Developing “friend or foe” protocol in residue number system code for satellite authentication

Low-earth orbit (LEO) satellite communication systems are successfully used in control and monitoring systems for the production and transportation of hydrocarbons from fields located beyond the Arctic Circle. As the number of countries engaged in the development of such fields expands, the number of groupings of LEO satellite communication systems grows as well. To prevent the possibility of intercepting and imposing a delayed command to control the intruder satellite, it is necessary to use the “friend or foe” identification system for the LEO satellite communication systems. At the same time, it is proposed to use authentication protocols with zero knowledge to ensure high imitation resistance in such systems. To increase their efficiency, the article proposes to use the codes of the residual number system (RNS). The novelty of this idea lies in the fact that the use of parallel RNS codes will reduce the time spent on performing arithmetic operations implemented in authentication protocols. This will reduce the likelihood of an intruder satellite picking up the correct response signal. Therefore, the development of an authentication protocol for LEO satellite communication systems based on RNS codes, the use of which will reduce the time for satellite identification, is an urgent task.

Since the RNS codes are implemented in a ring of integers, the following equality holds true: where * denotes addition, subtraction and multiplication operations; The analysis of equality (3) showed that the use of RNS codes enables to reduce the time spent on performing modular operations. This is determined by the low bit depth of the RNS code remainders, as well as the parallel execution of these operations on the basis of the code. Therefore, RNS codes are widely used in real-time systems. Thus, the work [7] shows the implementation of a digital filter in the RNS. The work [8] presents a method of increasing the reliability of telemetric well information transmitted by the wireless communication channel. The work [9] shows the use of RNS codes when performing Fourier-like orthogonal transformations of signals.
However, RNS codes can be used in authentication protocols based on zero knowledge proofs. These protocols provide high imitation strength of authentication without the use of encryption systems. In [10], a new authentication scheme based on the Fiat-Shamir protocol was developed for the exchange of confidential information in the Internet of Things technology. The works [11,12] show the application of the Feige-Fiat-Shamir authentication protocol for machine authentication in the integration of external networks and the Internet of vehicles (IoV). However, these protocols cannot be used in a friend or foe system for satellites since the identification process requires 20 to 40 times of authentication. Therefore, an analysis enabling to identify authentication protocols that have one stage of recognition was carried out. These include the Guillou-Quisquater and Shnor protocols [13,14]. However, analysis of these protocols has showed that the authentication stage includes four steps required to determine the status of the applicant. The authentication protocol described in [15] enables to reduce the number of such steps. In this protocol, the identification procedure is reduced to three steps being as follows: the question of the examiner, the calculation of the answer by the applicant and the verification of the correctness of the answer. However, this protocol uses a large prime number to perform authentication. And all the calculations are performed with regards to its modulus. Let us develop this protocol in the RNS code.
3. The applicant chooses the following numbers 4. The applicant calculates the modified status of the spacecraft . This "question" is passed on to the applicant.
2. Having received the question, the applicant, calculates the answers The applicant sends the following signal ) to the relying party.
3. The relying party checks the correctness of the answers to the question is obtained after checking, then the relying party assigns the applicant the "friend" status. Let us carry out a comparative analysis of the considered authentication protocols implemented in the RNS code.
to the relying party.
3. The relying party checks the answers in accordance with (10) .
In this case, the relying party assigns the applicant the "friend" status.
In order to conduct a comparative analysis of the developed authentication protocols implemented in RNS codes, a hardware design of the structural model of the authentication system has been created using the FPGA FPLD Xilinx Virtex-7. The bit depth of the RNS code base has been chosen to be 32. When implementing the hardware design of the system, the environment Vivado HLS 2019.2 has been used. The clock frequency of the FPLD was 250 MHz. Comparative analysis has showed that 3.7 ms was required for one round of the authentication stage using the Guillou-Quisquater protocol, 3.1 ms for the Shnor protocol, and 1.2 ms for the developed protocol. The greatest time expenditure for the Guillou-Quisquater protocol has been associated with the fact that at the authentication stage it is necessary to perform two exponentiation operations in it. In the authentication protocol Shnor, at this stage, one exponentiation operation is performed to modulo. However, in the developed protocol, there is no such operation. Based on the data obtained, it can be concluded that the use of the developed authentication protocol implemented in the RNS codes enables to increase the information secrecy of the LEO satellite communication systems by 2.58 times compared to the Shnor protocol and 3.08 times compared to the Guillou-Quisquater protocol.

Conclusion
To ensure the information secrecy of the LEO satellite communication systems and to prevent the possibility of imposing an intercepted and delayed control command, it is proposed to use the "friend or foe" identification system for satellites. To reduce the likelihood of selecting the correct response signal by the intruder satellite, that is, to further increase information secrecy, it is proposed to implement authentication protocols in RNS codes. The novelty of this idea lies in the fact that the use of parallel RNS codes will reduce the time spent on performing arithmetic operations implemented in authentication protocols. In order to carry out a comparative analysis of the developed authentication protocols implemented in RNS codes, a hardware design of the structural model of the authentication system with a base width of 32 bits was developed. The results obtained showed that the use of the developed authentication protocol implemented in RNS codes enables to increase the information secrecy of the LEO satellite communication systems by 2.58 times compared to the Shnor protocol and 3.08 times compared to the Guillou-Quisquater protocol.