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ACM Asia Conference on Computer and Communications Security (ASIA CCS)

Physical-Layer Public Key Encryption Through Massive MIMO

Senlin Liu, Tianshun Gao, Yijian Liu, Xianhui Lu

Published Jun 28, 2024• 3 citations
Publisher

Abstract

We propose a new physical-layer public key encryption scheme and establish a trapdoor one-way function through Massive MIMO techniques and precoding designs. Under standard arguments, we show that the eavesdropper's decoding complexity grows exponentially with the number of antennas, while the legitimate receiver's decoding complexity grows only quadratically. The proposed scheme builds a bridge between information-theoretic security and cryptographic security. Compared to the traditional physical-layer security, the proposed scheme is secure when the number of the eavesdropper's antennas is infinite or much larger than the number of transmitter/receiver antennas, provided that the eavesdropper's distance from the legitimate receiver is less than one-half of the wavelength, or that the channel estimation process between the sender-receiver pair is broken by the eavesdropper. Because the scheme is based on lattice, not on channel reciprocity, it can be applied to both time-division duplex and frequency-division duplex channels, and utilizes the simple physical layer characteristics of Massive MIMO to resist the currently known quantum attacks. The proposed scheme is adapted to the future requirements of 6G for the security of communication, and provides a new idea for the post-quantum cryptosystem. The simulation results show that the proposed scheme has a decoding bit error rate (BER) close to 0.5 at the eavesdropper and almost 0 at the legitimate receiver.

DOI
10.1145/3634737.3656284

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We propose a new physical-layer public key encryption scheme and establish a trapdoor one-way function through Massive MIMO techniques and precoding designs. Under standard arguments, we show that the eavesdropper's decoding complexity grows exponentially with the number of antennas, while the legitimate receiver's decoding complexity grows only quadratically. The proposed scheme builds a bridge between information-theoretic security and cryptographic security. Compared to the traditional physical-layer security, the proposed scheme is secure when the number of the eavesdropper's antennas is infinite or much larger than the number of transmitter/receiver antennas, provided that the eavesdropper's distance from the legitimate receiver is less than one-half of the wavelength, or that the channel estimation process between the sender-receiver pair is broken by the eavesdropper. Because the scheme is based on lattice, not on channel reciprocity, it can be applied to both time-division duplex and frequency-division duplex channels, and utilizes the simple physical layer characteristics of Massive MIMO to resist the currently known quantum attacks. The proposed scheme is adapted to the future requirements of 6G for the security of communication, and provides a new idea for the post-quantum cryptosystem. The simulation results show that the proposed scheme has a decoding bit error rate (BER) close to 0.5 at the eavesdropper and almost 0 at the legitimate receiver.
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 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 hard to solve, the proposed encryption scheme has a more robust notion of security than that of the most common encryption methods used today such as RSA and Diffie-Hellman. In addition, we show that this scheme could be used to securely communicate without a pre-shared secret and little computational overhead. Thus, by exploiting the physical layer properties of the radio channel, the massive MIMO system provides for low-complexity encryption commensurate with the most sophisticated forms of application-layer encryption that are currently known.
We present two attacks on two different versions of physical layer cryptography schemes based on massive multiple-input multiple-output (MIMO). Both cryptosystems employ a singular value decomposition (SVD) precoding technique. For the first one, we show that the eavesdropper (who knows its own channel and the channel between legitimate users) can decrypt the information data under the same condition as the legitimate receiver. We study the signal-to-noise advantage ratio for decoding by the legitimate user over the eavesdropper in a more generalized scheme when an arbitrary precoder at the transmitter is employed. On the negative side, we show that if the eavesdropper uses a number of receive antennas much larger than the number of legitimate user antennas, then there is no advantage, independent of the precoding scheme employed at the transmitter. On the positive side, for the case where the adversary is limited to have the same number of antennas as legitimate users, we give an O(n2)O\left(n^2\right)O(n2) upper bound on the advantage and show that this bound can be approached using an inverse precoder. For the second cryptosystem, we show that the required security conditions prevent the legitimate user from decoding the plaintext uniquely.
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.
Recently, MIMO (multiple-input-multiple-output) physical layer secure transmission has attracted great attentions. However, current schemes cannot defend against the passive eavesdroppers with arbitrary number of antennas. To address this problem, in this work, we propose a practical physical layer MIMO secure communication scheme (PLSC) to defend against such an eavesdropper with arbitrary number of antennas. In the proposed scheme, the transmitter first independently generates a random binary sequence as the “key bits (KB)” to “encrypt” (XOR) the confidential information. After that, the transmitter sends the “encrypted information” over the wireless channel, along with mapping key bits to the legitimate receiver simultaneously. The key principle lies in that the KB information is coded in the indexes of the activated/non-activated antennas combination of the legitimate user. Then, the legitimate receiver first observes his/her activated antenna indexes to obtain the corresponding key bits. After that, he/she demodulates the “encrypted information” at the activated antennas, and finally “decrypts” (XOR) the confidential information by using the observed key bits. However, due to the uniqueness and independence of MIMO wireless channel, for any other eavesdroppers who suffer an independent channel from legitimate users, we prove that it cannot observe any information about KB from the received signals, regardless of how many antennas it has used. Consequently, without knowledge of KB, it cannot decrypt any information about the confidential information, too. The reliability and security of PLSC are theoretically demonstrated. The simulation and numerical results fully verified the validity and effectiveness of the proposed scheme.
The exploration of the physical layer characteristics of the wireless channel is currently the object of intensive research in order to develop advanced secrecy schemes that can protect information against eavesdropping attacks. Following this line of work, in this manuscript we consider a massive MIMO system and jointly design the channel precoder and security scheme. By doing that we ensure that the precoding operation does not reduce the degree of secrecy provided by the security scheme. The fundamental working principle of the proposed technique is to apply selective random rotations in the transmitted signal at the antenna level in order to achieve a compromise between legitimate and eavesdropper channel capacities. These rotations use the phase of the reciprocal wireless channel as a common random source between the transmitter and the intended receiver. To assess the security performance, the proposed joint scheme is compared with a recently proposed approach for massive MIMO systems. The results show that, with the proposed joint design, the number of antenna elements does not influence the eavesdropper channel capacity, which is proved to be equal to zero, in contrast to previous approaches.
We present an attack on correctness of the latest version of the physical layer cryptography scheme based on massive multiple-input multiple-output (MIMO). This cryptosystem employs a singular value decomposition (SVD) precoding technique. We show that the required security conditions prevent the legitimate user from decoding the plaintext uniquely. On the positive side, for the case where the eavesdropper is limited to have the same number of antennas as legitimate users, we give an O(n2)\mathcal{O}\left( {{n^2}} \right)O(n2) upper bound on the signal-to-noise advantage ratio for decoding by the legitimate user over the eavesdropper and show that this bound can be approached using an inverse precoder.