Mimo transmissions with information theoretic secrecy for secret key agreement in wireless networks
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Xiaohua (Edward) Li 1 and E. Paul Ratazzi 2 1 Department of Electrical and Computer Engineering PowerPoint PPT Presentation

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MIMO Transmissions with Information Theoretic Secrecy for Secret-Key Agreement in Wireless Networks. Xiaohua (Edward) Li 1 and E. Paul Ratazzi 2 1 Department of Electrical and Computer Engineering State University of New York at Binghamton [email protected],

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Xiaohua (Edward) Li 1 and E. Paul Ratazzi 2 1 Department of Electrical and Computer Engineering

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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

[email protected],


2Air Force Research Lab, AFRL/IFGB, [email protected]



  • Introduction

  • Secure MIMO transmission scheme

  • Transmission weights design

  • Transmission secrecy

  • Simulations

  • Conclusions


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


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


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


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


PHY-layer Transmission Secrecy Model

  • Information theoretic secrecy realizable with model different than Shannon’s

    • Eve’s channels, and thus received signals, are different from Alice’s or Bob’s

    • A reality in quantum communication, and wireless transmissions


Information-Theoretic Secrecy

  • Wyner’s wire-tap channel: secret capacity

  • Maurer’s common information concept

  • High secret channel capacity requires Eve’s channel being noisier not practical enough


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


Transmission Scheme

  • Alice: antenna array (secure, public, pilot)

    • Does not send training signals

  • Bob: estimate symbols, no channel knowledge required


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.


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


3. Transmission Weights Design

  • Existing array transmission schemes are susceptible to Eve’s blind deconvolution attack?

    • Eve can easily estimate by blind deconvolution

      if with optimal transmit beamforming


Select Weights with Randomization

  • W1(n): Redundancy in transmitting weights

  • Procedure:


4. Transmission Secrecy

  • Eve’s received signal becomes

    which has distribution

  • Objective: Eve can not estimate channel Hu from xe(n), which relies on

    • Assumption that Eve & Bob’s channels are sufficiently different  wireless channels fade independently when separated a fractional of wavelength

    • Unknown to Eve:


Indeterminacy of Blind Channel Estimation

  • Proposition:


Indeterminacy of Blind Symbol Estimation

  • Proposition:

  • Result:

    • Eve’s error rate: high

    • Bob’s error rate: low (identical to optimal MIMO eigen-beamforming)

    • Cost paid: higher transmission power


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


Eve’s 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,


5. Simulations

  • BER of the proposed transmission scheme





  • Secret channel capacity with the simulated BER



  • 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 adversary’s receiving error

    • Proof of secrecy with weight randomization and limit of blind deconvolution


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