET_accept` and `GNUNET_SET_prepare`. The result callback with a status indicating either that an element was received, or the operation failed or succeeded. The interpretation of the received element depends on the result mode. The callback needs to know which result mode it is used in, as the arguments do not indicate if an element is part of the full result set, or if it is in the difference between the original set and the final set.

## The SETI Client-Service Protocol

### Creating Intersection Sets

For each set of a client, there exists a client connection to the service. Sets are created by sending the `GNUNET_SERVICE_SETI_CREATE` message over a new client connection. Multiple operations for one set are multiplexed over one client connection, using a request id supplied by the client.

### Listeners for Intersection

Each listener also requires a separate client connection. By sending the `GNUNET_SERVICE_SETI_LISTEN` message, the client notifies the service of the application id and operation type it is interested in. A client rejects an incoming request by sending `GNUNET_SERVICE_SETI_REJECT` on the listener’s client connection. In contrast, when accepting an incoming request, a `GNUNET_SERVICE_SETI_ACCEPT` message must be sent over the set that is supplied for the set operation.

### Initiating Intersection Operations

Operations with remote peers are initiated by sending a `GNUNET_SERVICE_SETI_EVALUATE` message to the service. The client connection that this message is sent by determines the set to use.

### Modifying Intersection Sets

Sets are modified with the `GNUNET_SERVICE_SETI_ADD` message.

### Intersection Results and Operation Status

The service notifies the client of result elements and success/failure of a set operation with the `GNUNET_SERVICE_SETI_RESULT` message.

## The SETI Intersection Peer-to-Peer Protocol

The intersection protocol operates over CADET and starts with a GNUNET_MESSAGE_TYPE_SETI_P2P_OPERATION_REQUEST being sent by the peer initiating the operation to the peer listening for inbound requests. It includes the number of elements of the initiating peer, which is used to decide which side will send a Bloom filter first.

The listening peer checks if the operation type and application identifier are acceptable for its current state. If not, it responds with a GNUNET_MESSAGE_TYPE_SETI_RESULT and a status of GNUNET_SETI_STATUS_FAILURE (and terminates the CADET channel).

If the application accepts the request, the listener sends back a `GNUNET_MESSAGE_TYPE_SETI_P2P_ELEMENT_INFO` if it has more elements in the set than the client. Otherwise, it immediately starts with the Bloom filter exchange. If the initiator receives a `GNUNET_MESSAGE_TYPE_SETI_P2P_ELEMENT_INFO` response, it beings the Bloom filter exchange, unless the set size is indicated to be zero, in which case the intersection is considered finished after just the initial handshake.

### The Bloom filter exchange in SETI

In this phase, each peer transmits a Bloom filter over the remaining keys of the local set to the other peer using a `GNUNET_MESSAGE_TYPE_SETI_P2P_BF` message. This message additionally includes the number of elements left in the sender’s set, as well as the XOR over all of the keys in that set.

The number of bits ‘k’ set per element in the Bloom filter is calculated based on the relative size of the two sets. Furthermore, the size of the Bloom filter is calculated based on ‘k’ and the number of elements in the set to maximize the amount of data filtered per byte transmitted on the wire (while avoiding an excessively high number of iterations).

The receiver of the message removes all elements from its local set that do not pass the Bloom filter test. It then checks if the set size of the sender and the XOR over the keys match what is left of its own set. If they do, it sends a `GNUNET_MESSAGE_TYPE_SETI_P2P_DONE` back to indicate that the latest set is the final result. Otherwise, the receiver starts another Bloom filter exchange, except this time as the sender.

### Intersection Salt

Bloom filter operations are probabilistic: With some non-zero probability the test may incorrectly say an element is in the set, even though it is not.

To mitigate this problem, the intersection protocol iterates exchanging Bloom filters using a different random 32-bit salt in each iteration (the salt is also included in the message). With different salts, set operations may fail for different elements. Merging the results from the executions, the probability of failure drops to zero.

The iterations terminate once both peers have established that they have sets of the same size, and where the XOR over all keys computes the same 512-bit value (leaving a failure probability of 2-511).