Space-Time Transmissions for Wireless Secret-Key Agreement with Information-Theoretic Secrecy

1. Space-Time Transmissions for Wireless Secret-Key Agreementwith Information-Theoretic Secrecy 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 • An innovative way of secure waveform design: use antenna redundancy/diversity, instead of spread spectrum • Practical solutions for a challenge in information theory: Wyner’s wire-tap channel with perfect secrecy • New wireless security techniques for secret-key agreement with provable, unconditional secrecy

3. Contents • Introduction • Randomized space-time transmission • Transmission secrecy • Simulations • Conclusions

4. 1. Introduction • Physical-layer built-in security: • Guarantee Low-Probability-of-Interception (LPI) based on transmission properties, not data encryption • No a priori secret keys required, different from spread-spectrum-based traditional secure waveform designs • Physical-layer transmissions with information-theoretic secrecy • Secure transmissions in the physical-layer • Provide ways for secret-key agreement: assist upper-layer security techniques, support cross-layer security design for end-to-end security • An innovative idea • Use antenna redundancy and channel diversity, not spread-spectrum

5. Classic Shannon secrecy model • Alice & Bob exchange messages for secret key agreement • Eve can acquire all (and identical) messages received by Alice or Bob • Perfect secrecy impractical under Shannon model • Perfect secrecy: Eve’s received signals give no more information for eavesdropping than guessing • Provably secure: information-theoretic secrecy • Computational secrecy achievable • Based on intractable computation problem • Intractability unproven

6. New secrecy models in wireless transmissions • Eve’s channels and received signals are different from Alice’s or Bob’s • Provide new ways to realize information-theoretic secrecy, to design transmissions with build-in security

7. Wire-tap channel (Wyner, 1975) • Secret channel capacity from Alice to Bob • Positive secret channel capacity requires Eve’s channel being noisier  not practical enough • Theoretically significant

8. If Alice & Bob exchange information by public discussion, secret channel capacity increases to • Large capacity requires Eve have large error rate  still not practical enough

9. Objectives: • Based on the new model, design new transmissions to realize information-theoretic secrecy • Investigate two fundamental problems of physical-layer security • Achievable secret channel capacity • Cost of achieving such secret channel capacity

10. 2. Randomized Space-Time Transmission • Can we guarantee a large or in practice? • Yes, use randomized space-time transmission and the limit of blind deconvolution (CISS’2005) • This paper: what if Eve knows the channel? • Basic idea: • Use redundancy of antenna array transmissions to create intentional ambiguity • Eve can not resolve such ambiguity, can not estimate symbols • High secret channel capacity guaranteed

11. Assumptions • Alice: J transmit antenna • Alice and Bob: can estimate their own channel, do not know Eve’s channel. No a priori secret key shared. • Eve: knows her own channel, but not know Alice & Bob’s channel. Has infinitely high SNR

12. Transmission and signal models Alice can estimate h via reciprocity. Traditional transmit beamforming has no secrecy.

13. Alice select weights by solving • Bob receives signal • By estimating received signal power, Bob can detect signals • Key points: • Bob need not know F, {ci(n)} • Redundancy in selecting weights • Transmission power larger than optimal transmit beamforming

14. 3. Transmission secrecy • Why do we need randomized array transmission? • Eve can easily estimate by training/blind deconvolution methods otherwise • Examples: if using optimal transmit beamforming, Eve’ deconvolution is possible

15. Consider the extreme case: Eve knows her channel and has extremely high SNR, then Eve’s received signal becomes • Secrecy relies on • Alice uses proper for randomization: requires transmission redundancy • Eve’s knowledge on is useless

16. In our scheme, are used to create intentional ambiguity to Eve, but not Bob • Proposition 1: • Proposition 2:

17. Information-theoretic secrecy • Eve’s received signal gives no more information for symbol estimation  an error rate as high as purely guessing • 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 • Ways for implementing secret-key agreement protocol to be developed

18. Complexity of Eve’s exhaustive search • Increases with block time-varying channels • Complexity can be much higher with MIMO and space-time transmissions by using the limit of blind deconvolution  Eve has to search Hu too. • Trade-off in transmission power and secrecy • Cost of realizing secrecy: increased transmission power while using antenna redundancy • Transmission data rate (spectrum efficiency) is not traded

19. 4. Simulations • BER of the proposed transmission scheme • J=4, QPSK. Bob has identical performance as optimal transmit beamforming.

20. Secret channel capacity with the simulated BER • Eve can not estimate symbols. Capacity calculated as C1 and C2. • For “Unsec”, Eve has the same error rate as Bob.

21. Total transmission power and standard deviation • Proposed scheme trades transmission power for secrecy

22. Transmission power and deviation of a single transmitter

23. 5. Conclusions • Propose a randomized array transmission scheme for wireless secret-key agreement • Use array redundancy (more antenna, higher power) to create intentional ambiguity • Demonstrate that information-theoretic secrecy concept is practical based on the redundancy and diversity of space-time transmissions