1. Resilient Network Coding in the Presence of Eavesdropping Byzantine Adversaries Michael Langberg Sidharth Jaggi Open University of Israel ISIT 2007 Tsinghua University Hongyi Yao Proof incorrect! 2009

2. Network Codes Resilient to Eavesdropping and Jamming Michael Langberg Sidharth Jaggi OR How to share a secret when a (bad) person’s listening and trying to fool the receiver Open University of Israel Tsinghua University Hongyi Yao University of Campinas Danilo Silva NetCod 2010

3. Multicast ALL of Alice’s information decodable EXACTLY by EACH Bob Network Model

4. Multicast Network Model ALL of Alice’s information decodable EXACTLY by EACH Bob [ACLY00] With mixing, C = min{C i } achievable [LCY02],[KM01],[JCJ03],[HKMKE03] Simple (linear) distributed codes suffice

5. Problem! Eavesdropped Links Z I Attacked Links Z O Corrupted links

6. Existence proofs/Conver ses Efficient random distributed schemes Cryptographic schemes Universal schemes Privacy (Secrecy) [CY02], …, [RS07], … [FMSS04],…[OB08], …[SK08],… Security (Error Correction) [CY06]/[YC06], …, [M06], … [JLKKHM07],…[CJL06], [GP06], [ZKMH07], … [KK07], [SKK08]… Background

7. Setup 1.Scheme A B C 2.Network C 3.Data A 4.Code C 5.Bad links C 6.Randomness A 7.Transmission A B C 8.Decode B Eureka Eavesdropped links Z I Attacked links Z O Who knows what Stage Privacy

8. Background Efficient algorithms[SK08][JLKKHM07],[SKK08]  “Optimal” rates (Secrecy) C-Z I (Security) C-2Z O  Poly-time  Distributed  End-to-end  Packet-based  Topology unknown a priori  Information-theoretically secure, private

9. Privacy at rate C-Z I ([CY02],…) Z I random symbols C-Z I rate Network coding + one-time pad Optimal Z I eavesdropped links

10. Security at rate C-2Z O (…,[SKK08]) Optimal rate R = C-2Z O Error-correcting code Network (Operator channel [KK07], Rank-metric codes [SKK08]) Z O corrupted links

11. Privacy + Security at rate C-2Z O -Z I Optimal rate for zero-error codes Network error- correcting code Rate C-2Z O Z I random symbols Overall rate C-2Z O -Z I [NY09], [SK10] ε -error?

12. Shared-secret Security at rate C-Z O [JLKKHM07] Invertible w.h.p. [HKMKE03] C 2 secret hashes of X Linear list with C 2 variables* Secure transmission at rate C-Z O ! Secure + private transmission at rate C-Z O -Z I ! w.h.p., unique decoding! * Different list-decoding used

13. Upper bound: C-Z O -Z I

14. Just one (secret) bit for Bob… [JL07] ??

15. Just one (secret) bit for Bob… [YSJL10] Privacy: [SK08] (Only sees Z I links) Security:

16. Questions?