Re: [TLS] Combining Secrets in Hybrid Key Exchange in TLS 1.3

[Nimrod Aviram <[e-mail]>]

The APOP attack demonstrates that concatenating secrets may be dangerous,
as a general cryptographic practice.
As to the TLS KDF, if future SHA256 cryptanalysis results in collisions, an
attacker that can establish multiple PSKs of their choice with another
party can cause two sessions with two different PSKs to share the same
early_secret. If the other party reuses ECDH(E) values, the attacker can
also cause the handshake_secret to be identical.
This likely violates the security proof for TLS 1.3, in and of itself.
A similar violation of the security guarantee seems to arise when using
hybrid key exchange with a PQ KEM.

Or if that's what you're asking: As we write, we are unaware of a way to
apply the APOP attack to the TLS KDF.
We view this as an opportunity to defend-in-depth against such issues,
while the document is not yet finalized.


On Wed, 1 Sept 2021 at 23:34, Blumenthal, Uri - 0553 - MITLL <[e-mail]>
wrote:

> How does the described AOAP attack apply to TLS KDF?
>
>
>
> --
>
> Regards,
>
> Uri
>
>
>
> *There are two ways to design a system. One is to make is so simple there
> are obviously no deficiencies.*
>
> *The other is to make it so complex there are no obvious deficiencies.*
>
> *
>                                                                                                                    -
> C. A. R. Hoare*
>
>
>
>
>
> *From: *TLS <[e-mail]> on behalf of Nimrod Aviram <
> [e-mail]>
> *Date: *Wednesday, September 1, 2021 at 15:58
> *To: *"<[e-mail]>" <[e-mail]>
> *Cc: *Eylon Yogev <[e-mail]>, Ilan Komargodski <
> [e-mail]>, Benjamin Dowling <[e-mail]>, Eyal
> Ronen <[e-mail]>
> *Subject: *[TLS] Combining Secrets in Hybrid Key Exchange in TLS 1.3
>
>
>
> (This note is also available on Github
> <https://github.com/nimia/kdf_public#readme> for ease of reading.)
>
>
>
> This note identifies a possible security problem in the "Hybrid key
> exchange in
> TLS 1.3" document, stemming from how cryptographic secrets are combined. In
> short: constructions that concatenate secrets are vulnerable when the
> underlying
> hash function is not collision-resistant. We are unaware of a full attack
> that leverages the underlying problem. However, we view this as an
> opportunity
> to defend-in-depth against such issues, while the document is not yet
> finalized.
> We propose a new construction that seems robust to this potential issue,
> and we
> are in the process of writing a technical report that includes a full
> security
> proof.
>
> # Concatenating Secrets May Be Dangerous
>
> The APOP attack (see appendix for a brief description) demonstrates that
> concatenating secrets to potentially attacker-controlled input might be
> dangerous. Currently, the "Hybrid key exchange in TLS 1.3" document uses
> secret
> concatenation as the preferred way to combine secrets. (This was an
> understandable design choice given how little this issue has been studied.)
>
> We recommend a defense-in-depth approach against this potential issue. We
> should
> not concede to an attacker even the ability to cause a collision in an
> internal
> state of the key schedule. Moreover, this part of TLS is likely
> particularly
> amenable to ossification: Whatever we standardize will likely persist for
> 5-10
> years. (We do note that TLS mixes in the client and server nonces, so
> additional
> offensive techniques would be required to exploit this for a full attack.)
>
> We note that concatenation is also used in the "TLS 1.3 Extended Key
> Schedule"
> document.
>
> # Our proposed construction
>
> We have identified an alternative construction that we believe could
> provide
> defense-in-depth against this issue. We are in the process of writing a
> technical report that includes a full security proof.
> The required assumptions on the hash function appear to be much milder than
> collision resistance; instead, we likely only need
> multi-preimage-resistance:
> Essentially, requiring only that computing preimages for multiple images is
> hard.
>
> The construction is:
> combined_key = H(HMAC(key=H1(k1), data=2||F(k2)) xor HMAC(key=H2(k2),
> data=1||F(k1)))
> where || denotes concatenation, H denotes the underlying hash function,
> and:
> H1(k) = H('derive1' || k)
> H2(k) = H('derive2' || k)
> F is defined as follows:
> Let m denote the input to F. We split m into blocks, according to the
> block size
> of H:
> m = m1||m2||...||mn
> Let j~=3 denote an “expanding factor” (the value chosen for j in practice
> depends on how strong an assumption we want to rely on; we expect 3 to be
> enough).
> Then
> F(m) =
> H(0||m1)||H(1||m1)||...||H(j-1||m1)||H(0||m2)||H(1||m2)||...||H(j-1||m2)||H(0||mn)||H(1||mn)||...||H(j-1||mn)
>
> This construction is cheap to calculate and would be used only in the key
> schedule, which is not a bottleneck for TLS performance.
>
> # Adding another layer to the TLS key schedule may also be problematic
>
> Another strategy for mixing secrets is to add the second secret to another
> layer
> of the TLS key schedule. This strategy is already used to mix a PSK and an
> ECDHE
> secret in TLS 1.3, as well as in AuthKEM, and it was also considered for
> the
> Hybrid key exchange document. This strategy is vulnerable as well to
> collisions
> in the underlying hash function, and we propose using one secure
> construction
> for mixing secrets.
>
> Consider a standard PSK+ECDHE TLS 1.3 handshake. Then
> handshake_secret = HKDF_Extract(IKM=ECDHE_secret,
> salt=Derive_Secret(early_secret))
> early_secret = HKDF_Extract(IKM=PSK, salt=000)
> HKDF_Extract(IKM, salt) = HMAC(k=salt, data=IKM)
>
> Therefore, early_secret = HMAC(k=000, data=PSK).
> Assume a non-collision-resistant hash function. Then an attacker that can
> establish multiple PSKs of their choice with another party can cause two
> sessions with two different PSKs to share the same early_secret. If the
> other
> party reuses ECDH(E) values, the attacker can also cause the
> handshake_secret to
> be identical.
>
> Furthermore,
> Client_Handshake_Traffic_Secret =
>   HMAC(k=Handshake_Secret, data=Label||H(ClientHello...ServerHello))
> If the attacker is the server, and the hash function allows for
> chosen-prefix
> collisions, the attacker can choose two ServerHello messages such that for
> two
> different ClientHello messages, H(ClientHello...ServerHello) is identical.
> This leads to identical values for an actual key output of the key
> schedule,
> Client-Handshake-Traffic-Secret (if the client reuses an ECDH(E) value, or
> in a
> hypothetical PQ TLS, which uses a KEM and the server chooses the
> encapsulated
> key).
>
> We note that the full version of the HKDF paper explicitly disclaims
> security in
> the presence of attacker-controlled entropy. Also, note that by
> definition, a
> KEM allows one party to control the secret.
>
> # Appendix: The APOP Attack
>
> APOP is an old challenge-response protocol used in email, relevant here
> because
> it demonstrates the attack well. Broadly, in APOP the challenger sends a
> challenge, and the responder needs to respond with:
> MD5(challenge || password)
> where || denotes concatenation.
>
> The attacker wants to e.g. test whether the password starts with 'a'. They
> pick an MD5 collision x, y such that MD5(x) = MD5(y) and both x and y end
> with
> 'a'. They wait for the client to connect in two different sessions, and
> send
> x[:-1] and y[:-1] as the challenges, where [:-1] denotes removing the last
> byte
> from a string. If the password starts with 'a', and the MD5 blocks align,
> then
> the response will be the same for both challenges. The attacker can
> therefore
> test a single guess for the starting byte with two sessions, and learn
> that byte
> after at most 512 sessions. See [1], [2].
>
> best wishes,
> Nimrod Aviram, Benjamin Dowling, Ilan Komargodski, Kenny Paterson, Eyal
> Ronen, Eylon Yogev
>
> References:
> [1] Practical key-recovery attack against APOP, an MD5-based
> challenge-response authentication. Leurent, Gaetan.
>
> [2] Practical Password Recovery on an MD5 Challenge and Response.
> Sasaki, Yu and Yamamoto, Go and Aoki, Kazumaro.
>
>
>