A Randomized Space-Time Transmission Scheme for Secret-Key Agreement

1. A Randomized Space-Time Transmission Scheme for Secret-Key Agreement Xiaohua (Edward) Li1, Mo Chen1 and E. Paul Ratazzi2 1Department of Electrical and Computer Engineering State University of New York at Binghamton {xli, mchen0}@binghamton.edu, http://ucesp.ws.binghamton.edu/~xli 2Air Force Research Lab, AFRL/IFGB, paul.ratazzi@afrl.af.mil

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. Contents • Introduction • Randomized space-time transmission scheme • Transmission weights design • Trade power for secrecy • Simulations • Conclusions

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

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

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

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

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. 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. 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. Transmission Power • Assume weights have zero mean

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

24. Secret channel capacity with the simulated BER

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

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

27. 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