There are a few issues with the Proof of Possession challenge as
currently spec'ed
(https://github.com/ietf-wg-acme/acme/blob/master/draft-ietf-acme-acme.md#proof-of-possession-of-a-prior-key).

1. A TLS handshake using DHE or ECDHE involves the server automatically
signing something that begins with 32 bytes of client data*, followed by
some non-client controlled data. Proof of Posession asks for a signature
over a JSON body, the order of which is chosen by the client. If someone
can figure out a way to order a JSON response so that the important
parts are in the first 32 bytes, and the remainder of the message is
ignored, they might be able to use a signature obtained simply by
handshaking with a server that has the relevant cert deployed.

2. The response to the Proof of Posession challenge is expected to be
JWS signed by a key in one of the provided certs, rather than the
account key. This means that a third party who doesn't possess the
account key could complete the PoP challenge. Arguably this is a
benefit, but it requires very different handling from other challenge
types, and is likely to complicate implementations.

Possibilities:
 - Ask the client to sign a CSR containing a random token, with one of
the appropriate private keys, and POST to the challenge URL with JWS
signed by the account key and containing that CSR base64-encoded.* CSRs
are already intended as a way to prove possession of a given key, and
their format is more strictly specified so it is harder to manipulate
the order of elements.
 - Use a weaker form of PoP, call it "Live Cert Check:" the CA connect
to a running TLS server with a valid certificate for the name in
question, validates the cert, and fetches a file under .well-known. This
winds up being very similar to SimpleHTTP plus a valid certificate
requirement.

Any other suggestions?

*Thanks to Adam Langley for pointing this out.
*Thanks to Andrew Ayer for suggesting this.

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