Application Of Chinese Remainder Theorem Research Articles

Research and application of Chinese remainder theorem

The Chinese remainder theorem (denoted it as " the theorem" in this article) was originally an important theorem in number theory. It played a vital role in the integer solution of the congruence equation in ancient times. With the continuous development of the algebraic system, the theorem naturally has different forms. This paper will show some research and applications based on the theorem. For example, the theorem in polynomial form, the theorem in the form of group theory, the theorem on unitary rings, the theorem on polynomial ring modules, etc. It is not difficult to know that integers and polynomials are special rings, so this the two forms of the theorem are the theorems that can be covered on the unitary ring. In fact, the theorem in the form of group theory is also covered. This paper will elaborate the first three forms of the theorem and give their specific applications.

IP Traceback using Flow Based Classification

Background:Distributed Denial of Service (DDoS) attack is a major threat over the internet. The IP traceback mechanism defends against DDoS attacks by tracing the path traversed by attack packets. The existing traceback techniques proposed till now are found with few short comings. The victim required many number of packets to trace the attack path. The requirement of a large number of packets resulted in more number of combinations and more false positives.Methods:To generate a unique value for the IP address of the routers in the attack path Chinese Remainder theorem is applied. This helped in combining the exact parts of the IP address at the victim. We also applied K-Nearest Neighbor (KNN) algorithm to classify the packets depending on their traffic flow, this reduced the number of packets to reconstruct the attack path.Results:The proposed approach is compared with the existing approaches and the results demonstrated that the attack graph is effectively constructed with higher precision and lower combination overhead under large scale DDoS attacks. In this approach, packets from diverse flows are separated as per flow information by applying KNN algorithm. Hence, the reconstruction procedure could be applied on each group separately to construct the multiple attack paths. This results in reconstruction of the complete attack graph with fewer combinations and false positive rate.Conclusion:In case of DDoS attacks the reconstruction of the attack path plays a major role in revealing IP addresses of the participated routers without false positives and false negatives. Our algorithm FRS enhances the feasibility of information pertaining to even the farthest routers by incorporating a flag condition while marking the packets. The rate of false positives and false negatives are drastically reduced by the application of Chinese Remainder Theorem on the IP addresses of the router. At the victim, the application of KNN algorithm reduced the combination overhead and the computation cost enormously.

Оптимизация процесса коррекции ошибок в системе остаточных классов за счет применения Китайской теоремы об остатках с дробными числами

Оптимизация процесса коррекции ошибок в системе остаточных классов за счет применения Китайской теоремы об остатках с дробными числами

Complex convolutions using rectangular transforms

Following the earlier technique1 and using the modular arithmetic, a method is proposed to compute error-free complex convolutions using rectangular transforms with reduced number of multiplications. Application of Chinese remainder theorem is suggested to implement the complex convolution with parallel digital machines of shorter word-length, thereby allowing higher speed with no increase in hardware.