1. On Detecting Pollution Attacks in Inter-Session Network Coding Anh Le, Athina Markopoulou University of California, Irvine

2. Linear Inter-Session Network Coding Anh Le, UC Irvine, Inter-Session Pollution Detection 2 S1S1 S2S2 R2R2 R1R1 A B x 1 +x 2 x2x2 x2x2 x1x1 x1x1 x2x2 x2x2 x1x1 x1x1 x2x2 x2x2 x1x1 x1x1 x2x2 x2x2 x1x1 x1x1 Multiple sources Packets from different sources may be (linearly) coded together

3. Pollution Attacks in Inter-Session Coding Malicious Intermediate Nodes 3 S1S1 S2S2 R2R2 R1R1 A B x2x2 x2x2 x1x1 x1x1 x2x2 x2x2 y y y y x1x1 x1x1 x1x1 x1x1 x2x2 x2x2 Can be detected by existing intra-session approaches y y Anh Le, UC Irvine, Inter-Session Pollution Detection

4. Homomorphic MAC-Based Detection No Pollution 4 S1S1 S2S2 R2R2 R1R1 A B x 1, t 1 x 2,t 2 x 1, t 1 x 2,t 2 x 1, t 1 x 1 +x 2, t 1 +t 2 Anh Le, UC Irvine, Inter-Session Pollution Detection

5. Homomorphic MAC-Based Detection Attack Case 5 S1S1 S2S2 R2R2 R1R1 A B x 1, t 1 x 2,t 2 x 1, t 1 x 2,t 2 x 1, t 1 x 1 +x’ 2, t  Anh Le, UC Irvine, Inter-Session Pollution Detection

6. Pollution Attacks in Inter-Session Coding 6 S1S1 S2S2 R2R2 R1R1 A B x' 2 x1x1 x1x1 x1x1 x1x1 x2x2 x2x2 Malicious sources Inconsistent source packets New and main challenge in inter-session pollution The main focus of the paper x1x1 x1x1 x 1 +x 2 Anh Le, UC Irvine, Inter-Session Pollution Detection

7. Intra-Session MAC-Based Detection Failed for Malicious Sources 7 S1S1 S2S2 R2R2 R1R1 A B x 1, t 1 x 2, t 2 Anh Le, UC Irvine, Inter-Session Pollution Detection x' 2, t’ 2 x’ 2, t’ 2 x 1 +x 2, t 1 +t 2

8. Prior Work on Inter-Session Pollution Defense 8 Homomorphic signature for Detection [Agrawal, PKC ’10] Expensive computation Large signature Signature-based Identification [Dong, WiNC ‘09] Anh Le, UC Irvine, Inter-Session Pollution Detection

9. 1.Background and Motivation oInter-Session Pollution Attacks oMain Challenges 2.Prior Work 3.InterMac Detection (more in the paper: Hash and SpaceMac based Detection) 4.Evaluation 5.Conclusion Outline 9 Anh Le, UC Irvine, Inter-Session Pollution Detection

10. InterMac: Threat Model 10 S - 1 sources may be malicious Intermediate nodes may be malicious Receivers are trusted Anh Le, UC Irvine, Inter-Session Pollution Detection

11. Main Challenge and Key Observation 11 Main Challenge: Malicious sources Sources must generate tags using different keys S1S1 S2S2 R2R2 R1R1 A B x1x1 x1x1 x2x2 x2x2 Anh Le, UC Irvine, Inter-Session Pollution Detection

12. Overview of InterMac 12 Homomorphic (MAC) for inter-session network coding – Each source generate MAC tags using different keys – The tags are still combinable without knowing the key Anh Le, UC Irvine, Inter-Session Pollution Detection

13. 13 InterMac Detection Main technique Anh Le, UC Irvine, Inter-Session Pollution Detection x 2, t 2 =x 2 ·k 2 S1S1 S2S2 R2R2 R1R1 A B k1k1 k1k1 k 1, k 2 x 1, t 1 =x 1 ·k 1 k2k2 k2k2 k 1, k 2 x 1 +x 2, t 1 +t 2 Verify: (x 1 + x 2 ) (k 1 + k 2 ) = t 1 + t 2 x 1 k 1 + x 2 k 2 + x 1 k 2 + x 2 k 1 = t 1 + t 2 Inner Product Homomorphic MAC [Le, NetCod ’10] [Li, INFOCOM ’10] Inner Product Homomorphic MAC [Le, NetCod ’10] [Li, INFOCOM ’10] Main technique: Orthogonality of k i and x j

14. InterMac Construction 14 Anh Le, UC Irvine, Inter-Session Pollution Detection Inner Product Homomorphic MAC [Le, NetCod ’10] [Li, INFOCOM ’10] Inner Product Homomorphic MAC [Le, NetCod ’10] [Li, INFOCOM ’10] Multiple Keys Using a Trusted Controller: k i · x j = 0 Using a Trusted Controller: k i · x j = 0

15. InterMac: Security Game 15 Anh Le, UC Irvine, Inter-Session Pollution Detection S1S1 S2S2 R2R2 R1R1 A B x 1, t 1 x 2,t 2 (id i, V i ) V i : committed source space (id*, y *, t * ) Tags of basis vectors of V i S-1 keys of V i Adversary Challenger

16. Security of InterMac Anh Le - UCI - NC Pollution Defense16

17. Basic Key Generation in InterMac 17 k 1, k 2 x1x1 x2x2 commit x 1 commit x 2 C k 1, p 1 k 2, p 2 (x 1 | p 1 ) · k 2 = 0 (x 2 | p 2 ) · k 1 = 0 S1S1 S2S2 Send (x 1 | p 1 ) Send (x 2 | p 2 ) Anh Le, UC Irvine, Inter-Session Pollution Detection Key Property: Orthogonality of k i and (x j | p j )

18. Efficient Key Generation in InterMac 18 k 1 = ( ḵ 1 | k’ 1 ) k 2 = ( ḵ 2 | k’ 2 ) x1x1 x2x2 commit Enc(x 1 · ḵ 2 ) commit Enc(x 2 · ḵ 1 ) k 1, p 1 k 2, p 2 (x 1 · ḵ 2 ) + p 1 k’ 2 = 0 Enc( ḵ 2 ) Enc( ḵ 1 ) C S1S1 S2S2 (x 2 · ḵ 1 ) + p 2 k’ 1 = 0 Bandwidth Efficiency: Sending Enc. of a single symbol instead of a full vector Anh Le, UC Irvine, Inter-Session Pollution Detection

19. x2x2 x2x2 k 1, k 2 19 S1S1 S2S2 R2R2 R1R1 A B InterMac Detection Illustration C Gen k 1, p 1 k 2, p 2 p 1, t 1 p 1 +p’ 2, t 1 +t’ 2 p' 2, t’ 2 (p 1 +p’ 2 ) dropped because p’ 2 not orthogonal to k 1 ! (p 1 k 1 +p’ 2 k 2 +p’ 2 k 1 ) ≠ t 1 +t’ 2 (p 1 +p’ 2 ) dropped because p’ 2 not orthogonal to k 1 ! (p 1 k 1 +p’ 2 k 2 +p’ 2 k 1 ) ≠ t 1 +t’ 2 p2, t2p2, t2 p2, t2p2, t2 now what S 2 sends must be orthogonal to k 1 Anh Le, UC Irvine, Inter-Session Pollution Detection x1x1 x1x1 k 1, k 2

20. 1.Background and Motivation oInter-Session Pollution Attacks oMain Challenges 2.Prior Work 3.InterMac Detection 4.Evaluation 5.Conclusion Outline 20 Anh Le, UC Irvine, Inter-Session Pollution Detection

21. 21 InterMac Performance Evaluation Bandwidth Overhead [27] Agrawal et al. [PKC ‘10] [20] Zhang et al. [INFOCOM ‘11] Anh Le, UC Irvine, Inter-Session Pollution Detection

22. 22 InterMac Performance Evaluation Computation Overhead [27] Agrawal et al. [PKC ‘10] [20] Zhang et al. [INFOCOM ‘11] Anh Le, UC Irvine, Inter-Session Pollution Detection

23. o Inter-session: Malicious sources o InterMac: First multi-key MAC scheme for inter-session Each source signs using its own key Still homomorphic o In-network detection based on InterMac 100 times faster than [PKC ‘10] 5 times less bandwidth than [PKC ’10] Require a trusted controller ( [PKC ’10] does not ) o More in the paper: Hash and SpaceMac-based detection Conclusion 23 Anh Le, UC Irvine, Inter-Session Pollution Detection

24. 24 Links: Network Coding Security: http://www.ics.uci.edu/~anhml/projects.html#nc-security http://www.ics.uci.edu/~anhml/projects.html#nc-security UC Irvine Networking Group – Network Coding Project: http://odysseas.calit2.uci.edu/doku.php/public:network-coding http://odysseas.calit2.uci.edu/doku.php/public:network-coding Anh Le, UC Irvine, Inter-Session Pollution Detection