A Randomized Space-Time Transmission Scheme for Secret-Key Agreement

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A Randomized Space-Time Transmission Scheme for
Secret-Key Agreement

• 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

• Develop new wireless security schemes with
  unconditional secrecy
• Provide a practical solution for the interesting
  challenge in information theory Wyners wire-tap
  channel for perfect secrecy
• Propose cross-layer security designs, integrating
  redundancy of space-time transmission, limit of
  blind deconvolution, and secret key distribution

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Contents

1. Introduction
2. Randomized space-time transmission scheme
3. Transmission weights design
4. Trade power for secrecy
5. Simulations
6. Conclusions

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Introduction

• Secret-key agreement
• Classic Shannon model
• Alice Bob try to exchange encryption keys for
  encrypted data transmission
• Eve can acquire all (and identical) messages
  received by Alice or Bob
• Perfect secrecy impractical under Shannon model
• Computational secrecy achievable
• Based on some intractable computation problem
• Intractability unproven

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Perfect Secrecy

• Perfect secrecy significant theoretically,
  important practically
• Increased computing power, new computation
  concepts (such as Quantum computer) are
  challenging computational secrecy schemes
• Ways for achieving perfect secrecy
• Quantum communications quantum secrecy
• Wireless transmissions (possibly)
  information-theoretical secrecy

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Wireless Secrecy

• Quantum secrecy
• Successful, but unknown of wireless network
  applications
• Unconditional wireless secrecy
• Provide an alternative to quantum secrecy for
  network key management
• Target to the wide spread of wireless
  communications and wireless networks
• Objective
• Design information-theoretically secret wireless
  transmission schemes

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New Secrecy Model

• Perfect secrecy realizable with model different
  than Shannons
• Eves channels, and thus received signals, are
  different from Alices or Bobs
• A reality in quantum communication, and wireless
  transmissions

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Background of Information-Theoretic Secrecy A.
D. Wyners wire-tap channel (1975)

• Secret channel capacity from Alice to Bob
• Positive secret channel capacity requires Eves
  channel being noisier ? not practical enough
• Theoretically significant
• Widely referred
• One of his major contributions

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Background of Information-Theoretic Secrecy U.
Maurer Common Information (1993,2003)

• 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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2. Randomized Space-Time Transmission

• Can we guarantee a large or in
  practice?
• Possible randomized space-time transmission
• Basic idea
• Use redundancy of antenna array to create a
  difficult blind deconvolution problem
• Exploit the limit of blind deconvolution
• Eve can not estimate channel/symbol blindly

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Transmission Scheme

• Alice antenna array (secure, public, pilot)
• Does not send training signals
• Bob estimate symbols, no channel knowledge

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Signal Model and Assumptions
Alice, Bob Eve do not know channels. Alice
estimate h by reciprocity. Eve depends on blind
channel estimation.
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3. Transmission Weights Design

• Alice select proper weights so that
• Bob receives signal
• By estimating received signal power, Bob can
  detect signals
• Key points
• No channel information required for Bob, no
  training required ? no training available to Eve
• Redundancy in selecting weights

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Blind Deconvolution Attack

• Why do we need randomized array transmission?
• Eve can easily estimate by blind
  deconvolution methods otherwise
• Examples with optimal transmit beamforming

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Select Weights with Randomization

• Objective choose transmitting weights so that
• Procedure

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4. Trade-off Power and Secrecy

• Eves received signal becomes
• Secrecy relies on
• Assumption that Eve Bobs channels are
  sufficiently different ? wireless channels fade
  independently when separated a fractional of
  wavelength
• Eve can not estimate channels blindly
• Eves knowledge on
  is useless

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Secrecy Against Blind Deconvolution Attack

• Blind deconvolution requires strong source
  statistical properties,
• Example known distribution, independence,
  non-Gaussian distribution, distinct power
  spectral
• Weights are selected randomly and unknown to Eve,
  blind deconvolution property can all be violated
• Example can have a distribution
  unknown to Eve, with certain mean and variance
• Weights are selected by Alice, no need to tell
  Bob ? equivalently one-time pad

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Secrecy Under Known

• Randomization eliminates the possibility of
  exploiting such information
• We have been able to show

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Information-Theoretic Secrecy

• The ambiguity for Eve when estimating channel and
  symbols increases her error rate
• 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 ? information theoretic
  secrecy
• Ways for implementing secret-key agreement
  protocol remains unknown

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Complexity of Exhaustive Attack

• Eve may exhaustively estimate channels
  (both ).
• The complexity can be at least ,
  according to quantization level
• Low quantization level reduces complexity, by
  increases symbol estimation error ? still makes
  high positive secret channel capacity possible
• Example,
• Complexity can be much higher with MIMO and
  space-time transmissions

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Trade-off in Transmission Power

• Cost of realizing secrecy increased transmission
  power
• transmission rate is not traded
• Transmission power has to be controlled to avoid
  the possibility of blind deconvolution
• One transmitting antenna with dominating
  transmission power should be avoided

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Transmission Power

• Assume weights have zero mean

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5. Simulations

• BER of the proposed transmission scheme

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• Secret channel capacity with the simulated BER

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Analysis Results on Transmission Power

• Choice of parameters changes power

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Simulation Results on Transmission Power

• Total transmission power and the power of a
  single transmitter

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Conclusions

• Propose a randomized array transmission scheme
  for wireless secret-key agreement
• Enhance information-theoretic secret channel
  capacity by increasing the adversarys receiving
  error
• Demonstrate that information-theoretic secrecy
  concept may be practical based on space-time
  transmissions and the limit of blind deconvolution