1 Space-Time Transmissions for Wireless Secret-Key Agreement with Information-Theoretic Secrecy 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, 2 Air Force Research Lab, AFRL/IFGB,

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 1.Introduction 2.Randomized space-time transmission 3.Transmission secrecy 4.Simulations 5.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 Alice can estimate h via reciprocity. Traditional transmit beamforming has no secrecy. Transmission and signal models

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, {c i (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 H u 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 C 1 and C 2. –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