It sounds like you are assuming that if the data were modified, decryption would fail catastrophically and you'd end up with garbage. This is precisely the point of AEAD: providing cryptographic guarantee that decryption will fail catastrophically if things are tampered with.

That guarantee is not provided with unauthenticated stream ciphers. For example, some stream ciphers work by essentially using a deterministic but unpredictable PRNG seeded with the key and IV to generate a bitstream, and then XOR the plaintext with that bitstream to generate the ciphertext.

With such a stream cipher, If Eve knows that the data format is, e.g., the an 8-byte unsigned integer user ID followed by the rest of the payload, Eve can take the first 8 bytes of the ciphertext and XOR it with Bob's user ID (public information) and her own user ID to corrupt the message in such a way that the ID in the resulting cleartext would contain her user ID instead of Bob's, and thus pass the validation that it seems like you are proposing.

Let C[] be the cipher text, K[] be the key stream, B be Bob's ID, and E be Eve's ID:

C[:8] = B ^ K[:8]

C[:8] ^ B = K[:8]

C' = C[:8] ^ B ^ E ++ C[8:]

C' would decrypt, validate as "belonging" to Eve, and contain Bob's data.

Nowhere did I say I used an unauthenticated cipher. It was all authenticated cipher. Indeed, usually it was still AEAD (AES-GCM), but instead of using the offset as the AD I simply derived a new key from the offset, thus not using the AD part. This way I would swap out the algorithm to an authenticated cipher that wasn't AEAD (e.g. AES-CBC+HMAC) without breaking how anything worked.

It sounds like the source of confusion is in terminology. I would consider AES-CBC+HMAC to be an AEAD construction, and I would consider whatever "secret key" you pass into HMAC along with the ciphertext to be the "associated data". AES-GCM is an AEAD construction that gives you the MAC organically as part of the cipher, but that is not what makes it AEAD as I understand it.

If you are using an AEAD cipher mode, then you always have AD, but sometimes that AD might be the empty string. In that case, the advantage to using contextual AD as opposed to using the empty string as AD and then doing additional verification on the decrypted object is that it prevents some kinds of timing attacks, because cryptographic libraries will often implement AEAD constructions to fail in constant time, where as your scheme will take longer if post-decryption validation of contextual data encoded in the plaintext fails compared to if decryption fails.

> I would consider AES-CBC+HMAC to be an AEAD construction

OK fair.

> and I would consider whatever "secret key" you pass into HMAC along with the ciphertext to be the "associated data"

The secret key isn't associated data. You take your base HKDF key and expand new crypto for an authenticated cipher from the offset as info (+ maybe other parameters like file name). That key is then used to decrypt. If you squint I guess you could call that AD but it's functionally a very different role.

> because cryptographic libraries will often implement AEAD constructions to fail in constant time, where as your scheme will take longer if post-decryption validation of contextual data encoded in the plaintext fails compared to if decryption fails.

I think you've misunderstood what I said. As I repeat above, the AEAD key is derived from the offset. There's no post-decryption validation of contextual data because the plaintext is empty. HKDF derivation is constant time and authenticated decryption is constant time. Once decrypted you have a valid block at that location. There's nothing extra left to validate (or perhaps the decrypted contents, but that's irrelevant for cryptographic purposes).

My broader point is that I have yet to encounter a use-case for a non-empty AD string.

There are several of them on this thread. For example: encrypt a 10 gigabyte file. You'll need to chunk it; each chunk will exist at an offset. Encode the chunk offset into the Associated Data. Notice that you never store this Associated Data; you simply have it in the context of encrypting and decrypting the file. But the AEAD MAC captures it, and now you can't cut and paste chunks of a ciphertext.

Or alternatively, as I said, derive a new key for each chunk where the offset is part of the info used to derive the key and have an empty AD. Same effect.

It sounds like you have constructed a way to encrypt data such that it can only be decrypted by someone who has the same (secret) key and (non-secret) associated data that was used to encrypt it, or else decryption fails.

As you said, same effect: the scheme you have described is not an alternative to AEAD. It is an example of AEAD. You're still using the offset as associated data, you just happen to be composing your AEAD scheme out of another AEAD scheme into which you pass an empty string as associated data.

Other than differences in the limit to the number of messages you can encrypt before nonce exhaustion or the number of bits of secrecy or authentication strength provided, the external interface and use case of your system perfectly matches that of AES-GCM or other popular AEAD constructions.

> Other than differences in the limit to the number of messages you can encrypt before nonce exhaustion or the number of bits of secrecy or authentication strength provided, the external interface and use case of your system perfectly matches that of AES-GCM or other popular AEAD constructions.

Ahh, but that’s not a trivial part of the design and why this is strictly better than using a single AES-GCM key with AD. And also it’s more generic across whatever type of key you choose to derive.

Whatever else using a KDF to mix Associated Data into your key might be, it's not "strictly better" than GCM. I'm not sure there's much wrong with it (it's the same approach XAES uses for extended nonces) other than how slow it is, but there's a reason cryptographers don't design all the AEADs to work this way.

I may be missing a subtlety here but it seems like you've essentially reinvented Associated Data but with an extra KDF extraction and an AES key expansion for every chunk.