Chinese Remainder Theory Research Articles

CRT-Based Clock Synchronization for Millimeter-Wave Communication with Asymmetric Propagation Delays

The rapid advancement of millimeter-wave communication technology has presented new challenges for time synchronization, driven by the need for high-speed and low-latency data transmission. Ethernet synchronization technologies, such as Precise Time Protocol (PTP), have emerged to overcome the limitations of point-to-point architecture and enable precise synchronization across multiple devices. A key drawback of conventional PTP is its reliance on symmetric packet exchange delays, which may not hold in real-world scenarios where there is relative mobility between master and slave nodes, leading to asymmetric propagation delays and clock offset errors. To address this issue, a novel clock synchronization protocol that integrates Chinese Remainder Theory (CRT) has been proposed. This protocol enhances conventional PTP by incorporating distance estimation based on CRT using multi-carrier phase measurement. By combining a coarse estimation of one-way propagation delay from conventional PTP with a fine estimation of remainder distance from CRT, the protocol accurately determines the distance between master and slave nodes, reducing motion errors and enhancing clock synchronization accuracy. Simulation results indicate that the Root Mean Square Error (RMSE) of distance estimation remains below 10−5 m, with a corresponding motion time error of approximately 0.01 picosecond.

VREFL: Verifiable and Reconnection-Efficient Federated Learning in IoT scenarios

The privacy of social IoT data needs to be ensured while it is used by Federated Learning (FL). Secure aggregation is a cryptographic primitive that can ensure the privacy of social IoT data. However, in IoT scenarios, the secrecy of secure aggregation inputs makes the aggregated results less credible and the frequent disconnection and reconnection of IoT workers will cause prohibited communication overhead. In this work, we propose the Verifiable and Reconnection-Efficient Federated Learning (VREFL) framework, which can simultaneously support secure aggregation of local updates, verification of aggregated results, and rapid reconnection of dropped workers. Specifically, the novelty can be twofold: (1) we let each worker generate its homomorphic hash proof for the verification while updating locally. These hash proofs will be bound together through the Merkle Tree (MT) for further investigation by the central server; (2) we use the Chinese Remainder Theory (CRT) to help each worker efficiently update its “obsolete mask” after reconnection. We also theoretically prove that VREFL is secure. In addition, we implement a prototype of VREFL and conduct experiments on real-world datasets with different settings. Extensive experimental results prove that our protocol is feasible and efficient.

A lightweight and secure handover authentication scheme for 5G network using neighbour base stations

The emerge of fifth-generation (5G) wireless networks has started a new era of the development of wireless mobile networks. Security of the 5G wireless networks is the major concern when they are deployed for commercial applications. The third-generation partnership project (3GPP) has specified the security functionality of 5G wireless in its standard release 16. However, it is prone to different attacks such as Denial of Service (DoS) attacks and false base-station attacks. Particularly, secure handover becomes a critical issue in the operation of the 5G mobile networks. In the paper, we propose an efficient and secure handover authentication protocol using the Chinese remainder theory at neighbour base stations, gNodeBs (gNBs) for secure handovers. The security of the proposal is formally evaluated to demonstrate its ability against various malicious attacks. The performance of the proposed scheme in terms of the delay incurred and energy consumption is evaluated by using JAVA simulation. The results obtained show that our scheme is secure and efficient with relatively low energy consumption, which is suitable for devices in high-speed movements.

Symmetry Degree Measurement and its Applications to Anomaly Detection

Anomaly detection is an important technique used to identify patterns of unusual network behavior and keep the network under control. Today, network attacks are increasing in terms of both their number and sophistication. To avoid causing significant traffic patterns and being detected by existing techniques, many new attacks tend to involve gradual adjustment of behaviors, which always generate incomplete sessions due to their running mechanisms. Accordingly, in this work, we employ the behavior symmetry degree to profile the anomalies and further identify unusual behaviors. We first proposed a symmetry degree to identify the incomplete sessions generated by unusual behaviors; we then employ a sketch to calculate the symmetry degree of internal hosts to improve the identification efficiency for online applications. To reduce the memory cost and probability of collision, we divide the IP addresses into four segments that can be used as keys of the hash functions in the sketch. Moreover, to further improve detection accuracy, a threshold selection method is proposed for dynamic traffic pattern analysis. The hash functions in the sketch are then designed using Chinese remainder theory, which can analytically trace the IP addresses associated with the anomalies. We tested the proposed techniques based on traffic data collected from the northwest center of CERNET (China Education and Research Network); the results show that the proposed methods can effectively detect anomalies in large-scale networks.

BLE Neighbor Discovery Parameter Configuration for IoT Applications

Since the Internet of Things (IoT) applications today employ many different sensors to provide information, a large number of the Bluetooth low energy (BLE) devices will be developed as part of the IoT systems. The low-power and low-cost requirements of all BLE nodes are among the most challenging issues when supporting the neighbor discovery process (NDP) for such a large number of devices. Since the parameter settings are essential to achieve the required performance for the NDP, a parameter configuration method for neighbor discovery in BLE can be beneficial for determining some critical parameter metrics, such as the AdvInterval, ScanInterval, and ScanWindow. In this paper, we propose a parameter configuration scheme to balance the tradeoff between discovery latency and energy consumption. In the proposed scheme, the neighbor discovery latency and average energy consumption are expressed based on the Chinese Remainder Theory (CRT). With the expected primary performance, the parameters are configured accordingly using the parameter configuration algorithm. The experimental results show that the performance of the neighbor discovery varies with the parameter settings. Furthermore, two typical IoT applications are assessed in this paper. Compared with the simulation results, the proposed parameter configuration scheme can achieve high accuracy.

A novel construction method of QC-LDPC codes based on CRT for optical communications

A novel construction method of quasi-cyclic low-density parity-check (QC-LDPC) codes is proposed based on Chinese remainder theory (CRT). The method can not only increase the code length without reducing the girth, but also greatly enhance the code rate, so it is easy to construct a high-rate code. The simulation results show that at the bit error rate (BER) of 10−7, the net coding gain (NCG) of the regular QC-LDPC(4 851, 4 546) code is respectively 2.06 dB, 1.36 dB, 0.53 dB and 0.31 dB more than those of the classic RS(255, 239) code in ITU-T G.975, the LDPC(32 640, 30 592) code in ITU-T G.975.1, the QC-LDPC(3 664, 3 436) code constructed by the improved combining construction method based on CRT and the irregular QC-LDPC(3 843, 3 603) code constructed by the construction method based on the Galois field (GF(q)) multiplicative group. Furthermore, all these five codes have the same code rate of 0.937. Therefore, the regular QC-LDPC(4 851, 4 546) code constructed by the proposed construction method has excellent error-correction performance, and can be more suitable for optical transmission systems.

High-efficient quantum secret sharing based on the Chinese remainder theorem via the orbital angular momentum entanglement analysis

We investigate a novel quantum secret sharing (QSS) based on the Chinese remainder theory (CRT) in multi-dimensional Hilbert space with the orbital angular momentum (OAM) entanglement analysis. The secret is divided and then allotted to two or more participants who prepare pairs of photons in the OAM-entanglement states. The initial secret can be restored jointly by legal participants via the OAM-entanglement analysis on the corresponding photons. Its security is guaranteed from the OAM entanglement of photons that are established through the spin angular momentum (SAM) entanglement analysis performed on the generated SAM-based OAM hybrid entanglement photons. It provides an alternative technique for the QSS while producing the OAM entanglement photons in the combined multi-dimensional OAM Hilbert space, where the CRT is conducted properly for sharing the conventional secret among legal participants.

An efficient RNS parity checker for moduli set {2 n − 1, 2 n + 1, 22n + 1} and its applications

Residue number system (RNS) has received considerable attention since decades before, because it has inherent carry-free and parallel properties in addition, subtraction, and multiplication operations. For an odd moduli set, the fundamental problems in RNS, such as number comparison, sign determination, and overflow detection, can be solved based on parity checking. The paper proposes a parity checking algorithm along with related propositions and the certification based on the celebrated Chinese remainder theory (CRT) and mixed radix conversion (MRC) for the moduli set {2 n − 1, 2 n + 1, 22n + 1}. The parity checker consists of two modular adders and a carry-look-ahead chain. The hardware implementation requires less area and path delay. Besides, the implementations of number comparison, sign determination, and overflow detection, which are based on this parity checker, are also performed in this paper. And this kind of parity checker can be used as a basic element to design ALUs and DSP module in RNS.

Fast evaluation of iterated multiplication of very large polynomials: An application to chinese remainder theory

We consider the problem of exactly computing the number of integers in a Chinese Remainder Representation (CRR) whose pseudorank does not equal the rank. We call this number the census. The rank is key in developing CRR-intrinsic methods for comparing integers in CRR, a problem known to be notoriously difficult. Pseudorank can be computed in highly restrictive computation models. We have developed and implemented a fast, efficient algorithm for computing the census based on using a variant of the FFT to compute iterated products of polynomials of very large degree, and with arbitrary size integer coefficients. Experimental census results are tabulated. This census information makes possible a new approach to exploring the fine structure of CRR. References J. Hee. Fast convolution using polynomial transforms. http://jenshee.dk/signalprocessing/polytrans.pdf , 2004. W. Hesse. Division is in uniform tc0. In ICALP '01: Proceedings of the 28th International Colloquium on Automata, Languages and Programming , pages 104--114, London, UK, 2001. Springer--Verlag. Also available as http://people.clarkson.edu/ whesse/div.ps . D. Knuth. Seminumerical Algorithms , volume 1 of The Art of Computer Programming , section 4.3.2. Addison--Wesley, third edition, 1997. W. Kuich and A. Salomaa. Semirings,Automata,Languages . Springer-Verlag, 1986. B. Litow and D. Laing. A census algorithm for chinese remainder pseudorank with experimental results. James Cook University, School of IT Tech Report http://www.cs.jcu.edu.au/ftp/pub/techreports/2005-3.pdf , 2005. H. J. Nussbaumer. Fast Fourier Transform and Convolution Algorithms . Springer, 1982. 2nd ed. A. Salomaa and S. Soittola. Automata Theoretic Aspects of Formal Power Series . Springer--Verlag, 1978. M. P. Schutzenberger. On a theorem of {Jungen}. Proc. Am. Math. Soc. , 13:885--890, 1962. R. Tanaka and N. Szabo. Residue Arithmetic and its Application to Computer Technology . McGraw--Hill, 1968. S. P. Tarasov and M. N. Vyalyi. Semidefinite programming and arithmetic circuit evaluation. Technical report, 2005. Available as http://arxiv.org/abs/cs/0512035v1 . G. Davida A. Chiu and B. Litow. Division in logspace-uniform NC$^1$. Theoretical Informatics and Applications , 35:259--275, 2001. doi:10.1051/ita:2001119 I. M. Vinagradov. Elements of Number Theory . Dover, 1954. S. A. Cook and S. O. Aanderaa. On the minimum computation time of functions. Transactions of the American Mathematical Society , 142:291--314, Aug 1969. K. Culik and J. Kari. Handbook of Formal Languages , chapter 10, pages 599--616. Springer, 1997. G. Davida and B. Litow. Fast parallel arithmetic via modular representation. SIAM J. Comp. , 20,4:756--765, 1991. doi:10.1137/0220048