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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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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
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
Multicast Network Model ALL of Alice’s information decodable EXACTLY by EACH Bob
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
Problem! Corrupted links Eavesdropped Links ZI Attacked Links ZO
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
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
Privacy at rate C-ZI ([CY02],…) C-ZI rate ZI eavesdropped links ZI random symbols Network coding + one-time pad Optimal
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
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
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
Just one (secret) bit for Bob… [JL07] ??
Just one (secret) bit for Bob… [YSJL10] Security: Privacy: [SK08] (Only sees ZI links)