LDPC Codes for Physical Layer Security Demijan Klinc ∗ , Jeongseok Ha † , Steven W. McLaughlin ∗ , Jo˜ ao Barros ‡ , and Byung-Jae Kwak § ∗ School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, USA Email: {demi, swm}@ece.gatech.edu † School of Electrical and Computer Engineering, Information and Communications University 119, Munjiro, Daejeon, 305-732, Korea Email: jsha@icu.ac.kr ‡ Instituto de Telecomunicac ¸˜ oes, Departamento de Engenharia Electrot´ ecnica e de Computadores Faculdade de Engenharia da Universidade do Porto, Portugal Email: jbarros@fe.up.pt § Electronics and Telecommunications Research Institute 161 Gajeong-dong, Yuseong-gu Daejeon, 305-700, Korea Email: bjkwak@etri.re.kr Abstract—This paper 1 presents a coding scheme for the Gaus- sian wiretap channel based on low-density parity-check (LDPC) codes. The messages are transmitted over punctured bits to hide data from eavesdroppers. It is shown that this method is asymptotically effective in the sense that it yields a BER very close to 0.5 for an eavesdropper whose SNR is lower than the threshold SNR E, even if the eavesdropper has the ability to use a bitwise MAP decoder. Such codes also achieve high reliability for the friendly parties provided they have an SNR above a second threshold SNR B. It is shown how asymptotically optimized LDPC codes can be designed with differential evolution where the goal is to achieve high reliability between friendly parties and security against a passive eavesdropper while keeping the security gap SNR B/SNRE as small as possible. The proposed coding scheme is applicable at finite block lengths and can be combined with existing cryptographic schemes to deliver improved data security by taking advantage of the stochastic nature of many communication channels. I. I NTRODUCTION It was proved by Shannon in [1] that information- theoretically secure communication is possible only if the communicating parties, say Alice and Bob, share a secret key whose entropy is larger or equal to that of the message. In that case Alice and Bob can use the one-time pad scheme and any potential eavesdropper Eve who does not have access to the secret key is provably unable to extract any information about the message. Unfortunately, the one-time pad scheme only translates the problem of sharing a message to sharing a secret key. To circumvent this difficulty, a variety of cryptographic algorithms were invented that employ shorter secret keys, but rely on unproved mathematical assumptions and limited computational resources at Eve for secrecy. Shannon’s assumption, though, was that Bob’s and Eve’s observations of the transmitted ciphertexts are identical. Quite often that assumption is not realistic due to the stochastic nature of many communication channels. A few decades after Shannon’s work it was shown in [2]–[5] that information 1 This work was partly supported by the IT R&D program of MKE/IITA. [2008-F-002-01, Development of original technology for next-generation Tactical Defense Communication Network] theoretically secure communication is possible exclusively by means of coding at the physical layer if Eve has a worse channel then Bob. Equivocation at Eve, which is an established metric for in- formation theoretic security, is difficult to measure or analyze on noisy coded sequences, especially at finite block lengths. That may be one of the main reasons why no practical code constructions at finite block lengths for secure communication exist at this point. To get around his problem, the bit-error-rate (BER) over message bits, which is much easier to analyze and measure, is used as a measure for security in this paper. For ex- ample, if Eve observes data through a channel with BER close to 0.5 (the errors are IID), then she would be able to extract little information about the message. It should be noted at the outset that BER is a different metric than the equivocation, therefore this paper does not address information theoretic security, but rather physical layer security. Nevertheless, it is argued that a high BER at Eve is useful and can, possibly in conjunction with standard cryptographic techniques, deliver improved resilience against eavesdropping.                       Fig. 1. The Gaussian wiretap channel. Consider the Gaussian wiretap model depicted in Figure 1. Alice wants to transmit an s-bit message M s to Bob. She uses an error-correcting code to encode M s to an n-bit codeword X n and transmits it over an AWGN channel to Bob. Eve listens to the transmission over a noisier, independent AWGN channel and tries to reconstruct the message M s . She is This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2009 proceedings. 978-1-4244-4148-8/09/$25.00 ©2009