Resilient Network Coding
in the Presence of
Eavesdropping Byzantine
Adversaries
Proof incorrect!
Hongyi
Yao
Sidharth Jaggi
Michael Langberg
Open University of
Israel
Tsinghua University
NetCod 2010
Network Codes
How
to share
Resilient
toa secret
OR
when
a (bad) person’s
Eavesdropping
and listening
and
trying to fool the receiver
Jamming
Hongyi
Yao
Tsinghua University
Danilo
Silva
University of
Campinas
Sidharth
Jaggi
Michael
Langberg
Open University of
Israel
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
Background
Privacy
(Secrecy)
Existence
proofs/Conver
ses
Efficient
random
distributed
schemes
Cryptographic
schemes
Universal
schemes
[CY02], …,
[RS07], …
[FMSS04],…
[OB08], …
[SK08],…
[JLKKHM07],…
[CJL06],
[GP06],
[ZKMH07], …
[KK07],
[SKK08]…
Security (Error [CY06]/[YC06],
Correction)
…, [M06], …
Setup
Eureka
1.
2.
3.
4.
5.
6.
7.
8.
Stage
Scheme
Network
Data
Code
Bad links
Randomness
Transmission
Decode
Who
knows
what
ABC
C
A
C
C
A
ABC
B
Privacy
Eavesdropped
links ZI
Attacked
links ZO
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
Network Error-correcting code
(Operator channel [KK07],
Rank-metric codes [SKK08])
Optimal rate
R = C-2ZO
Privacy + Security at rate C-2ZO-ZI
[NY09], [SK10]
Network errorcorrecting code
Rate C-2ZO
ZI random symbols
Overall rate C-2ZO-ZI
ε-error?
Optimal rate for zero-error codes
Shared-secret Security at rate C-ZO
[JLKKHM07]
X 
Y  TX  T' Z  T T' 
Z 
X 
1
  T T' Y
Z 
Linear list with
Invertible
C2 variables*
w.h.p.
w.h.p., unique[HKMKE03]
decoding!

C2 secret hashes of X
Secure transmission at rate C-ZO!
Secure + private transmission at rate C-ZO-ZI!
* Different list-decoding used
Upper bound: C-ZO-ZI
Just one (secret) bit for Bob… [JL07]
??
Just one (secret) bit for Bob… [YSJL10]
R }
ZI
0   
0  } C  Z I

R  }
ZI
1   
R' } C  Z I

0, rank(Y)  C
Decode(Y)  
1, rank(Y)  C

Security:
Privacy: [SK08]
ZI links)

(Only sees
R R 
   , only ZO  C  Z I packets
0  R''

R  R'' 
w.h.p.    , doesn' t know R, R'
R' R'''
Questions?