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Resilient Network Coding in the Presence of Eavesdropping Byzantine Adversaries

ISIT 2007. Resilient Network Coding in the Presence of Eavesdropping Byzantine Adversaries. Proof incorrect!. 2009. Hongyi Yao. Sidharth Jaggi. Michael Langberg. Open University of Israel. Tsinghua University. NetCod 2010. OR. Network Codes Resilient to Eavesdropping and Jamming.

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Resilient Network Coding in the Presence of Eavesdropping Byzantine Adversaries

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

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

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

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

  5. Problem! Corrupted links Eavesdropped Links ZI Attacked Links ZO

  6. Background +

  7. Setup Eureka Who knows what Stage • Scheme A B C • Network C • Data A • Code C • Bad links C • Randomness A • Transmission A B C • Decode B Eavesdropped links ZI Attacked links ZO Privacy

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

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

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

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

  12. Shared-secret Security at rate C-ZO [JLKKHM07] Linear list with C2 variables* Invertible w.h.p. [HKMKE03] w.h.p., unique decoding! C2 secret hashes of X Secure transmission at rate C-ZO! Secure + private transmission at rate C-ZO-ZI! * Different list-decoding used

  13. Upper bound: C-ZO-ZI

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

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

  16. Questions?

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