Improved Modular Division Implementation with the Akushsky Core Function

The residue number system (RNS) is widely used in different areas due to the efficiency of modular addition and multiplication operations. However, non-modular operations, such as sign and division operations, are computationally complex. A fractional representation based on the Chinese remainder theorem is widely used. In some cases, this method gives an incorrect result associated with round-off calculation errors. In this paper, we optimize the division operation in RNS using the Akushsky core function without critical cores. We show that the proposed method reduces the size of the operands by half and does not require additional restrictions on the divisor as in the division algorithm in RNS based on the approximate method.

Multiple Error Correction in Redundant Residue Number Systems: A Modified Modular Projection Method with Maximum Likelihood Decoding

Error detection and correction codes based on redundant residue number systems are powerful tools to control and correct arithmetic processing and data transmission errors. Decoding the magnitude and location of a multiple error is a complex computational problem: it requires verifying a huge number of different possible combinations of erroneous residual digit positions in the error localization stage. This paper proposes a modified correcting method based on calculating the approximate weighted characteristics of modular projections. The new procedure for correcting errors and restoring numbers in a weighted number system involves the Chinese Remainder Theorem with fractions. This approach calculates the rank of each modular projection efficiently. The ranks are used to calculate the Hamming distances. The new method speeds up the procedure for correcting multiple errors and restoring numbers in weighted form by an average of 18% compared to state-of-the-art analogs.

Zero-Aware Low-Precision RNS Scaling Scheme

Scaling is one of the complex operations in the Residue Number System (RNS). This operation is necessary for RNS-based implementations of deep neural networks (DNNs) to prevent overflow. However, the state-of-the-art RNS scalers for special moduli sets consider the 2k modulo as the scaling factor, which results in a high-precision output with a high area and delay. Therefore, low-precision scaling based on multi-moduli scaling factors should be used to improve performance. However, low-precision scaling for numbers less than the scale factor results in zero output, which makes the subsequent operation result faulty. This paper first presents the formulation and hardware architecture of low-precision RNS scaling for four-moduli sets using new Chinese remainder theorem 2 (New CRT-II) based on a two-moduli scaling factor. Next, the low-precision scaler circuits are reused to achieve a high-precision scaler with the minimum overhead. Therefore, the proposed scaler can detect the zero output after low-precision scaling and then transform low-precision scaled residues to high precision to prevent zero output when the input number is not zero.

Efficient Identity-Based Broadcast Encryption Scheme on Lattices for the Internet of Things

In an identity-based broadcast encryption (IBBE) scheme, the ciphertext is usually appended with a set of user identities to specify intended recipients. However, as IBBE is adopted in extensive industries, the demand of anonymity for specific scenarios such as military applications is urgent and ought no more to be ignored. On the contrary, how to optimize computation and communication is an unavoidable challenge in the IBBE scheme construction, especially in the large-scaled resource-limited wireless networks such as the Internet of Things (IoT), where the cost of computation and communication should be mitigated as much as possible since other functions including connectivity and privacy should be given the top priority. Thus, we present an IBBE scheme from the lattice, in which we employ the Chinese remainder theorem and lattice basis delegation in fixed dimensions to obtain several desirable characteristics, such as constant-size public parameter, private key, and ciphertext. In addition, our encryption and decryption algorithms are more efficient than broadcast encryption (BE) schemes based on number-theoretic problems. To be noticed, our scheme can simultaneously achieve confidentiality and outsider anonymity against the chosen-plaintext attack under the hardness of the learning with error (LWE) problem.

The Opinions of Mathematics Teachers about Using Mathematical Modeling in the Solution of Daily Life Problems and an Application of the Chinese Remainder Theorem

The opinions of mathematics teachers about using mathematical modeling (MM) in daily life problems and their use of MM in solving a daily life problem were examined within the scope of the graduate-level MM course in this study. The research was designed as a case study. Participants are five mathematics teachers selected by the purposive sampling method. The data were obtained through a structured form containing questions about a daily life problem and using MM in a daily life problem. Teachers were given one week to answer the questions on this form. Descriptive analysis was performed on the data obtained from the teachers’ problem solving, and content analysis was carried out on the data containing the teachers’ opinions. The findings determined that although the modeling processes were generally used appropriately by the teachers in solving a daily life problem, the process of understanding the problem was quickly mentioned, the teachers had difficulties in giving the most effective solution during the evaluation stage, and the communication stage was mostly ignored. It was also found out that MM could be beneficial in many ways in solving daily life problems. On the other hand, it was indicated that there may be difficulties in terms of student-teacher-environment and that teachers give very limited space to MM in classroom practices. It can be stated that the tendency of teachers to use the approaches they are accustomed to instead of MM in the solution of daily life problems is effective in the emergence of this situation.

Edge Computing Assisted an Efficient Privacy Protection Layered Data Aggregation Scheme for IIoT

The emergence of edge computing has improved the real time and efficiency of the Industrial Internet of Things. In order to achieve safe and efficient data collection and application in the Industrial Internet of Things, a lot of computing and bandwidth resources are usually sacrificed. From the perspective of low computing and communication overhead, this paper proposes an efficient privacy protection layered data aggregation scheme for edge computing assisted IIoT by combining the Chinese Remainder Theorem (CRT), improved Paillier homomorphic algorithm, and hash chain technology (edge computing assisted an efficient privacy protection layered data aggregation scheme for IIoT, EE-PPDA). In EE-PPDA, first, a layered aggregation architecture based on edge computing is designed. Edge nodes and cloud are responsible for local aggregation and global aggregation, respectively, which effectively reduces the amount of data transmission. At the same time, EE-PPDA achieves data confidentiality through improved Paillier encryption, ensuring that neither attackers nor semitrusted nodes (e.g., edge nodes and clouds) can know the private data of a single device, and it can resist by simply using hash chains to resist tampering and pollution attacks ensure data integrity. Second, according to the CRT, the cloud can obtain the fine-grained aggregation results of subregions from the global aggregation results, thereby providing fine-grained data services. In addition, the EE-PPDA scheme also supports fault tolerance. Even if some IIoT devices or communication links fail, the cloud can still decrypt incomplete aggregated ciphertexts and obtain the expected aggregation results. Finally, the performance evaluation shows that the proposed EE-PPDA scheme has less calculation and communication costs.

A Secure and Efficient Lightweight Vehicle Group Authentication Protocol in 5G Networks

When mobile network enters 5G era, 5G networks have a series of unparalleled advantages. Therefore, the application of 5G network technology in the Internet of Vehicles (IoV) can promote more intelligently vehicular networks and more efficiently vehicular information transmission. However, with the combination of 5G networks and vehicular networks technology, it requires safe and reliable authentication and low computation overhead. Therefore, it is a challenge to achieve such low latency, security, and high mobility. In this paper, we propose a secure and efficient lightweight authentication protocol for vehicle group. The scheme is based on the extended chaotic map to achieve authentication, and the Chinese remainder theorem distributes group keys. Scyther is used to verify the security of the scheme, and the verification results show that the security of the scheme can be guaranteed. In addition, through security analysis, the scheme can not only effectively resist various attacks but also guarantee security requirements such as anonymity and unlinkability. Finally, by performance analysis and comparison, our scheme has less computation and communication overhead.