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

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 xli@binghamton.edu, http://ucesp.ws.binghamton.edu/~xli 2Air Force Research Lab, AFRL/IFGB, paul.ratazzi@afrl.af.mil 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