MIMO Transmissions with Information Theoretic Secrecy for Secret-Key Agreement in Wireless Networks

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MIMO Transmissions with Information Theoretic
Secrecy for Secret-Key Agreement in Wireless
Networks

• Xiaohua (Edward) Li1 and E. Paul Ratazzi2
• 1Department of Electrical and Computer
  Engineering
• State University of New York at Binghamton
• xli_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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Contents

1. Introduction
2. Secure MIMO transmission scheme
3. Transmission weights design
4. Transmission secrecy
5. Simulations
6. Conclusions

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1. Introduction

• Secure wireless transmission necessary PHY
  security techniques for wireless information
  assurance
• Wireless transmissions have no boundary,
  susceptible to listening/analyzing, location,
  jamming
• Wireless nodes have severe energy and bandwidth
  constraints ? light techniques
• Unreliable link and dynamic network topology

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Secure Wireless Transmissions

• Traditional secure transmission design
• Data encryption, spread spectrum, etc
• New idea use antenna array diversity and array
  redundancy
• A completely different approach of secure (LPI)
  waveform design

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Significance to Cryptography

• Provable (information-theoretic) secrecy
• Inherently secure transmission, no encryption
  keys involved
• Comparable to quantum cryptography
• Provide PHY-layer LPI, and assist higher layer
  data encryption
• PHY-layer assisted secret key agreement

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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

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PHY-layer Transmission Secrecy Model

• Information theoretic 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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Information-Theoretic Secrecy

• Wyners wire-tap channel secret capacity
• Maurers common information concept
• High secret channel capacity requires Eves
  channel being noisier ? not practical enough

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2. Secure MIMO transmission scheme

• Can we guarantee a large or in
  practice?
• Possible randomized MIMO transmission
• Basic idea
• Use redundancy of antenna array
• 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
  required

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Signal Model and Assumptions

• Alice, Bob Eve do not know channels.
• Alice estimate H by reciprocity
• Bob need not know channel.
• Eve depends on blind estimation.

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MIMO Transmission Procedure

• Alice select transmit antenna 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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3. Transmission Weights Design

• Existing array transmission schemes are
  susceptible to Eves blind deconvolution attack?
• Eve can easily estimate by blind
  deconvolution
• if with optimal transmit beamforming

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Select Weights with Randomization

• W1(n) Redundancy in transmitting weights
• Procedure

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4. Transmission Secrecy

• Eves received signal becomes
• which has distribution
• Objective Eve can not estimate channel Hu from
  xe(n), which relies on
• Assumption that Eve Bobs channels are
  sufficiently different ? wireless channels fade
  independently when separated a fractional of
  wavelength
• Unknown to Eve

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Indeterminacy of Blind Channel Estimation

• Proposition

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Indeterminacy of Blind Symbol Estimation

• Proposition
• Result
• Eves error rate high
• Bobs error rate low (identical to optimal MIMO
  eigen-beamforming)
• Cost paid higher transmission power

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Transmission secrecy

• Weights are selected randomly and unknown to Eve,
  blind deconvolution is made impossible
• Weights are selected by Alice, no need to tell
  Bob ? equivalently one-time pad
• Information theory guarantees high and positive
  secret channel capacity ? provable (information
  theoretic) secrecy

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Eves Exhaustive Search Attack

• Eve may exhaustively try all possible channels
  (both ).
• The complexity can be at least
  , according to quantization level Q
• Low quantization level reduces complexity, but
  increases symbol estimation error ? still makes
  high positive secret channel capacity possible
• Example,

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5. Simulations
J6. K4. QPSK.

• BER of the proposed transmission scheme

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• Secret channel capacity with the simulated BER

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Conclusions

• Proposed a randomized MIMO transmission scheme
• Use array redundancy and channel diversity for
  transmission security
• Enhance transmission LPI in the PHY-layer by
  increasing the adversarys receiving error
• Proof of secrecy with weight randomization and
  limit of blind deconvolution