1. 1 A Randomized Space-Time Transmission Scheme for Secret-Key Agreement Xiaohua (Edward) Li 1, Mo Chen 1 and E. Paul Ratazzi 2 1 Department of Electrical and Computer Engineering State University of New York at Binghamton {xli, mchen0}@binghamton.edu, http://ucesp.ws.binghamton.edu/~xli 2 Air Force Research Lab, AFRL/IFGB, paul.ratazzi@afrl.af.mil

2. 2 Major Contributions Develop new wireless security schemes with unconditional secrecy Provide a practical solution for the interesting challenge in information theory: Wyner’s 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

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

4. 4 1.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

5. 5 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

6. 6 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

7. 7 New Secrecy Model Perfect 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

8. 8 Background of Information-Theoretic Secrecy: A. D. Wyner’s wire-tap channel (1975) Secret channel capacity from Alice to Bob Positive secret channel capacity requires Eve’s channel being noisier  not practical enough Theoretically significant –Widely referred –One of his major contributions

9. 9 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

10. 10 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

11. 11 Transmission Scheme Alice: antenna array (secure, public, pilot) –Does not send training signals Bob: estimate symbols, no channel knowledge

12. 12 Signal Model and Assumptions Alice, Bob & Eve do not know channels. Alice estimate h by reciprocity. Eve depends on blind channel estimation.

13. 13 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

14. 14 Blind Deconvolution Attack Why do we need randomized array transmission? –Eve can easily estimate by blind deconvolution methods otherwise –Examples: with optimal transmit beamforming

15. 15 Select Weights with Randomization Objective: choose transmitting weights so that Procedure:

16. 16 4. Trade-off: Power and Secrecy Eve’s received signal becomes Secrecy relies on –Assumption that Eve & Bob’s channels are sufficiently different  wireless channels fade independently when separated a fractional of wavelength –Eve can not estimate channels blindly –Eve’s knowledge on is useless

17. 17 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

18. 18 Secrecy Under Known Randomization eliminates the possibility of exploiting such information We have been able to show

19. 19 Information-Theoretic Secrecy The ambiguity for Eve when estimating channel and symbols increases her error rate Bob’s error rate is due to noise and Alice’s channel knowledge mismatch. It can be much less than Eve’s error rate Information theory guarantees high and positive secret channel capacity  information theoretic secrecy Ways for implementing secret-key agreement protocol remains unknown

20. 20 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

21. 21 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

22. 22 Transmission Power Assume weights have zero mean

23. 23 5. Simulations BER of the proposed transmission scheme

24. 24 Secret channel capacity with the simulated BER

25. 25 Analysis Results on Transmission Power Choice of parameters changes power

26. 26 Simulation Results on Transmission Power Total transmission power and the power of a single transmitter

27. 27 6.Conclusions Propose a randomized array transmission scheme for wireless secret-key agreement Enhance information-theoretic secret channel capacity by increasing the adversary’s receiving error Demonstrate that information-theoretic secrecy concept may be practical based on space-time transmissions and the limit of blind deconvolution