Say we have xSalsa20 authenticated using Poly1305. If $ X $ is the ciphertext, $N$ is the nonce value, and $H$ is the authentication tag such that the final ciphertext is $ N || X || H $, then given the key $K$, is it possible to extend $ X $ with more data, without decrypting it, updating $N$ and $Y$ as needed? (I’m not sure if $N$ would need to be changed.)
Salsa20 is a stream cipher so it produces a CSPR key-stream, $ S $, and then then ciphertext becomes $ X = S oplus P $, where $P$ is the plaintext. So I intuitively feel as though this should be a lot easier to do than with a block cipher. Perhaps by generating the same key-stream up until the size of the ciphertext and encrypting the new data with the part of the key-stream past that point. If the authentication tag is generated from the ciphertext then decryption wouldn’t be necessary for that either. Also the nonce would not really be reused in a scheme like this as far as I can see.
How well would this translate to other stream ciphers like XChaCha20-Poly1305?