Note: this post will probably only really make sense to cryptography geeks.

In “When a KEM is not enough”, I described how to construct multi-recipient (public key) authenticated encryption. A naïve approach to this is vulnerable to insider forgeries: any recipient can construct a new message (to the same recipients) that appears to come from the original sender. For some applications this is fine, but for many it is not. Consider, for example, using such a scheme to create auth tokens for use at multiple endpoints: A and B. Alice gets an auth token for accessing endpoints A and B and it is encrypted and authenticated using the scheme. The problem is, as soon as Alice presents this auth token to endpoint A, that endpoint (if compromised or malicious) can use it to construct a new auth token to access endpoint B, with any permissions it likes. This is a big problem IMO.

I presented a couple of solutions to this problem in the original blog post. The most straightforward is to sign the entire message, providing non-repudiation. This works, but as I pointed out in “Digital signatures and how to avoid them”, signature schemes have lots of downsides and unintended consequences. So I developed a weaker notion of “insider non-repudiation”, and a scheme that achieves it: we use a compactly-committing symmetric authenticated encryption scheme to encrypt the message body, and then include the authentication tag as additional authenticated data when wrapping the data encryption key for each recipient. This prevents insider forgeries, but without the hammer of full blown outsider non-repudiation, with the problems it brings.

I recently got involved in a discussion on Mastodon about adding authenticated encryption to Age (a topic I’ve previously written about), where abacabadabacaba pointed out that my scheme seems incompatible with streaming encryption and decryption, which is important in Age use-cases as it is often used to encrypt large files. Age supports streaming for unauthenticated encryption, so it would be useful to preserve this for authenticated encryption too. Doing this with signatures is fairly straightforward: just sign each “chunk” individually. A subtlety is that you also need to sign a chunk counter and “last chunk” bit to prevent reordering and truncation, but as abacabadabacaba points out these bits are already in Age, so its not too hard. But can you do the same without signatures? Yes, you can, and efficiently too. In this post I’ll show how.

One way of thinking about the scheme I described in my previous blog post is to think of it as a kind of designated-verifier signature scheme. (I don’t hugely like this term, but it’s useful here). That is, we can view the combination of the committing MAC and authenticated KEM as a kind of signature scheme where the signature can only be verified by recipients chosen by the sender, not by third-parties. If we take that perspective, then it becomes clear that we can just do exactly the same as you do for the normal signature scheme: simply sign each chunk of the message separately, and include some chunk counter + last chunk marker in the signature.

How does this work in practice?

Firstly, we generate a fresh random data encryption key (DEK) for the message. This is shared between all recipients. We then use this DEK to encrypt each chunk of the message separately using our compactly-committing AEAD. To prevent chunk reordering or truncation we can use the same method as Age: Rogaway’s STREAM construction, which effectively just encodes the chunk counter and last-chunk bit into the AEAD nonce. (Personally, I prefer using a symmetric ratchet instead, but that’s for another post). This will produce a compactly committing tag for each chunk—typically 16 bytes per chunk (or 32 bytes if we care about malicious senders).

The original scheme I proposed then fed this tag (of which there was only 1) as associated data when wrapping the DEK for each recipient using an authenticated key-wrap algorithm and a per-recipient wrapping-key derived from an authenticated KEM. If the DEK is 32 bytes, and the key-wrapping algorithm produces a 16-byte tag then this outputs 48 bytes per recipient. We can do exactly the same thing for the new scheme, but we only feed the tag from the first chunk as the associated data, producing wrapped keys that commit to the first chunk only.

We then simply repeat the process for each subsequent chunk, but as the DEK is unchanged we can leave it empty: effectively just computing a MAC over the commitment for each chunk in turn. In our example, this will produce just a 16-byte output per recipient for each chunk. If we compare this to typical signature schemes that would be used for signing chunks otherwise, we can fit 4 recipient commitments in the same space as a single Ed25519 signature (64 bytes), or 16 recipients in the same space as an RSA-2048 signature.

To support such a scheme, the interface of our KEM would need to change to include a new operation that produces an intermediate commitment to a particular chunk tag, with an indication of whether it is the last tag or not. The KEM is then free to reuse the shared secrets derived for each recipient, avoiding the overhead of computing new ones for each chunk. This is an efficiency gain over using a normal digital signature for each chunk.

Here is a sketch of what the overall process would look like, to hopefully clarify the ideas presented. Alice is sending a message to Bob and Charlie. The message consists of three “chunks” and is using an authenticated KEM based on X25519.

1. First, Alice generates a random 32-byte DEK and uses it to encrypt the message, producing tags t₁, t₂, and t₃.
2. Alice generates a random ephemeral X25519 keypair: (esk, epk).
3. She computes a shared secret with Bob, ss_b, via something like HPKE’s DH-AKEM.
4. Likewise, she computes a shared secret with Charlie, ss_c.
5. Alice then wraps the DEK from step 1 for Bob and Charlie, using a key-wrap algorithm like AES in SIV mode (keyed with ss_b and then ss_c), including t₁ as additional authenticated data. She outputs the two wrapped keys plus the ephemeral public key (epk) as the encapsulated key blob. This will be 32 bytes for the epk, plus 48 bytes for each key blob (one for Bob, another for Charlie), giving 128 bytes total.
6. She then calls a new “commit” operation on the KEM for each subsequent chunk tag: i.e., t₂ and t₃. This commit operation performs the same as step 5, but with a blank DEK, outputting just a 16-byte SIV for each recipient for a total of 32 bytes per chunk. These commitment blocks can then be appended to each chunk. (In fact, they can replace the normal AEAD tag, saving even more space).

The total space taken is then 128 + 32 + 32 = 192 bytes, and we can remove the 3 original 16-byte AEAD tags, giving a net overhead of just 144 bytes. Compared to signing each chunk with Ed25519 which would need 192 bytes, or RSA-2048 which needs 768 bytes.

Decryption then performs the obvious operations: decrypting and recomputing the MAC tag for each chunk using the decapsulated DEK and then verifying the commitment blocks match at the end of each subsequent chunk.

This is still very much a sketch, and needs to be reviewed and fleshed out more. But I believe this is quite a neat scheme that achieves streaming authenticated encryption without the need for tricksy little signatureses, and potentially much more efficient too.