# Underlying Security Transmission Design for Orthogonal Time Frequency Space (OTFS) Modulation
###### Abstract
Compared with traditional encryption methods, without considering the computational power of attackers, the physical layer security technology can make full use of the instantaneity and randomness of wireless channels to achieve secure transmission without sharing the key between the legitimate transmitter and receiver. The principle of physical layer key generation technology is to use the reciprocity, time variability, and spatial uniqueness of wireless channels to generate the key. Depending on the randomness of a wireless channel, the key generation schemes are mainly divided into the following four types: Channel State Information (CSI)-based key generation technology [18], signal strength-based key generation technology [19], phase-based key generation technology [20], and eavesdropping encoding key generation technology [21]. Further, ref. [22] proposed the key generation scheme under active attack, which used random detection signals to combine the user-generated randomness and channel randomness. Ref. [23] proposed an adaptive channel detection scheme based on a proportional-integral-derivative controller, which can achieve the desired Key Generation Rate (KGR) by adjusting the detection rate. As far as we know, the current research on OTFS secure transmission is still in its infancy. In particular, ref. [13] studied the secrecy performance of an OTFS-based uplink LEO Sat-Com system, where a cooperative UAV was employed to send jamming signals against the reconnaissance satellite. However, the study only targeted the uplink LEOSat-Com scenario and is not universal. Ref. [14] studied the security performance of the unicast-multicast streaming system by deriving and analyzing the maximum secrecy rate and positive secure capacity probability (PSCP) of unicast transmission. Ref. [24] proposed a novel physical layer security transmission scheme by encrypting the Discrete Fourier Transform (DFT) matrix to guarantee the underlying security property of the OFDM. It is very unfortunate that there is currently no research on physical layer security via control of the modulation matrix in the OTFS. Against the background above, we are motivated to study secure transmission by controlling the modulation matrix for the OTFS transmission in high-mobility communication scenarios. Our key contributions are summarized as follows:  
* We propose a 2D permutation OTFS secure transmission scheme that uses the Go-sudarstvennyi Standard (GOST) algorithm to perform disturbance control on the OTFS modulation domain so as to realize the underlying security of the OTFS transmission. By utilizing the instantaneities and uniquenesses of wireless channels, the GOST algorithm can generate a control sequence to perturb the ISFFT matrix under OTFS modulation. * We propose a so-called Selective Mapping (SLM) algorithm, which can significantly improve the PAPR problem of our secure OTFS transmission. With very low complexity, the SLM algorithm aims to select the best transition matrix to multiply with the TF domain signal for the sake of ensuring the low PAPR characteristic. * We conduct a security analysis for our OTFS secure transmission. We prove our scheme has a promising resistance performance to a range of effective attacks, including brutal force, chosen-plaintext, statistical attacks, etc. * We carry out a comprehensive simulation evaluation. Our experimental results show that our proposed transmission scheme can guarantee the underlying security property of the OTFS. Furthermore, compared to the OFDM scheme, our proposed scheme can reduce the PAPR by 20% and improve the BER by at least 4 dB under the same security requirements. The rest of this paper will be organized as follows: In Section 2, we briefly introduce the OTFS system model. In Section 3, we propose the design for a 2D permutation-aided OTFS secure transmission scheme. In Section 4, we introduce the principle of the key generation algorithm and analyze its performance. In Section 5, we conduct a security performance analysis of the proposed transport mechanism.