Chinese Remainder Theorem Research Articles

Construction of low-hit-zone frequency-hopping sequence sets with strictly optimal partial Hamming correlation based on Chinese Remainder Theorem

Construction of low-hit-zone frequency-hopping sequence sets with strictly optimal partial Hamming correlation based on Chinese Remainder Theorem

Reversible Data Hiding in Shared JPEG Images

Reversible data hiding (RDH) in encrypted images has emerged as an effective technique for securely storing and managing confidential images in the cloud. However, most RDH methods in shared images (RDHSI) are designed for uncompressed images and cannot be applied for JPEG images. To address this issue, we propose a novel RDH in shared JPEG images. Our method consists of JPEG image sharing and data hiding in JPEG shares, which are both conducted on JPEG bit-stream. Specifically, the DC appended bits (DCA) and AC appended bits (ACA) derived from the original JPEG bit-stream are shared by ( \(k\) , \(n\) ) threshold Chinese remainder theorem based secret sharing (CRTSS) with two different constraints, one for DC sharing and another for AC sharing. The constraint of DC sharing ensures that the DC coefficient shares do not overflow. The constraint of AC sharing ensures the sizes of ACA shares are less than the sizes of the original ACA so that the embedding room can be vacated from each shared JPEG bit-stream. Each data-hider can embed the secret data into the personal JPEG share. The original JPEG image can be recovered losslessly from any \(k\) JPEG shares. The proposed sharing and data hiding are both well compatible with the JPEG standard. Experimental results demonstrate that the proposed method not only well preserves the file size whether the JPEG shares or marked JPEG shares, but also achieves outstanding security performance and a high embedding capacity.

Partition theorems and the Chinese Remainder Theorem

The famous partition theorem of Euler states that partitions of n into distinct parts are equinumerous with partitions of n into odd parts. Another famous partition theorem due to MacMahon states that the number of partitions of n with all parts repeated at least once equals the number of partitions of n where all parts must be even or congruent to 3(mod6). These partition theorems were further extended by Glaisher, Andrews, Subbarao, Nyirenda and Mugwangwavari. In this paper, we utilize the Chinese Remainder Theorem to prove a comprehensive partition theorem that encompasses all existing partition theorems. We also give a natural generalization of Euler's theorem based on a special complete residue system. Furthermore, we establish interesting congruence connections between the partition function p(n) and related partition functions.

Unlinkable and Revocable Signcryption Scheme for VANETs

Vehicular ad-hoc networks (VANETs) can significantly improve the level of urban traffic management. However, the sender unlinkability has become an intricate issue in the field of VANETs’ encryption. As the sender signcrypts a message, the receiver has to use the sender’s identity or public key to decrypt it. Consequently, the sender can be traced using the same identity or public key, which poses some security risks to the sender. To address this issue, we present an unlinkable and revocable signcryption scheme (URSCS), where an efficient and powerful signcryption mechanism is adopted for communication. The sender constructs a polynomial to generate a unique session key for each communication, which is then transmitted to a group of receivers, enabling the same secret message to be sent to multiple receivers. Each time a secret message is sent, a new key pair is generated, and an anonymization mechanism is introduced to conceal the true identity of the vehicle, thus preventing malicious attackers from tracing the sender through the public key or the real identity. With the introduction of the identification public key, this scheme supports either multiple receivers or a single receiver, where the receiver can be either road side units (RSUs) or vehicles. Additionally, a complete revocation mechanism is constructed with extremely low communication overhead, utilizing the Chinese remainder theorem (CRT). Formal and informal security analyses demonstrate that our URSCS scheme meets the expected security and privacy requirements of VANETs. The performance analysis shows that our URSCS scheme outperforms other represented schemes.

Optimised Implementation of Adaptive Rns Using Power-Aware CRT

In order to get an efficient comprehensive analysis on Doppler estimation in RADAR; need an enhanced arithmetic formulation procedure for density, power and latency optimisations. Modular adders and multipliers are very crucial components in the performance of residue number system-based applications. The Residue Number System (RNS) is a non-positional number system that allows parallel computations without transfers between digits. However, some operations in RNS require knowledge of the positional characteristic of a number. Among these operations is the conversion from RNS to the positional number system. The methods of reverse conversion for general form moduli based on the Chinese remainder theorem and the mixed-radix conversion are considered, as well as the optimized methods for special form moduli. A modified New CRT-I & New CRT-II with conjugate moduli set is considered to implement adder, multipliers and subtractions with optimised algorithms. This paper mainly deals with the conversion of numbers from binary to RNS as well RNS to binary with the specific modulo {2^n±k} which proves this new method. Modified Radix16 booth encoding algorithm and square carry bypass adder are used in implementation of RNS system to reduce parameter constraints.

Progressive reversible data hiding in encrypted images based on polynomial secret sharing and Chinese remainder theorem

Progressive reversible data hiding in encrypted images based on polynomial secret sharing and Chinese remainder theorem

Chinese Remainder Theorem-Based Encoding of Text to Point Elliptic Curve Cryptography

One of the most crucial requirements in this digital age is data security. The number of data usage increased drastically now a days, but how far the data is secured is the very big problem, though we have enough cryptographic algorithms for securing real time applications, but the level of the security against modern attacks is not determined. Elliptic Curve based Cryptography (ECC) is the most important cryptographic algorithm for confidentiality and authentication, providing high security level with small length keys when compared to other asymmetric algorithms like RSA, Diffie-Hellman, etc. The real time system usage of ECC is very less due to computational complexity. So, to increase the real time system usage we propose the novel method of combining the ECC with the Chinese Remainder Theorem (CRT), to reduce the larger values to the smaller one, so that the complexity of constructing ECC points can be reduced nearly 40% when compared to the existing ECC based algorithms. Also, its proved that the level of security getting increased and can be used as the fundamental component in real time communication system.

New q-analogues of Van Hamme’s (F.2) supercongruence and of some related supercongruences

Abstract In terms of a very-well-poised 6 ϕ 5 summation formula, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials, we establish four new q-supercongruences for truncated basic hypergeometric series. One of these results is a new q-analogue of the (F.2) supercongruence of Van Hamme.

Reversible image secret sharing based on quantum logistic mapping and Chinese remainder theorem

A reversible image secret sharing algorithm is proposed based on quantum logistic mapping and Chinese remainder theorem. In this algorithm, the hash value of the original image is generated using the SHA-3 algorithm, and then encrypted using the RSA algorithm to obtain the encrypted hash value and the public key, which are the initial values in the quantum logistic mapping equations. Next, the quantum logistic mapping algorithm will be utilized to generate the chaotic sequence. After scrambling the original image matrix with the chaotic sequence, the pre-encryption part will be completed. Finally, the cover images are binarized and then the pre-encrypted secret image is embedded into them, adding the Chinese remainder theorem. According to the simulation results, the present algorithm improves the key sensitivity of Chinese remainder theorem-based image secret sharing and has high robustness to salt and pepper noise and cut-off attack.

Adder-Only Reverse Converters for 5-Moduli Set {2 q , 2 q − 1, 2 q+1 ± 1, 2 q+2 − 1}

We propose a balanced 5 -moduli set P = { 2 q , 2 q − 1 , 2 q + 1 − 1 , 2 q + 1 + 1 , 2 q + 2 − 1 } , for odd q ≥ 3 . Our reverse conversion scheme is based on a multi-stage new Chinese remainder theorem, where some of the difficult-to-derive multiplicative inverse coefficients are expressed as geometric series. Only carry-save and ripple-carry adders are used as components of the corresponding circuits. Analytical gate-level evaluations are performed on the proposed and reference converters, whose results are confirmed by the synthesis tool. A comparison of the converters for moduli sets with equal dynamic range shows that P is similar to previous 5-moduli set { 2 q , 2 q − 1 , 2 q + 1 , 2 q + 1 − 1 , 2 q − 1 − 1 } and shows slight advantage in delay and energy consumption.

A group key agreement protocol for Vanet based on Chinese remainder theorem and blockchain

AbstractVehicular ad hoc Network (VANET) is a wireless self‐organizing network for obtaining information about road conditions, vehicle speed, vehicle location and traffic congestion. Traditional key negotiation protocols create many problems when dealing with a group of vehicles that need to communicate over a public channel. For example, traditional key negotiation protocols rely too much on the participation of trusted institutions and suffer from a single point of failure. Meanwhile, group session key negotiation is usually inefficient with high computational cost and communication overhead. To solve these problems, this paper proposes a blockchain‐based Chinese Remainder Theorem (CRT) VANET group key agreement. In addition, the protocol supports dynamic management of vehicles, including joining and exit. Formal security proofs show that our solution satisfies basic security requirements. Experiments using ProVerif show that the protocol functions properly even under many active and passive attacks, such as eavesdropping attacks. Performance analysis shows that the protocol is more efficient in the face of multi‐vehicle communication, in particular by reducing the computational cost by up to 75% and the communication overhead by up to 66%.

Enhanced Local Binary Pattern Algorithm for Facial Recognition Using Chinese Remainder Theorem

Current biometrics research focuses on achieving a high authentication success rate for identity management and discussing the threat of various security attacks. Local Binary Pattern (LBP), one of the methods for feature extraction, and Chicken Swarm Optimization (CSO), one of the strategies for feature selection, were used for user identification and authentication. LBP requires high computational time to extract features from the facial images. The Chinese Remainder Theorem (CRT) was used to reduce its computational time by formulating an Enhanced Local Binary Pattern (ELBP). Michael Olugbenga Banji Abolarinwa (MOBA) database was created specifically for this study. 600 frontal facial images of 200 people were collected, each with three images. 360 images were used for training while 240 images were used for testing. MATLAB (R2016a) was used to run the simulation. The time it took to classify the facial images when LBP and CSO were combined and when ELBP and CSO were combined were enumerated. The LBP-CSO achieved a false-positive rate (FPR) of 11.67%, a sensitivity (SEN) of 92.78%, a specificity (SPEC) of 88.33%, a precision (PREC) of 95.98%, and an accuracy of 91.67% in 119.10 seconds at 0.80 thresholds for face recognition. ELBP-CSO obtained an FPR of 5.00%, SEN of 95.00%, SPEC of 95.00%, PREC of 98.28%, and accuracy of 95.00% in 79.16 seconds. The results showed that LBP-CSO took an average of 119.10 seconds and ELBP-CSO took an average of 79.16 seconds. In conclusion, the performance of CSO-ELBP justifies the usage of LBP enhancement with CRT.

An Efficient Lightweight Authentication Scheme for Smart Meter

With the rapid development of the information age, smart meters play an important role in the smart grid. However, there are more and more attacks on smart meters, which mainly focus on the identity authentication of smart meters and the security protection of electricity consumption data. In this paper, an efficient lightweight smart meter authentication scheme is proposed based on the Chinese Remainder Theorem (CRT), which can realize the revocation of a single smart meter user by publishing a secret random value bound to the smart meter identity. The proposed scheme not only protects the security of smart meter electricity consumption data by using encryption, but also resists identity attacks from both internal and external adversaries by using hash functions and timestamps. Experiment shows that the proposed scheme has lower computation overhead and communication overhead than other authentication schemes and is more suitable for smart meter authentication.

ПРО ОДИН ПІДХІД ДО ПЕРЕТВОРЕННЯ ЧИСЕЛ У СИСТЕМАХ ЗАЛИШКОВИХ КЛАСІВ ІЗ РІЗНИМИ МОДУЛЯМИ

The purpose of the study is an analytical consideration of the system of residual classes for the implementation of the operation of converting numbers from one system of residual classes to another. System analysis, number theory, and the Chinese remainder theorem are tools of the research methodology. The method uses the representation of the number both by its remainders and in the polyadic code. The methodology is based on determining the positional characteristics for this module on the basis of the received positional characteristics for the remaining modules of the original system, with the subsequent construction on their basis of the residuals for the modules of the sought system. The theoretical justification of the approach for obtaining an effective solution of this non-modular operation is performed. The considered solutions have high speed and can be effective in the development of modular computing structures for promising information technologies.

Attribute-Based Data Sharing Scheme Using Blockchain for 6G-Enabled VANETs

The advent of 6G communications technology will bring about a transition from the “Internet of Everything” to the “Intelligent Connection of Everything”. 6G-enabled vehicular ad hoc networks (VANETs) will enjoy lower latency, higher speed, and greater capacity network services. Nevertheless, achieving secure data sharing will be an even tougher challenge. Given this, we propose an attribute-based data sharing scheme with blockchain for 6G-enabled VANETs. First, we propose an efficient multi-tree-based user revocation mechanism. With the Chinese remainder theorem, our mechanism supports user batch revocation and batch joining. Second, we achieve distributed data storage by utilizing the blockchain and smart contracts. To solve the problem of insufficient storage capacity on the blockchain, we adopt a combination of on-chain and off-chain storage. Third, to reduce the computation burden on users, our proposal supports online/offline encryption and verifiable outsourced decryption. Meanwhile, our mechanism supports policy hiding, data revocation, and cross-domain data sharing. The proposed scheme is proven to satisfy the indistinguishability under chosen plaintext attack (IND-CPA) in the standard model. Theoretical analysis shows that our mechanism outperforms existing schemes in functionality and security. Simulation experiments show that our proposal is efficient and suitable for 6G-enabled VANETs.

An Efficient Multi-Party Secure Aggregation Method Based on Multi-Homomorphic Attributes

The federated learning on large-scale mobile terminals and Internet of Things (IoT) devices faces the issues of privacy leakage, resource limitation, and frequent user dropouts. This paper proposes an efficient secure aggregation method based on multi-homomorphic attributes to realize the privacy-preserving aggregation of local models while ensuring low overhead and tolerating user dropouts. First, based on EC-ElGamal, the homomorphic pseudorandom generator, and the Chinese remainder theorem, an efficient random mask secure aggregation method is proposed, which can efficiently aggregate random masks and protect the privacy of the masks while introducing secret sharing to achieve tolerance of user dropout. Then, an efficient federated learning secure aggregation method is proposed, which guarantees that the computation and communication overheads of users are only O(L); also, the method only performs two rounds of communication to complete the aggregation and allows user dropout, and the aggregation time does not increase with the dropout rate, so it is suitable for resource-limited devices. Finally, the correctness, security, and performance of the proposed method are analyzed and evaluated. The experimental results indicate that the aggregation time of the proposed method is linearly related to the number of users and the model size, and it decreases as the number of dropped out users increases. Compared to other schemes, the proposed method significantly improves the aggregation efficiency and has stronger dropout tolerance, and it improves the efficiency by about 24 times when the number of users is 500 and the dropout rate is 30%.

Authenticable dynamic quantum multi-secret sharing based on the Chinese remainder theorem

Authenticable dynamic quantum multi-secret sharing based on the Chinese remainder theorem

Cryptanalysis of Two Conditional Privacy Preserving Authentication Schemes for Vehicular Ad Hoc Networks

Conditional Privacy Preserving Authentication (CPPA) schemes are an effective way of securing communications in vehicular ad hoc networks (VANETs), as well as ensuring user privacy and accountability. Cryptanalysis plays a crucial role in pointing out the vulnerabilities in existing schemes to enable the development of more resilient ones. In 2019, Zhang proposed a CPPA scheme for VANET security (PA-CRT), based on identity batch verification (IBV) and Chinese Remainder Theorem (CRT). In this paper, we cryptanalyze Zhang’s scheme and point out its vulnerability to impersonation and repudiation attacks. In 2023, Zhang’s scheme was cryptanalyzed by Tao; however, we point out flaws in Tao’s cryptanalysis due to invalid assumptions; hence, we propose countermeasures to Tao’s attacks. Furthermore, in 2021, Xiong proposed a Certificateless Aggregate Signature (CLAS) scheme which is also cryptanalyzed in this paper. Finally, we analyze the causes and countermeasures by pointing out the vulnerabilities in each scheme that enabled us to launch successful attacks and proposing changes that would fortify these schemes against similar attacks in the future.

An Information Theoretic Condition for Perfect Reconstruction.

A new information theoretic condition is presented for reconstructing a discrete random variable X based on the knowledge of a set of discrete functions of X. The reconstruction condition is derived from Shannon's 1953 lattice theory with two entropic metrics of Shannon and Rajski. Because such a theoretical material is relatively unknown and appears quite dispersed in different references, we first provide a synthetic description (with complete proofs) of its concepts, such as total, common, and complementary information. The definitions and properties of the two entropic metrics are also fully detailed and shown to be compatible with the lattice structure. A new geometric interpretation of such a lattice structure is then investigated, which leads to a necessary (and sometimes sufficient) condition for reconstructing the discrete random variable X given a set {X1,…,Xn} of elements in the lattice generated by X. Intuitively, the components X1,…,Xn of the original source of information X should not be globally "too far away" from X in the entropic distance in order that X is reconstructable. In other words, these components should not overall have too low of a dependence on X; otherwise, reconstruction is impossible. These geometric considerations constitute a starting point for a possible novel "perfect reconstruction theory", which needs to be further investigated and improved along these lines. Finally, this condition is illustrated in five specific examples of perfect reconstruction problems: the reconstruction of a symmetric random variable from the knowledge of its sign and absolute value, the reconstruction of a word from a set of linear combinations, the reconstruction of an integer from its prime signature (fundamental theorem of arithmetic) and from its remainders modulo a set of coprime integers (Chinese remainder theorem), and the reconstruction of the sorting permutation of a list from a minimal set of pairwise comparisons.

Q-Supercongruences from Jackson's [formula omitted] summation and Watson's [formula omitted] transformation

q-Supercongruences modulo the fifth and sixth powers of a cyclotomic polynomial are very rare in the literature. In this paper, we establish some q-supercongruences modulo the fifth and sixth powers of a cyclotomic polynomial in terms of Jackson's ϕ78 summation, Watson's ϕ78 transformation, the creative microscoping method recently introduced by Guo and Zudilin, and the Chinese remainder theorem for coprime polynomials. More concretely, we give a q-analogue of a nice formula due to Long and Ramakrishna [Adv. Math. 290 (2016), 773–808] and two q-supercongruences involving double series.