We consider keyless cryptosystem proposed recently by Dean and Goldsmith. We show by simulation that this scheme is secure even so the eavesdropper uses suboptimal decoding (zero-forcing attack) with linear complexity but if the number of legitimate and eavesdropper antennas are equal to one another. But if eavesdropper has even small advantage in number of antennas, the proposed cryptosystem occurs insecure that we prove both theoretically and experimentally. We investigate a modified scheme with inverse precoder and show that it requires untractable values of the legitimate user transmitter power. Thus Dean-Goldsmith cryptosystem seems to be insecure with practical point of view.
We consider keyless cryptosystem proposed recently by Dean and Goldsmith. We show by simulation that this scheme is secure even so the eavesdropper uses suboptimal decoding (zero-forcing attack) with linear complexity but if the number of legitimate and eavesdropper antennas are equal to one another. But if eavesdropper has even small advantage in number of antennas, the proposed cryptosystem occurs insecure that we prove both theoretically and experimentally. We investigate a modified scheme with inverse precoder and show that it requires untractable values of the legitimate user transmitter power. Thus Dean-Goldsmith cryptosystem seems to be insecure with practical point of view.
The term “keyless cryptography” as it is commonly adopted, applies to secure message transmission either directly without any key distribution in advance or as key sharing protocol between communicating users, based on physical layer security, before ordinary encryption/decryption procedures. In the current chapter the results are presented concerning to keyless cryptography that have been obtained by authors recently. Firstly Shamir’s protocol of secure communication is considered where commutative encryption procedure is executed. It has been found out which of the public key algorithms can be used with such protocol. Next item of consideration concerns Dean’s and Goldsmith’s cryptosystem based on multiple-input, multiple-output (MIMO) technology. It has been established under which conditions this cryptosystem is in fact secure. The third example under consideration is EVSkey scheme proposed recently by D. Qin and Z. Ding. It has been proven that such key distribution method is in fact insecure, in spite of the authors’ claims. Our main result is a description of a key sharing protocol executing over public noiseless channels (like internet) that provides a key sharing reliability and security without any cryptographic assumptions.
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) 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.
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 investigate signaling and linear precoding designs for secure downlink communications in a multiuser MIMO (MU-MIMO) network. The network is tapped by an external eavesdropper (Eve) who is equipped with a large number of antennas. In addition to the transmission of several (unicast) information signals to downlink users (Bobs), the transmitter (Alice) generates friendly jamming (FJ), aiming to prevent Eve from decoding Alice’s signals. To mitigate both multiuser interference (MUI) and FJ on Bobs, MU-MIMO systems often rely on zero-forcing (ZF) precoders. A condition for the application of such precoders is that the network must beunderloaded, i.e., Alice has more antennas than all Bobs combined. Foroverloadedscenarios, ZF-based precoding cannot guarantee nullification of both MUI and FJ at legitimate receivers. Accordingly, we propose a combined signaling-and-precoding scheme that can also be applied to an overloaded MU-MIMO network. In an underloaded scenario, our technique is shown to impose a more stringent antenna requirement on Eve than a classical ZF-based precoding, i.e., Eve must utilize more antennas if she is to successfully eavesdrop on Alice’s transmissions. Although our scheme is comparable to antenna selection (AS) approaches in terms of Eve’s antenna requirement, it incurs much less delay and complexity by avoiding frequent on/off switching of the RF chains at Bobs. For underloaded scenarios, we provide security analysis that establishes the conditions under which our scheme is superior to the ZF scheme. Using computer simulations, we validate the advantages of our design and contrast it with ZF and AS schemes in terms of the symbol error rate, the EVM, and the achievable rate in both underloaded and overloaded scenarios.
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.