space-time transmissions for wireless secret-key agreement with information-theoretic secrecy
DESCRIPTION
Space-Time Transmissions for Wireless Secret-Key Agreement with Information-Theoretic Secrecy. Xiaohua (Edward) Li 1 , Mo Chen 1 and E. Paul Ratazzi 2 1 Department of Electrical and Computer Engineering State University of New York at Binghamton {xli, mchen0}@binghamton.edu, - PowerPoint PPT PresentationTRANSCRIPT
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Space-Time Transmissions for Wireless Secret-Key Agreementwith Information-Theoretic Secrecy
Xiaohua (Edward) Li1, Mo Chen1 and E. Paul Ratazzi2 1Department of Electrical and Computer Engineering
State University of New York at Binghamton{xli, mchen0}@binghamton.edu,
http://ucesp.ws.binghamton.edu/~xli2Air Force Research Lab, AFRL/IFGB, [email protected]
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Major Contributions
• An innovative way of secure waveform design: use antenna redundancy/diversity, instead of spread spectrum
• Practical solutions for a challenge in information theory: Wyner’s wire-tap channel with perfect secrecy
• New wireless security techniques for secret-key agreement with provable, unconditional secrecy
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Contents
1. Introduction
2. Randomized space-time transmission
3. Transmission secrecy
4. Simulations
5. Conclusions
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1. Introduction
• Physical-layer built-in security:– Guarantee Low-Probability-of-Interception (LPI) based on
transmission properties, not data encryption– No a priori secret keys required, different from spread-spectrum-
based traditional secure waveform designs • Physical-layer transmissions with information-theoretic
secrecy– Secure transmissions in the physical-layer– Provide ways for secret-key agreement: assist upper-layer
security techniques, support cross-layer security design for end-to-end security
• An innovative idea– Use antenna redundancy and channel diversity, not spread-
spectrum
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• Classic Shannon secrecy model– Alice & Bob exchange messages for secret key
agreement• Eve can acquire all (and identical) messages received by
Alice or Bob
– Perfect secrecy impractical under Shannon model• Perfect secrecy: Eve’s received signals give no more
information for eavesdropping than guessing• Provably secure: information-theoretic secrecy
– Computational secrecy achievable• Based on intractable computation problem• Intractability unproven
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• New secrecy models in wireless transmissions– Eve’s channels and received signals are different from
Alice’s or Bob’s– Provide new ways to realize information-theoretic
secrecy, to design transmissions with build-in security
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• Wire-tap channel (Wyner, 1975)– Secret channel capacity from Alice to Bob
– Positive secret channel capacity requires Eve’s channel being noisier not practical enough
– Theoretically significant
)1log()1(log)( here w
better) channel(Eve' else,0
noiser) channel s(Eve' if),()(1
ppppph
hhC
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• If Alice & Bob exchange information by public discussion, secret channel capacity increases to
– Large capacity requires Eve have large error rate still not practical enough
)()2(2 hhC
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• Objectives: – Based on the new model, design new
transmissions to realize information-theoretic secrecy
– Investigate two fundamental problems of physical-layer security
• Achievable secret channel capacity• Cost of achieving such secret channel capacity
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2. Randomized Space-Time Transmission
• Can we guarantee a large or in practice?– Yes, use randomized space-time transmission and
the limit of blind deconvolution (CISS’2005)– This paper: what if Eve knows the channel?
• Basic idea: – Use redundancy of antenna array transmissions to
create intentional ambiguity– Eve can not resolve such ambiguity, can not
estimate symbols– High secret channel capacity guaranteed
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• Assumptions– Alice: J transmit antenna– Alice and Bob: can estimate their own channel, do
not know Eve’s channel. No a priori secret key shared.
– Eve: knows her own channel, but not know Alice & Bob’s channel. Has infinitely high SNR
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)()()()( :receives Eve
)()()()( :receives Bob
nnbnn
nvnbnnx
uuu
H
vwHx
wh
Alice can estimate h via reciprocity.Traditional transmit beamforming has no secrecy.
• Transmission and signal models
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• Alice select weights by solving
• Bob receives signal • By estimating received signal power, Bob can detect
signals
• Key points:– Bob need not know F, {ci(n)}
– Redundancy in selecting weights – Transmission power larger than optimal transmit beamforming
)}({ and ],,[chosen randomly with
)(
)(
)( where,)(
)(
11
11
11
nc
nc
nc
nn
n
iJ
JJ
H
H
ffF
f
f
aa
hw
F
h
)()()( nvnbnx h
)()(ˆ1nxnb
h
)(nw
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3. Transmission secrecy
• Why do we need randomized array transmission?– Eve can easily estimate by training/blind
deconvolution methods otherwise– Examples: if using optimal transmit beamforming,
Eve’ deconvolution is possible
)(nb
)()()(
1)(
or
)()()/()(
nnbn
n
nnbn
uuu
uuu
vz
VHx
vhhHx
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• Consider the extreme case: Eve knows her channel and has extremely high SNR, then Eve’s received signal becomes
• Secrecy relies on– Alice uses proper for randomization:
requires transmission redundancy– Eve’s knowledge on is useless
)()()( nbnnu wx
hwh )(nH
)(nw
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• In our scheme, are used to create intentional ambiguity to Eve, but not Bob – Proposition 1:
– Proposition 2:
)}({, nciF
.11)}],({|[)}]({|[
i.e., , of column any from
tediscriminanot can Eve t,environmen noiseless
in worksand channel knows Eve ifEven
JinPnP uiu
i
u
xfxh
Ffh
H
. )( from )( tediscriminanot can Eve
1,n Propositio of condition Under the
nbcnb i
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• Information-theoretic secrecy– Eve’s received signal gives no more information for
symbol estimation an error rate as high as purely guessing
– Bob’s error rate is due to noise and Alice’s channel knowledge mismatch. It can be much less than Eve’s error rate
– Information theory guarantees high and positive secret channel capacity
– Ways for implementing secret-key agreement protocol to be developed
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• Complexity of Eve’s exhaustive search– – Increases with block time-varying channels– Complexity can be much higher with MIMO and
space-time transmissions by using the limit of blind deconvolution Eve has to search Hu too.
• Trade-off in transmission power and secrecy– Cost of realizing secrecy: increased transmission
power while using antenna redundancy– Transmission data rate (spectrum efficiency) is not
traded
h possible all of space and ,by Determined J
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4. Simulations
• BER of the proposed transmission scheme– J=4, QPSK. Bob has identical performance as optimal transmit beamforming.
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• Secret channel capacity with the simulated BER– Eve can not estimate symbols. Capacity calculated as C1 and C2. – For “Unsec”, Eve has the same error rate as Bob.
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• Total transmission power and standard deviation– Proposed scheme trades transmission power for secrecy
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• Transmission power and deviation of a single transmitter
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5. Conclusions• Propose a randomized array transmission
scheme for wireless secret-key agreement• Use array redundancy (more antenna, higher
power) to create intentional ambiguity• Demonstrate that information-theoretic secrecy
concept is practical based on the redundancy and diversity of space-time transmissions