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Distributed Key Generation
Serai uses a modification of Pedersen's Distributed Key Generation, which is actually Feldman's Verifiable Secret Sharing Scheme run by every participant, as described in the FROST paper. The modification included in FROST was to include a Schnorr Proof of Knowledge for coefficient zero, preventing rogue key attacks. This results in a two-round protocol.
Encryption
In order to protect the secret shares during communication, the dkg library
establishes a public key for encryption at the start of a given protocol.
Every encrypted message (such as the secret shares) then includes a per-message
encryption key. These two keys are used in an Elliptic-curve Diffie-Hellman
handshake to derive a shared key. This shared key is then hashed to obtain a key
and IV for use in a ChaCha20 stream cipher instance, which is xor'd against a
message to encrypt it.
Blame
Since each message has a distinct key attached, and accordingly a distinct shared key, it's possible to reveal the shared key for a specific message without revealing any other message's decryption keys. This is utilized when a participant misbehaves. A participant who receives an invalid encrypted message publishes its key, able to without concern for side effects, With the key published, all participants can decrypt the message in order to decide blame.
While key reuse by a participant is considered as them revealing the messages themselves, and therefore out of scope, there is an attack where a malicious adversary claims another participant's encryption key. They'll fail to encrypt their message, and the recipient will issue a blame statement. This blame statement, intended to reveal the malicious adversary, also reveals the message by the participant whose keys were co-opted. To resolve this, a proof-of-possession is also included with encrypted messages, ensuring only those actually with per-message keys can claim to use them.