1. Key Distribution in DTNs
Using Erasure Codes
Ed Birrane

2. Forward error correction code over an erasure channel.
Erasure Coding
Forward error correction code over an erasure channel.
Forward Error Correction Code
Store redundant information in a transmission
Reed-Solomon Code
Erasure Channel
Lossy Communication channel
Lost data is considered “erased” data
Concept
Message M captured in N chunks.
Require R < N chunks to re-create message.
Computationally infeasible to re-create message with C < R chunks. 2

3. Creating/Using Redundant Chunks
Produce initial set of K chunks in finite field
For binary files, choose power of 2 for field size (say, 2^1024)
Number of chunks = file size / chunk size
Name chunks 0 – (k-1)
Generate Lagrange Interpolation Polynomial p(x)
Calculate efficient polynomial through K points
p(0) = chunk 0, p(i) = chunk i…
Use polynomial to generate redundant points
Generate p(k) through p(n).
Receiver constructs polynomial from any k points
With polynomial, can extract p(0) through p(k-1). 3

4. Wikipedia Example Sender encodes two messages: a = 555 and b = 629
Polynomial: f(i) = a + (b - a)(i - 1)
f(1) = 555, f(2) = 629, f(3) = 703, f(4) = 777, f(5) = 851
Receiver only receives f(4) and f(5)
Can reconstruct polynomial and then extract f(1) and f(2) 4

5. Considerations Efficient Implementation as Reed-Solomon Coding
Use generator polynomial and send coefficients, not values
More efficient decoding of values
Need large enough chunk size and large # chunks
Larger the size, harder to brute-force guess a value when too few chunks received.
Need k to be large enough to span paths in the network
Chunk values should not repeat
Assume original data is compressed or otherwise entropy-encoded to reduce the chance of constructing chunks with the same value. 5

6. Erasure Codes as Key Distribution
Key is binary data
May include meta-data as part of key message.
To a point, bigger message is better.
Construct Key Chunks
No apparent need to generate redundant chunks
May produce small set of redundancy for reliability, but this is likely handled by other transmission mechanisms
Build discrete paths through network
Chunks sent from source to destination via discrete paths
No intermediate node may hold more than x% of chunks for a key message 6

7. Network Example Eight Chunks Separate Paths
Require all for re-assembly
Send through different paths
Separate Paths
Compromise of any one node or one link does not compromise key.
Relies on Nodes to reject messages based on what they have seen so far.
Restricted routing settings (limits on storage and forwarding)
F(1), F(2), F(3), F(4), F(5), F(6), F(7), F(8)
F(7), F(8)
F(1), F(2), F(3)
F(4), F(5), F(6)
F(1), F(2), F(3), F(4), F(5), F(6), F(7), F(8) 7

8. Issues/Mitigations Cut Vertices Cut Vertices Link Node Intelligence
Compromise of a cut vertex, or its links subverts the system
Separate transmission over time. Node does not hold all chunks at one time.
Cut Vertices Link
The vertex collects all data through the segmented network
Hop-by-hop confidentiality protects link transmission.
Node Intelligence
Nodes must actively refuse to collect too many chunks
Nodes must maintain some repository of chunks seen
Key Distribution protocol counts chunks received by hashing on destination node. Allowed collision count embedded in chunk message. 8

9. Issues/Mitigations Chunk Poisoning
Current system vulnerable to bogus data injection by a compromised node.
Exploit redundancy in the erasure coding approach. Calculate key using redundant messages from multiple paths and agree on quorum.
Rely on Authentication to avoid injection attacks.
Relies on authentication between nodes
Key distribution relying on key distribution…
Multiple keys exist in the system. Do not rely on key being updated, but other keys can be relied upon.
Use for distribution of partial key in combination with identity-based scheme. 9

10. Next Steps Draft key distribution protocol Detailed analysis
Chunk construction, addressing, meta-data
Intermediate Node actions
Endpoint node actions
Detailed analysis
Field space, chunk size, redundancy, entropy coding
Sample implementation
Performance measurement
Simulate link and node compromise and effects 10

11. Thank you!
Questions? 11