As an example, let's take a simple situation where AES-256-CBC with IV + MAC is used to encrypt a given plainText to offer both authentication and prevent identical cipherTexts.
The keys are derived using HMAC for simplicty (alternatively could be HKDF)
masterkey = [32 random bytes]; encryptionKey = hmac_sha256(masterkey,'encryption_key'); mac = hmac_sha256(masterkey,'mac_key'); ivInput = [2 random bytes]; iv = hmac_sha256(masterkey,ivInput);
Would this already deliver enough 'randomness' for almost any messaging system, since with 2 bytes the chance of arriving at an identical cipherText with an identical message would already be around 0.002% (1/(256*256)*100)?
(256 possibilities per byte, 2 bytes used for IV)