1. 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
2Air Force Research Lab, AFRL/IFGB,
MILCOM'2005

2. Contents Introduction Secure MIMO transmission scheme
Transmission weights design
Transmission secrecy
Simulations
Conclusions
MILCOM'2005

3. 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
MILCOM'2005

4. 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
MILCOM'2005

5. 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
MILCOM'2005

6. 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
MILCOM'2005

7. 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
MILCOM'2005

8. 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
MILCOM'2005

9. 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
MILCOM'2005

10. Transmission Scheme Alice: antenna array (secure, public, pilot)
Does not send training signals
Bob: estimate symbols, no channel knowledge required
MILCOM'2005

11. 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.
MILCOM'2005

12. 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
MILCOM'2005

13. 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
MILCOM'2005

14. Select Weights with Randomization
W1(n): Redundancy in transmitting weights
Procedure:
MILCOM'2005

15. 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:
MILCOM'2005

16. Indeterminacy of Blind Channel Estimation
Proposition:
MILCOM'2005

17. 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
MILCOM'2005

18. 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
MILCOM'2005

19. 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,
MILCOM'2005

20. 5. Simulations BER of the proposed transmission scheme J=6. K=4. QPSK.
MILCOM'2005

21. Secret channel capacity with the simulated BER
MILCOM'2005

22. 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 adversary’s receiving error
Proof of secrecy with weight randomization and limit of blind deconvolution
MILCOM'2005