Re: [sfc] [Last-Call] Secdir last call review of draft-ietf-sfc-proof-of-transit-08

[Christian Huitema <[e-mail]>]

On 9/25/2021 4:20 AM, Frank Brockners (fbrockne) wrote:
> Hi Christian,
>
> Thanks for the follow-up. Please see below.
>
>> -----Original Message-----
>> From: Christian Huitema <[e-mail]>
>> Sent: Friday, 24 September 2021 17:16
>> To: Frank Brockners (fbrockne) <[e-mail]>; [e-mail]
>> Cc: [e-mail]; [e-mail]; Youell, Stephen
>> <[e-mail]>; [e-mail]; draft-ietf-sfc-proof-of-
>> [e-mail]; [e-mail]
>> Subject: Re: [Last-Call] Secdir last call review of draft-ietf-sfc-proof-of-transit-
>> 08
>>
>>
>> On 9/24/2021 1:39 AM, Frank Brockners (fbrockne) wrote:
>>> Hi Christian,
>>>
>>> Thanks a lot for the detailed follow-up. Please see inline.
>>>
>>>> -----Original Message-----
>>>> From: Christian Huitema <[e-mail]>
>>>> Sent: Thursday, 23 September 2021 22:13
>>>> To: Frank Brockners (fbrockne) <[e-mail]>; [e-mail]
>>>> Cc: [e-mail]; [e-mail]; Youell, Stephen
>>>> <[e-mail]>; [e-mail]; draft-ietf-sfc-proof-of-
>>>> [e-mail]
>>>> Subject: Re: [Last-Call] Secdir last call review of
>>>> draft-ietf-sfc-proof-of-transit-
>>>> 08
>>>>
>>>>
>>>> On 9/23/2021 12:31 PM, Frank Brockners (fbrockne) wrote:
>>>>> Hi Christian,
>>>>>
>>>>> Thanks a lot for your detailed review. Please see inline.
>>>>>
>>>>>> -----Original Message-----
>>>>>> From: Christian Huitema via Datatracker <[e-mail]>
>>>>>> Sent: Monday, 20 September 2021 05:48
>>>>>> To: [e-mail]
>>>>>> Cc: [e-mail];
>>>>>> [e-mail]; [e-mail]
>>>>>> Subject: Secdir last call review of
>>>>>> draft-ietf-sfc-proof-of-transit-08
>>>>>>
>>>>>> Reviewer: Christian Huitema
>>>>>> Review result: Serious Issues
>>>>>>
>>>>>> I have reviewed this document as part of the security directorate's
>>>>>> ongoing effort to review all IETF documents being processed by the
>>>>>> IESG.  These comments were written primarily for the benefit of the
>>>>>> security
>>>> area directors.
>>>>>> Document editors and WG chairs should treat these comments just
>>>>>> like any other last call comments.
>>>>>>
>>>>>> This document proposes a security mechanism to prove that traffic
>>>>>> transited through all specified nodes in a path. The mechanism
>>>>>> works by adding a short option to each packet for which transit
>>>>>> shall be verified. The option consists of a random number set by
>>>>>> the originator of the packet, and a sum field to which each transit
>>>>>> node adds a value depending on public parameters, on the random
>>>>>> number and on secrets held by the node. The destination has access
>>>>>> to all the secrets held by the nodes on the path, and can verify
>>>>>> whether or not the final sum corresponds to the sum of expected
>>>>>> values. The proposed size
>>>> of the random number and the sum field is 64 bits.
>>>>>> In the paragraph above, I described the mechanism without
>>>>>> mentioning the algorithm used to compute these 64 bit numbers. The
>>>>>> 64 bit size is obviously a
>>>>>> concern: for cryptographic applications, 64 bits is not a large
>>>>>> number, and that might be a weakness whatever the proposed algorithm.
>>>>>> The actual algorithm appears to be a bespoke derivation of Shamir's
>>>>>> Secret Sharing algorithm (SSS). In other word, it is a case of
>>>>>> "inventing your
>>>> own crypto".
>>>>> ...FB: SSS is a well know algorithm and
>>>>> draft-ietf-sfc-proof-of-transit does not
>>>> modify it.
>>>>> All draft-ietf-sfc-proof-of-transit does is to operationalize the
>>>>> SSS algorithm
>>>> for the proof of transit use case.
>>>>> Also note that the draft does not require the use of 64 bit numbers.
>>>>> Nor does draft require a minimum time between changing the secrets.
>>>>> What particular attack are you concerned about where 64 bit numbers
>>>>> are a
>>>> concern?
>>>>>> SSS relies on the representation of polynomials as a sum of
>>>>>> Lagrange Basis Polynomials. Each of the participating nodes holds a
>>>>>> share of the secret represented by a point on the polynomial curve.
>>>>>> A polynomial of degree K on the field of integers modulo a prime
>>>>>> number N can only be revealed if at list K+1 participants reveal
>>>>>> the value of their point. The safety of the algorithm relies on the
>>>>>> size of the number N and on the fact that the secret shall be revealed only
>> once.
>>>>>> But the algorithm does not use SSS directly, so it deserves its own
>>>>>> security
>>>> analysis instead of relying simply on Shamir's work.
>>>>>> The proposed algorithm uses two polynomials of degree K for a path
>>>>>> containing
>>>>>> K+1 nodes, on a field defined by a prime number N of 64 bits. One
>>>>>> K+of the
>>>>>> polynomial, POLY-1, is secret, and only fully known by the verifying node.
>>>>>> The other, POLY-2 is public, with the constant coefficient set at a
>>>>>> random value RND for each packet.
>>>>>>
>>>>>> For each packet, the goal is compute the value of POLY-1 plus
>>>>>> POLY-2 at the point 0 -- that is, the constant coefficient of
>>>>>> POLY-3 = POLY-1 + POLY-
>>>> 2.
>>>>>> Without going in too much details, one can observe that the
>>>>>> constant coefficient of POLY-3 is equal to the sum of the constant
>>>>>> coefficients of POLY-1 and POLY-2, and that the constant
>>>>>> coefficient of POLY-2 is the value RND present in each packet. In
>>>>>> the example given in section 3.3.2, the numbers are computed modulo
>>>>>> 53, the constant coefficient of POLY-1 is 10, and the value RND is
>>>>>> 45. The final sum  CML is indeed
>>>>>> 10 + 45 = 2 mod 53.
>>>>>>
>>>>>> To me, this appears as a serious weakness in the algorithm. If an
>>>>>> adversary can observe the value RND and CML for a first packet, it
>>>>>> can retrieve the constant coefficient of POLY-1, and thus can
>>>>>> predict the value of CML for any other packet. That does not seem very
>> secure.
>>>>> ...FB: There seems to be a bit of confusion or misreading of how the
>>>>> method
>>>> works. In the above statement you seem to assume that the verifier
>>>> would not be part of the proof-chain, so that the final CML value
>>>> would be somehow exposed to an external entity along with RND. This
>>>> is not the case. The verifier is the last node (k+1) in the proof-chain.
>>>>> At concept level, the method reconstructs the polynomial hop by hop,
>>>>> picking
>>>> up a point on the curve at every hop. Only final node in the
>>>> proof-chain, which is also the verifier, acts on the information of
>>>> all the k+1 points and as such is able to reconstruct the polynomial.
>>>>> In section 3.2.1, the draft explicitly states that the verifier *is*
>>>>> part of the
>>>> proof-chain: "Each of the k+1 nodes (including verifier) are assigned
>>>> a point on the polynomial i.e., shares of the SECRET." The fact that
>>>> the verifier, i.e., the last node in the proof-chain ("k+1"),  can
>>>> retrieve the secret, is desired and intentional, because the verifier
>>>> needs to compare the result of the iterative construction of the secret with
>> the secret value it received from the controller.
>>>> This is how the system is designed, and the calculation of (10+45)
>>>> mod 53 = 2 is part of the verification.
>>>>
>>>> OK. That's slightly less bad. But it is still very bad crypto,
>>>> because you are effectively doing a linear combination.
>>>>
>>>> You are evaluating POLY-3 = POLY-1 + POLY-2
>>>>
>>>> POLY-2 can be written as POLY-2 = RND + POLY-2-NC, in which POLY2-NC
>>>> only contains the non constant terms -- that is, POLY-2-NC(0) = 0
>>>>
>>>> Then for any point X, we get POLY-3(X) = POLY-1(X) + POLY2-NC(X) +
>>>> RND For a given value Xj of X, this means we can express : POLY-3(Xj)
>>>> = Vj + RND In which Vj is a constant term = POLY-1(Xj) + POLY2-NC(Xj)
>>>>
>>>> Each node will increment the cumul by the value LPCj * POLY-3(Xj) =
>>>> LPCj
>>>> * (Vj + RND)
>>>>
>>>> Suppose that an adversary can observe the value of CML before and
>>>> after being incremented by node Xj. Suppose that it could do that
>>>> twice. Then it has the
>>>> values:
>>>>
>>>> CML1-before-j = C1b
>>>> CML1-after-j = C1a
>>>> D1 = C1a - C1b = LPCj * (Vj + RND1)
>>>>
>>>> CML1-before-j = C2b
>>>> CML1-after-j = C2a
>>>> D2 = C2a - C2b = LPCj * (Vj + RND2)
>>>>
>>>> D2-D1 = LPCj*(RND2-RND1)
>>>>
>>>> LPCj = (RND2-RND1)/(D2-D1)
>>>> Vj = D2/LPCj - RND2
>>>>
>>>> The inverse of numbers modulo a prime P is easily computed -- see
>>>> Fermat's little theorem.
>>>>
>>>> Once the input and output of a node have been observed twice, it
>>>> becomes easy to update the cumulative sum CML while bypassing these
>> nodes.
>>> ...FB: This is great. Thanks for spelling out the details.  You raise a good point:
>> For the solution to make sense, we need to ensure that an attacker cannot
>> observe the input and output of a node.
>>> To ensure this does not happen, we must require the communication to/from
>> the node to be encrypted, e.g., through link layer encryption of at least the
>> proof-of-transit data fields.
>>> We'll add this requirement to the draft - and also detail the threat you describe
>> above in detail in the security considerations section.
>>
>> That still will not be sufficient, because you also have to deal with the nodes
>> themselves. By definition, they see the intermediate results of other nodes. For
>> example, if the function chain is A->B->C->D->E, the node B sees the output of B
>> and the node D sees the input of D. If B and D  collude, they have access to the
>> input and output of C. They can easily find the secrets of C, and then execute a
>> chain A->B---->D->E in which the input of D is "corrected" to hide the absence of
>> C from the evaluator E.
> Thanks much. You raise another valid point and we will add it to the security considerations section.
> That said, IMHO we'd need to put the scenario you raise into perspective:
> If the nodes B and D would be compromised by an attacker, the deployment would face a much more serious security issue than what any proof-of-transit method could protect against.
>
>> The linear combination scheme in the draft is not sound crypto. My
>> recommendation is to present the problem and the threat model clearly to the
>> crypto community, for example by presenting to the CFRG, and solicit advice on
>> better algorithms.
> There has been quite a bit of discussion on proof of transit in several WGs, even before the SFC WG picked it up. And the SFC working group has considered different approaches early on in the solution specification, including e.g., using nested encryption, which is probably more in line with your preferences. See https://datatracker.ietf.org/doc/html/draft-ietf-sfc-proof-of-transit-01#section-3.5.1. From my recollection of the discussion - others please chime in - one main reason of why the current approach was chosen was its computational simplicity, i.e., hardware platforms which do not support native encryption capabilities like AES-NI can implement it without considerable impact on the computational latency. So in other words, the current method is the result of a trade-off decision.
We are discussing mathematics, not opinions. It is not a matter of 
preferences, it is a matter of threat model. The draft that I reviewed 
does not mention that the scheme should only be used in a benign 
environment in which no attacker can see the traffic and all nodes are 
fully trusted to not try gaming the system. The proposed scheme uses 
crypto vocabulary, with references to SSS and use of terms like "proof" 
or "cryptanalysis". Indeed, the header paragraph of the security 
considerations says:

    POT is a mechanism that is used for verifying the path through which
    a packet was forwarded.  The security considerations of IOAM in
    general are discussed in [I-D.ietf-ippm-ioam-data].  Specifically, it
    is assumed that POT is used in a confined network domain, and
    therefore the potential threats that POT is intended to mitigate
    should be viewed accordingly.  POT prevents spoofing and tampering;
    an attacker cannot maliciously create a bogus POT or modify a
    legitimate one.  Furthermore, a legitimate node that takes part in
    the POT protocol cannot masquerade as another node along the path.
    These considerations are discussed in detail in the rest of this
    section.

The previous discussions have shown that an attacker CAN "maliciously 
create a bogus POT or modify a legitimate one", provided it is able to 
see the traffic, or some of the traffic. The discussions also show that 
"a legitimate node that takes part in the POT protocol" CAN "masquerade 
as another node along the path". Contrary to statements in the 
"cryptanalysis" section, "A passive attacker observing CML values across 
nodes (i.e., as the packets entering and leaving)" CAN  "perform 
differential analysis". The attack cannot "be mitigated using a good 
PRNG for generating RND".

If the system was only designed for operation in a "benign environment" 
and you were only concerned with detecting operation failures, I am 
pretty sure that you could come out with something less complicated. For 
example you could exploit the analysis that I made to radically simplify 
the implementation and describe the scheme as "CML = Sum (Xj*RNDp)", 
where Xj is a secret coefficient provisioned to node j, and RNPp is per 
packet random number. The verification by the evaluator will check that 
"RND == CML + Xe*RND", where "Xe = 1 - Sum Xj". That would get you an 
easy-to-implement checksum. But you would need to be very clear about 
the domain of application, and the failure mode if the traffic can be 
observed or nodes can be compromised, and the draft should probably drop 
the references to Shamir's SSS, because they just obfuscate the analysis.

-- Christian Huitema