Last Call Review of draft-ietf-sfc-proof-of-transit-08
review-ietf-sfc-proof-of-transit-08-secdir-lc-huitema-2021-09-19-00

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".

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 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.

My recommendation would be to present the problem and ask the CFRG for 
algorithm recommendations.