Binary Hash Tree based Certificate Access Management for Connected Vehicles (BCAM)
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Presentation given at WiSec 2017 by Dr. Virendra Kumar. His, along with Drs. Jonathan Petit and William Whyte's, paper was one of six to receive the reproducibility label.
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Binary Hash Tree based Certificate Access Management for Connected Vehicles (BCAM)
- 1. Binary Hash Tree based Certificate Access Management for Connected Vehicles (BCAM) Virendra Kumar, Jonathan Petit, William Whyte
- 2. Background
- 6. The Big Dilemma Lifetime Supply Who pays for 2-way connectivity? What happens if the vehicle is hacked? 6
- 7. Current Certificate Model 3 years’ worth 3 years’ worth RA 7
- 9. Encrypted Batches of Certificates 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 … n 9
- 11. Compression using Binary Hash Trees 10 0100 10 11 000 001 010 011 100 101 110 111 seed 0 1 2 3 4 5 6 7 11
- 12. Day 1: No Revocation 10 0100 10 11 000 001 010 011 100 101 110 111 seed 0 1 2 3 4 5 6 7 Published node Derived node 12
- 13. Day 2: Vehicles 2, 4, 5 Revoked 10 0100 10 11 000 001 010 011 100 101 110 111 seed 0 1 2 3 4 5 6 7 Published node Derived node Revoked node 13
- 14. Pathological: Every Other Vehicle Revoked 10 0100 10 11 000 001 010 011 100 101 110 111 seed 0 1 2 3 4 5 6 7 Published node Derived node Revoked node 14
- 15. Binary Tree Encoding Encoding Size Decoding Time Unique index of each published node r * log2(n/r) * (log2(n) + 1) number of published nodes Same as searching Unique index of each revoked leaf node r * log2(n) No efficient algorithm known n: number of leaf-nodes, r: number of revoked vehicles, 1 ≤ r ≤ n/2 Can we get the best of both worlds? 15
- 16. A New Algorithm for Full Binary Trees Observations: 1. Topology known, only need to know which nodes are published and which are omitted. 2. Subtree of a published node can be ignored without any loss of information. Encoding: 1. Start from root with an empty string. 2. Do breadth-first traversal. 1. Append 0 for revoked node. 2. Append 1 for published node. 3. Do nothing for derived node. 0 0 0 1 0 0 1 0 1 0 0 0 00 1001 0100Encoded string: Disclaimer: Authors are not aware of any prior art with equivalent encoding sizes and decoding times. 1 2 3 Published nodes: 00, 11, 011 16
- 17. A New Algorithm for Full Binary Trees Contd. Decoding: 1. Start from root and process 1 level at a time. 2. At every level, look at the bit of interest 1. If 0, go to next level. 2. If 1, output the number of 1s so far, and stop. Example (vehicle 3 011): Disclaimer: Authors are not aware of any prior art with equivalent encoding sizes and decoding times. Encoding: 0 00 1001 0100 Bits at a level: # bits before bit of interest: 0 # bits after bit of interest: 0 Rules for going to next level: 1. # bits before = 2 * (# 0s in bits before bit of interest) 2. Add 1 to (# bits before), if next bit of vehicle ID is 1. 3. # bits after = 2 * (# 0s in bits after bit of interest) 4. Add 1 to (# bits after), if next bit of vehicle ID is 0. bit of interest Vehicle ID bit Bits at a level: # bits before bit of interest: 0 # bits after bit of interest: 1 Bits at a level: # bits before bit of interest: 1 # bits after bit of interest: 2 Bits at a level: # bits before bit of interest: 1 # bits after bit of interest: 2 3 1 2 3 17
- 18. Efficiency of Encoding Algorithm Encoding size – # published nodes ≈ # revoked nodes, i.e. encoding has roughly the same number of 0s and 1s. – Size ≈ 2*r*log2(n/r) – For n=240, r=1,000, encoding takes less than 1% of the full packet, i.e. about 20 times smaller than using unique index of each published node. Decoding time – Breadth-first but queue size ≤ r. – For n=240, r=10,000, a consumer laptop (2.7 GHz Intel Core i7, 16GB RAM) takes less than 3 milliseconds on average. 18 n: number of leaf-nodes, r: number of revoked vehicles, 1 ≤ r ≤ n/2
- 19. “Not all compromises are created equal.” Software Compromise Hardware Compromise Can be easily replicated and spread quickly Most likely require specialized hardware Can be easily fixed by over-the-air updates Most likely need to replace the hardware Attack can be distributed over the Internet requiring less effort and resources Most likely require lot of effort and resources 19
- 20. “So, we treat them differently.” Software compromise “soft revocation list” 0 1 2 3 4 5 6 7 8 9 … A compromised vehicle is put on the SRL first, by flipping its bit. If the vehicle on SRL continues to misbehave, it is “hard” revoked via binary tree approach. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 …1 1 1 20
- 21. Conclusion Positives – No need of bidirectional connectivity for certificate download – Revocation enforced at sender Soft/hard revocation prevent sender from sending valid messages Receivers don’t need to store revocation information Scales naturally, can handle a much higher rate of revocation than current system – Vehicles can be unrevoked Vehicles revoked in error Vehicles whose issues have been addressed Negatives – Less agile – Longer CA lifetimes Our belief is that positives outweigh the negatives. We hope you feel the same. 21 positives
- 22. Thank you! 22