A multi-message multi-recipient PKE (mmPKE) encrypts a batch of messages, in one go, to a corresponding set of independently chosen receiver public keys. The resulting ''multi-recipient ciphertext'' can be then be reduced (by any 3rd party) to a shorter, receiver specific, ''invidual ciphertext.'' Finally, to recover the i-th message in the batch from their indvidual ciphertext the i-th receiver only needs their own decryption key. A special case of mmPKE is multi-recipient PKE (mPKE) where all receivers are sent the same message. By treating (m)mPKE and their KEM counterparts as a stand-alone primitives we allow for more efficient constructions than trivially composing individual PKE/KEM instances. This is especially valuable in the post-quantum setting, where PKE/KEM ciphertexts and public keys tend to be far larger than their classic counterparts.

Continuous Group Key Agreement (CGKA) -- or Group Ratcheting -- lies at the heart of a new generation of scalable End-to-End secure (E2E) cryptographic multi-party applications. One of the most important (and first deployed) CGKAs is ITK which underpins the IETF's upcoming Messaging Layer Security E2E secure group messaging standard. To scale beyond the group sizes possible with earlier E2E protocols, a central focus of CGKA protocol design is to minimize bandwidth requirements (i.e. communication complexity).