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IET Communications

Physical layer encryption scheme using finite‐length polar codes

Reza Hooshmand, Mohammad Reza Aref, Taraneh Eghlidos

Published Sep 10, 2015• 17 citations
Publisher

Abstract

In this study, by exploiting the properties of finite‐length polar codes, the authors introduce a physical layer encryption scheme to make secure (from a computational security perspective) and efficient communication between a sender (Alice) and a legitimate receiver (Bob) against both active and passive attacks, simultaneously. To prevent active attacks, two techniques are considered: (i) a novel method is introduced to keep the generator matrix of polar code secret from an active attacker (Oscar); (ii) a proper joint polar encoding/encryption algorithm based on the hidden generator matrix is introduced. Two additional strategies are considered against passive attacks: (i) a new method is introduced to partition the bit‐channels into good and bad bit‐channels and then the scrambled information bits are transmitted over those bit‐channels that are good for Bob but bad for a passive attacker (Eve); (ii) the secret key cryptography is implemented at the physical layer, such that Eve cannot decode the eavesdropped data without the knowledge of the secret key shared between the authorised parties. Besides, this study discusses efficiency analysis results consisting key size, error performance and computational complexity of the proposed scheme.

DOI
10.1049/iet-com.2014.0933

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In this study, by exploiting the properties of finite‐length polar codes, the authors introduce a physical layer encryption scheme to make secure (from a computational security perspective) and efficient communication between a sender (Alice) and a legitimate receiver (Bob) against both active and passive attacks, simultaneously. To prevent active attacks, two techniques are considered: (i) a novel method is introduced to keep the generator matrix of polar code secret from an active attacker (Oscar); (ii) a proper joint polar encoding/encryption algorithm based on the hidden generator matrix is introduced. Two additional strategies are considered against passive attacks: (i) a new method is introduced to partition the bit‐channels into good and bad bit‐channels and then the scrambled information bits are transmitted over those bit‐channels that are good for Bob but bad for a passive attacker (Eve); (ii) the secret key cryptography is implemented at the physical layer, such that Eve cannot decode the eavesdropped data without the knowledge of the secret key shared between the authorised parties. Besides, this study discusses efficiency analysis results consisting key size, error performance and computational complexity of the proposed scheme.
In contrast to the network security that relies on upper-layer encryption for the confidentiality and authenticity of communications, physical layer security (PLS) exploits the uniqueness and randomness of the physical channel to encrypt information and enhance the security of the system. In this paper, we study the PLS of a polar-coded wireless communication system. To be more specific, we leverage the unique properties in polar code construction and propose a channel quality indicator (CQI)-based frozen-bit pattern generation scheme. The transmitter employs the Gaussian approximation algorithm to generate the corresponding frozen bit pattern according to the instantaneous CQI of the legitimate link. At the receiver, by leveraging the full channel reciprocity in the time-division duplex (TDD) mode, we can map the CQI to the corresponding frozen bit pattern and correctly decode the received bits. By contrast, the eavesdropper was unable to have the knowledge of the legal channel, and hence cannot determine the frozen bit pattern of the polar-coded bit sequence. Our simulation results demonstrate that by adopting the proposed PLS key generation scheme, Eve was hardly able to correctly decode a complete frame, leading to a high block error rate (BLER), while Bob was able to attain a 10−5 BLER.
Due to the broadcast and time‐varying natures of wireless channels, traditional communication systems that provide data encryption at the application layer suffer many challenges such as error diffusion. In this paper, we propose a code‐hopping based secrecy transmission scheme that uses dynamic nonsystematic low‐density parity‐check (LDPC) codes and automatic repeat‐request (ARQ) mechanism to jointly encode and encrypt source messages at the physical layer. In this scheme, secret keys at the transmitter and the legitimate receiver are generated dynamically upon the source messages that have been transmitted successfully. During the transmission, each source message is jointly encoded and encrypted by a parity‐check matrix, which is dynamically selected from a set of LDPC matrices based on the shared dynamic secret key. As for the eavesdropper (Eve), the uncorrectable decoding errors prevent her from generating the same secret key as the legitimate parties. Thus she cannot select the correct LDPC matrix to recover the source message. We demonstrate that our scheme can be compatible with traditional cryptosystems and enhance the security without sacrificing the error‐correction performance. Numerical results show that the bit error rate (BER) of Eve approaches 0.5 as the number of transmitted source messages increases and the security gap of the system is small.
This paper considers the use of polar codes to enable secure transmission over parallel relay channels. By exploiting the properties of polar codes over parallel channels, a polar encoding algorithm is designed based on Channel State Information (CSI) between the legitimate transmitter (Alice) and the legitimate receiver (Bob). Different from existing secure transmission schemes, the proposed scheme does not require CSI between Alice and the eavesdropper (Eve). The proposed scheme is proven to be reliable and shown to be capable of transmitting information securely under Amplify-and-Forward (AF) relay protocol, thereby providing security against passive and active attackers.
In this paper, we consider a secure communication over the physical layer. The objective of the system is, at the physical layer security, the randomness of the channel and the polar coded aided artificial noise provide the security to the system without any secret key generation in higher layer encryption. Artificial noise will be injected at the last codeword of the confidential bits of polar codes in transmission block. Jamming position algorithm is used to initialize the position of artificial noise. The Bhattacharya parameter is used to select the position of jamming with regard to the reliability of the channel. The legitimate receiver has the knowledge of artificial noise and the confidential bit position, so it will eliminate the AN but Eve does not have the knowledge of jamming position so it cannot eliminate the AN. Simulation results show the performance of secrecy rate and the security gap of the system with the help of adding artificial noise at the last transmission block.
Scrambling is a way of enhancing physical layer security presented in many papers. However, few of these papers have mentioned the scrambling effect on the polar coding secrecy. In this letter, we introduce a new scrambling module combined with a polar coding system, in which pre-assigned key is unnecessary. The presented scrambling module combines linear and nonlinear structure. The presented linear structure increases the branch number in a low-complexity way to enhance algorithm diffusion power, and the nonlinear part can resist the differential attack and reduces the mutual information between its input and output. With the proposed module, the bit channels, which are good for Bob and Eve, can also be applied to transmit secret message, making transmission rate of the secret massage configurable. Simulation results show that our method can guarantee the secrecy transmission between Alice and Bob.
We propose the new technique of physical-layer cryptography based on using a massive MIMO channel as a key between the sender and desired receiver, which need not be secret. The goal is for low-complexity encoding and decoding by the desired transmitter-receiver pair, whereas decoding by an eavesdropper is hard in terms of prohibitive complexity. The massive MIMO system has a channel gain matrix that is drawn i.i.d. according to a Gaussian distribution, subject to additive white Gaussian noise. The decoding complexity is analyzed by mapping the massive MIMO system to a lattice. We show that the eavesdropper's decoder for the MIMO system with M-PAM modulation is equivalent to solving standard lattice problems that are conjectured to be of exponential complexity for both classical and quantum computers. Hence, under the widely-held conjecture that standard lattice problems are of worst-case complexity, the proposed encryption scheme has security that exceeds that of the most common encryption methods used today such as RSA and Diffie-Hellman. Additionally, we show that this scheme could be used to securely communicate without a pre-shared secret key and little computational overhead. In particular, a standard parallel channel decomposition allows the desired transmitter-receiver pair to encode and decode transmissions over the MIMO channel based on the singular value decomposition of the channel, while decoding remains computationally hard for an eavesdropper with an independent channel gain matrix, even if it knows the channel gain matrix between the desired transmitter and receiver. Thus, the massive MIMO system provides for low-complexity encryption commensurate with the most sophisticated forms of application-layer encryption by exploiting the physical layer properties of the radio channel.