1. NC-Audit: Auditing for Network Coding Storage Anh Le and Athina Markopoulou University of California, Irvine

2. Outline 1.Background 2.Related Work 3.Key Techniques 4.NC-Audit 5.Evaluation 6.Conclusion NC-Audit: Auditing for NC Storage2Le and Markopoulou (UC Irvine)

3. NC-Audit: Auditing for NC Storage3 Key ideas: - Sub-packetization - Mixing when repair NC-Based Distributed Storage Le and Markopoulou (UC Irvine) [Dimakis, 2011]

4. NC-Audit: Auditing for NC Storage4 The Auditing Problem Data Audit Security Message Le and Markopoulou (UC Irvine)

5. Storage node hides data corruption NC-Audit: Auditing for NC Storage5 Threat Model TPA acquires data from the auditing Le and Markopoulou (UC Irvine)

6. NC-Audit: Auditing for NC Storage6 Desired Properties of NC-Audit Data correctness guarantee Privacy-preserving auditing Support for repair and data dynamics Low overhead Le and Markopoulou (UC Irvine)

7. NC-Audit: Auditing for NC Storage7 Related Work Integrity Checking for Remote Data Proof of Retrievability [Juels ’07], [Shacham ’08] Proof of Data Posession [Ateniese ’07] Support for Data Dynamics [Ateniese ’08], [Erway ’09] [Wang ’09] Privacy Preserving Auditing [Shah ’06], [Wang ’10] Le and Markopoulou (UC Irvine) For NC Storage Error Detection [Dikaliotis ’10] Proof of Retrievability [Chen ’10]

8. Outline 1.Background 2.Related Work 3.Key Techniques 4.NC-Audit 5.Evaluation 6.Conclusion NC-Audit: Auditing for NC Storage8Le and Markopoulou (UC Irvine)

9. 9 eiei eiei titi titi The Naïve Scheme t1t1 t1t1 e1e1 e1e1 tMtM tMtM eMeM eMeM … tktk tktk ekek ekek k tktk tktk ekek ekek Le and Markopoulou (UC Irvine)NC-Audit: Auditing for NC Storage HMAC Inefficient Does not support repair Violate privacy

10. c c t t SpaceMac - Homomorphic MAC NCrypt - CPA-secure encryption tktk tktk ekek ekek c c t t t t Σα i e i 10 eiei eiei titi titi Key Techniques of NC-Audit t1t1 t1t1 e1e1 e1e1 tMtM tMtM eMeM eMeM … k 1,.., k n tktk tktk ekek ekek Le and Markopoulou (UC Irvine)NC-Audit: Auditing for NC Storage HMAC SpaceMac k Σα i e i c c NCrypt t t Σα i e i

11. NC-Audit: Auditing for NC Storage11 SpaceMac [Le, NetCod 10] Homomorphic Message Authentication Codes Le and Markopoulou (UC Irvine)

12. NC-Audit: Auditing for NC Storage12 NCrypt Random Linear CPA-Secure Encryption Le and Markopoulou (UC Irvine)

13. Outline 1.Background 2.Related Work 3.Key Techniques 4.NC-Audit 5.Evaluation 6.Conclusion NC-Audit: Auditing for NC Storage13Le and Markopoulou (UC Irvine)

14. 1.Homomorphic MAC: SpaceMac 2.Random Linear Encryption: NCrypt e e t t 14 c c t t e e e e t t c c c c t t e e t t NC-Audit: Auditing for NC StorageLe and Markopoulou (UC Irvine) NC-Audit = SpaceMac + NCrypt

15. Le and MarkopoulouNC-Audit: Auditing for NC Storage15 Repairing with Regular Scheme t1t1 t1t1 e1e1 e1e1 t3t3 t3t3 e3e3 e3e3 t4t4 t4t4 e4e4 e4e4 t2t2 t2t2 e2e2 e2e2 t5t5 t5t5 e5e5 e5e5 t6t6 t6t6 e6e6 e6e6 Node 1 Node 2 Node 3 t7t7 t7t7 e7e7 e7e7 t8t8 t8t8 e8e8 e8e8 Node 4 α 5 e 5 + α 6 e 6 α 3 e 3 + α 4 e 4 α 1 e 1 + α 2 e 2 t' 7 e’ 7 t' 8 e' 8 t' 7 e’ 7 t' 8 e' 8 High cost

16. Le and MarkopoulouNC-Audit: Auditing for NC Storage16 Repairing with NC-Audit t1t1 t1t1 e1e1 e1e1 t3t3 t3t3 e3e3 e3e3 t4t4 t4t4 e4e4 e4e4 t2t2 t2t2 e2e2 e2e2 t5t5 t5t5 e5e5 e5e5 t6t6 t6t6 e6e6 e6e6 Node 1 Node 2 Node 3 t7t7 t7t7 e7e7 e7e7 t8t8 t8t8 e8e8 e8e8 Node 4 α 5 t 5 + α 6 t 6 α 5 e 5 + α 6 e 6 α 3 t 3 + α 4 t 4 α 3 e 3 + α 4 e 4 α 1 t 1 + α 2 t 2 α 1 e 1 + α 2 e 2 t' 7 e’ 7 t' 8 e' 8

17. 17NC-Audit: Auditing for NC StorageLe and Markopoulou (UC Irvine) Security Guarantees of NC-Audit Data Posession Privacy

18. Outline 1.Background 2.Related Work 3.Key Techniques 4.NC-Audit 5.Evaluation 6.Conclusion NC-Audit: Auditing for NC Storage18Le and Markopoulou (UC Irvine)

19. Performance Evaluation NC-Audit: Auditing for NC Storage19Le and Markopoulou (UC Irvine) Implementation: Java: - javax.crypto 80-bit security: - q = 2 8, l = 10 - 4 KB block Comparisons: [Wang et al., ESORICS ’09] [Wang et al., INFOCOM ’10] [Chen et al., CCSW ’10]

20. Performance Evaluation NC-Audit: Auditing for NC Storage20Le and Markopoulou (UC Irvine)

21. Conclusion NC-Audit: Auditing for NC Storage21Le and Markopoulou (UC Irvine) NC-Audit: Auditing scheme for NC storage Data correctness guarantee - SpaceMac Privacy-preserving auditing - NCrypt Support for repair and data dynamics Low overhead

22. This work is supported by NSF and AFOSR http://www.ics.uci.edu/~anhml/software.html