Identity

The base abstraction of the protocol is a knowledge-based identity interface, where the identity of an agent is defined entirely on the basis of whether or not they know some secret information.

Agents can use private information (likely randomness) to create an internal identity, from which they can derive an external identity to which it corresponds. The external identity is a name which can be shared with other parties. The agent who knows the internal identity can sign messages, which any agent who knows the external identity can verify, and any agent who knows the external identity can encrypt messages which the agent with knowledge of the internal identity can decrypt. This identity interface is independent of the particular cryptographic mechanisms, which may vary.

An identity is defined by two pairs of functions which are inverse to each other:

sign and verify, where sign takes a string to sign and produces a signature such that any sign-ed message is accepted by verify
encrypt and decrypt, where encrypt takes a string to encrypt such that any encrypt-ed message is opened by decrypt

data Identity where
    sign :: ByteString -> ByteString
    verify :: ByteString -> ByteString -> Bool

    verify m (sign m) = 1

    encrypt :: ByteString -> ByteString
    decrypt :: ByteString -> Maybe ByteString

    decrypt . encrypt = pure

The verify and encrypt functions together form the external identity, while the sign and decrypt operations together form the internal identity. In general, the external identity can be derived from the internal identity, but not vice-versa. The internal identity is a self-contained name which can be used to send messages from and decrypt messages sent by another agent to the corresponding external identity, while the external identity is a self-contained name which can be used to verify messages from and encrypt messages to any agent with knowledge of the internal identity.

For example, an identity can be the signature generation and decryption functions in a standard asymmetric public-key encryption scheme with secret key secret and public key key, where:

sign and decrypt are curried with the secret as sign'(secret) and decrypt'(secret)
verify and encrypt are curried with the key as verify'(key) and encrypt'(key)

The canonical representation of an external identity is defined as hash(verify, encrypt).

NOTE: Consider requiring ZKP that someone knows internal identity s.t. for some (a random?) m they can sign and decrypt it. This would go in the external identity in order to provide a guarantee that there is an agent with knowledge of the internal identity. Unclear yet if necessary.

Composition

Identities can be composed both internally and externally, by both conjunction and disjunction. Conjunction (&&) and disjunction (||) refer here to the secret information, such that to compose external identities by conjunction creates an external identity such that signed messages can be decrypted only by an agent with knowledge of both internal identities and verify will return true only if a valid signature from each composed identity is provided, while to compose external identities by disjunction creates an external identity such that signed messages can be decrypted with knowledge of either internal identity and verify will return true if a valid signature from either composed identity is provided.

Any agent with knowledge of two external identities a and b can compose them as follows:

Under conjunction, verify(msg, sig) := a.verify(msg, sig.0) && b.verify(msg, sig.1) and encrypt(msg) := a.encrypt(b.encrypt(msg))
Under disjunction, verify(msg, sig) : a.verify(msg, sig) || b.verify(msg, sig) and encrypt(msg) := (a.encrypt(msg), b.encrypt(msg))

The canonical representation of composed external identities is defined the same as above, just with the new verify and encrypt functions.

Compositions can be chained to create arbitrary combinations. For example, "threshold" identities, e.g. a 2-of-3 between a, b, and c, can be obtained with (a && c) || (a && b) || (b && c). Composition of identities is used throughout the protocol and implementations may substitute more efficient operational representations where appropriate.

TODO: Do more efficient operational representations require different canonical serialisations? Can we make this nicely abstract still?

Special identities

To illustrate the generality we can come up with the following special identities:

"True / All"

Anyone can sign and decrypt (verify returns true and encrypt returns the plaintext). No secret knowledge is required, so all agents can take on this identity.

The true identity preserves structure under conjunction (x && true == x) and forgets structure under disjunction (x || true == true).

"False / None"

No one can sign or decrypt (verify returns false and encrypt returns empty string). No secret knowledge exists that fulfills these requirements, so no agent can take on this identity.

The false identity forgets structure under disjunction (x && false == false) and preserves structure under disjunction (x || false == x).

Observer-dependence

The basic interface of an identity is stateless, but identities may also be stateful, where an identity is defined with respect to a logical DAG (described later). In that case, the logical DAG is taken as an additional parameter to encrypt and verify, and the external identity commits to the predicate function of the logical DAG and the verify function at the logical time of instantiation (such that from any later version of the identity there will exist a valid chain of signatures back to the origin point).

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Anoma Specification