Space-Time Transmissions for Wireless Secret-Key Agreement with Information-Theoretic Secrecy

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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_at_binghamton.edu,
• http//ucesp.ws.binghamton.edu/xli
• 2Air Force Research Lab, AFRL/IFGB,
  paul.ratazzi_at_afrl.af.mil

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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 Wyners 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 Eves 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
• Eves channels and received signals are different
  from Alices or Bobs
• 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 Eves
  channel being noisier ? not practical enough
• Theoretically significant

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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

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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 (CISS2005)
• 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 Eves channel. No a priori secret key
  shared.
• Eve knows her own channel, but not know Alice
  Bobs channel. Has infinitely high SNR

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• Transmission and signal models

Alice can estimate h via reciprocity. Traditional
transmit beamforming has no secrecy.
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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

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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

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• Consider the extreme case Eve knows her channel
  and has extremely high SNR, then Eves received
  signal becomes
• Secrecy relies on
• Alice uses proper for randomization
  requires transmission redundancy
• Eves knowledge on is
  useless

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• In our scheme, are used to
  create intentional ambiguity to Eve, but not Bob
• Proposition 1
• Proposition 2

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• Information-theoretic secrecy
• Eves received signal gives no more information
  for symbol estimation ? an error rate as
  high as purely guessing
• Bobs error rate is due to noise and
  Alices channel knowledge mismatch. It can be
  much less than Eves 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 Eves 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

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4. Simulations

• BER of the proposed transmission scheme
• J4, 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