# FuzzyTags

Anonymous messaging systems (and other privacy-preserving applications) often require a mechanism for one party
to learn that another party has messaged them.

Many schemes rely on a bandwidth-intensive "download everything and attempt-decryption" approach. Others rely on a trusted
3rd party, or non-collusion assumptions, to provide a "private" service.

It would be awesome if we could get an **untrusted**, **adversarial** server to do the work for us without compromising metadata-resistance!

**fuzzytags** is an experimental probabilistic cryptographic tagging structure to do just that! 

Specifically **fuzzytags** provides the following properties:

 * Correctness: Valid tags constructed for a specific public key will always validate when tested using a derived detection key.
 * Fuzziness: Tags will produce false positives with probability _p_ related to the security property (_γ_) when tested against detection keys they
 were not intended for.
 * Security: An adversarial server with access to the detection key **is unable to distinguish false positives from true positives**. (Detection Ambiguity)

## Security (hic sunt dracones)

This crate provides an experimental implementation of the `FMD2` scheme described in ["Fuzzy Message Detection"](https://eprint.iacr.org/2021/089). Using
Ristretto as the prime order group.

This code has not undergone any significant review.

Further, the properties provided by this system are highly dependent on selecting a **false positive rate** _p_ and 
**scheme constant** _γ_ for your system. There is no one-size-fits-all approach.

If _p_ is too low, then the probability of false positives will be very high.

If _p_ is too high, then an adversarial server will be able to link messages to recipients with low probability. 

Likewise a large _γ_ means higher bandwidth costs, but a small _γ_ reveals more of the secret keys to the server and
increases false positives. 

## More Detailed System Description

There exists a metadata resistant application that uses untrusted servers to mediate communication between parties. 

Each party can be identified with a set of cryptographic identifiers and there exists methods in or external to the system
to distribute keys securely and authentically.

Now, instead of each party adopting a download-everything approach to metadata privacy (or invoking non-collusion
or other assumptions) we can leverage fuzzytags to reduce the number of messages downloaded from the server by each party
while maintaining a formalized concept of metadata privacy.

Every party generates a `FuzzyTagKeyPair`, consisting of a `FuzzyTagSecretKey` and a `FuzzyTagPublicKey`. These keys will
be generated with a parameter _γ_ that relates to the minimum false-positive probability 2^-γ.

When submitting messages to the server for an intended **recipient**, the **sender** will generate a new tag
from the  **recipients** `FuzzyTagPublicKey`.

All parties will `extract` a `FuzzyTagDetectionKey` from their key pair. This key will be of length `n` and provide
a false positive detection probability of  0 <= 2^-n <= 2^-γ. This detection key can be given to an adversarial server.

When fetching new messages from the adversarial server, the server first runs a `test` of the tag of the message against
the parties' detection key. If the tag passes the test, the message (along with the tag) is provided to the **recipient**.

Finally, the **recipient** runs their own `test` of the tag against an extracted detection key such that 
`FuzzyTagSecretKey == FuzzyTagDetectionKey` i.e. the probability of a false positive will be 2^-n == 2^-γ. This will
produce a subset of messages likely intended for the **recipient**, with a smaller probability of false positives.

Alternatively the **recipient**  can simply try and decrypt every message in the subset of messages that the server
provided them (depending on the efficiency of the decryption method).

## Usage

Generate a key pair: 
    
    let gamma = 3;
    let key = FuzzyTagKeyPair::generate(gamma);

`key.public_key` can be given to parties who you want to be able to communicate with you over a specific anonymous
messaging service / privacy-preserving application.

`key.detection_key` can be given to untrusted _adversarial_ servers.

`gamma` is security property (_γ_) in the system. For a given gamma, a tag generated for a specific public key will
validate against a random public key with a maximum probability of 2^-gamma.

## Generating Tags

Once in possession of a public key, a party in a metadata resistant app can use it to generate tags:
    
      let tag = public_key.generate_tag();

These tags can then be attached to a message in a metadata resistant system.

## Testing Tags

First it is necessary to extract a detection key for a given false positive probability 0 <= 2^-n <= 2^-γ.

This extracted key can then be given to an adversarial server. The server can then test a given tag against the detection key e.g.:

    let detection_key = key.extract(5);
    if detection_key.test_tag(tag) {
        // the message attached to this tag *might* be for the party associated with the detection key 
    } else {
        // the message attached to this tag is definitely *not* for the party associated with the detection key.
    }




