May 27, 2016

CCN Network Name Equivalence Classes

Named data packets cut both ways in CCN. Perhaps their most beneficial quality is that they shift the communication emphasis from end hosts and fixed addresses to content. However, from a security perspective, there is a steep cost for this transition. Application names, being often-overloaded URIs, can leak a significant amount of information about the data being requested. Far beyond what’s leaked from an IP packet address and port tuple. (I’ve discussed this in a past post).

There are at least two ways to solve this problem:

  1. Wrap application names with encryption and carry them to their destination via unrelated network names (or locators). This is basically the TOR [1] equivalent of CCN [2].

  2. Obfuscate application names to flat (i.e., not wrapped) network names such that they can be compared to other network names without leaking the unobfuscated form.

Since (1) has been around for some time, I’m focusing on (2) in this post. To start, the description I gave might not be very clear. Let me give an example. Assume you are a consumer and wish to obtain the data named /foo/bar. Moreover, assume there existed the following set of functions at your disposal:

  • Hash($N$): Obfuscate an appliation name $N$ to a network name $N$’. Also, this function should be randomized (i.e., it should be the case, with overwhelming, probability that Hash($N$) != Hash($N$)).
  • Compare($N_1$’, $N_2$’): Compare two network names for equality. Return 1 if the underlying application names are equal and 0 otherwise.

Moreover, it should be difficult to learn the application name $N$ from its network name $N$’ = Hash($N$).

I claim that you can build the same packet forwarding logic using these two functions. (Albeit at significant performance costs.) But why would one bother? For one thing, the application name is no longer revealed to the network. This lets forwarders act on names without having any encryption context and without using encapsulation as in case #1 above.

From a theoretical perspective, such functions allow you to build name equivalence classes. That is, sets of different representations for the same name. We would like these equivalence classes to be formed such that, given two distinct names $N_1$ and $N_2$, the probability that Hash($N_1$) is in the equivalence class of Hash($N_2$) is overwhelmingly (negligibly) small.

Equivalence Class Construction

I’ll now present a trivial construction for these name equivalence classes by instantiating the Hash and Compare functions. The core idea is based on randomized hashing of the name and a deterministic comparison function. To begin, let $N = N_1,\dots,N_k$ be a name of $k$ components that we want to map to an element of its equivalence class. Next, let $G$ be a finite cyclic group in which the discrete log problem is hard, and let $g \in G$ be a generator of this group. Assume that there is some entity responsible for comparing obfuscated names, e.g., a router. This entity generates a secret key $k \overset{$}{\gets} G$ and the corresponding public key $p = g^k$ and gives them to other entities who wish to send names to be compared, e.g., consumers. Using these parameters, the Hash and Compare functions can be built as follows.

  • Hash(N): Split $N$ into $k$ segments. For each segment $N_i$, compute $N_i’$ as the (ryptographic) hash of the first $i$ segments. Then, sample a random $s \overset{$}{\gets} G$. For each transformed segment $N_i’$, compute the two values $\alpha_i = p^s$ and $\beta_i = g^{N_i’ + s}$, where $+$ is element addition, not concatenation. Return the list of $\alpha, \beta$ pairs $(\alpha_1,\beta_1), \dots, (\alpha_k, \beta_k)$.

  • Compare($N_1$, $N_2$): Return False if the names are of different lengths. Let each segment $i$ in these names be denoted as $(\alpha_{i,1},\beta_{i,1})$ and $(\alpha_{i,2},\beta_{i,2})$. Using these values, compute the following:

If $p_1 = p_2$, then it must be the case that $N_1$ and $N_2$ are in the same equivalence class, i.e., they are “hashed” versions of the same name. To prove this statement, let’s do the actual computations here. I’ll use the notation $s_1$ and $s_2$ to refer to the distinct $s$ values for $N_1$ and $N_2$, respectively. Assuming that $N_{i,1}’ = N_{i,2}’$ for each each segment $i=1,\dots,k$, it follows that:

Running Code

I implemented this basic scheme using the group of integers $Z$ modulo some sufficiently large prime $p$. (We could use a better group in which the DL problem is hard, but $Z_p$ works to illustrate the idea.) The code proceeds as follows. First, it fixes $p$ and then generates a generator $g$ and public and private key pair $k$ and $pk$ (denoted as $p$ in the previous section). Then the secret to be obfsucated is sampled at random along with the two random values $s_1$ and $s_2$ (denoted as $s$ and $r$ in the code). Finally, the program hashes both values and then compares them for equality. The result of this comparison is printed.

The complete listing is below. You may run it yourself to check its correctness.

Complexity Problems

While it’s great that we now have some way to compare names without revealing them, this general apprpach scheme presents some challenges. For instance, in vanilla CCN, we rely on names as given (encoded) to perform matching and indexing into data structures such as the FIB, PIT, and CS. That is, we use exact matching for names. However, since the “verifier” (router) can only determine equality between a pair of obfuscated names by invoking the compare function for each one, the time to index these data structures is necessarily linear with the number of entries.

I’m currently working on a paper that will show this result formally. And the moral of the story is that wrapping names a la TOR is the best we can do if we wish to hide information within packet headers.

References

  • [1] Dingledine, Roger, Nick Mathewson, and Paul Syverson. Tor: The second-generation onion router. Naval Research Lab Washington DC, 2004.
  • [2] S. DiBenedetto, P. Gasti, G. Tsudik and E. Uzun, ANDaNA: Anonymous Named Data Networking Application, the 19th Annual Network and Distributed System Security Symposium (NDSS), San Diego, CA, 2012.