The theory of groups, rings and modules is developed to a great depth. Group theory results include Zassenhaus’s theorem and the Jordan-Hoelder theorem. The ring theory development includes ideals, quotient rings and the Chinese remainder theorem. The module development includes the Nakayama lemma, exact sequences and Tensor products.

IP traceback is a defense method to help a victim to identifying the sources of attacking packets. In this paper, we propose an IP traceback method based on the Chinese Remainder Theorem to require routers to probabilistically mark packets with partial path information when packets traverse routers through the Internet. The routers with the proposed IP traceback method can interoperate seamless...

We prove the equidistribution of subsets (R/Z)n defined by fractional parts (Z/qZ)n that are constructed using Chinese Remainder Theorem.

Let F be the class of all 1-periodic real functions with absolutely convergent Fourier series expansion and let (xn)n≥0 be the van der Corput sequence. In this paper results on the boundedness of ∑N−1 n=0 f(xn) for f ∈ F are given. We give a criterion on the convergence rate of the Fourier coefficients of f such that the above sum is bounded independently of N . Further we show that our result ...

Using an adaptation of Qin Jiushao’s method from the 13th century, it is possible to prove that a system of linear modular equations ai1xi + · · · + ainxn = ~bi mod ~ mi, i = 1, . . . , n has integer solutions if mi > 1 are pairwise relatively prime and in each row, at least one matrix element aij is relatively prime to mi. The Chinese remainder theorem is the special case, where A has only one...

Recently, Chinese Remainder Theorem (CRT) based function sharing schemes are proposed in the literature. In this paper, we investigate how a CRT-based threshold scheme can be enhanced with the robustness property. To the best of our knowledge, these are the first robust threshold cryptosystems based on a CRT-based secret sharing.

A resolution of the intersection of a finite number of subgroups of an abelian group by means of their sums is constructed, provided the lattice generated by these subgroups is distributive. This is used for detecting singularities of modules over Dedekind rings. A generalized Chinese remainder theorem is derived as a consequence of the above resolution. The GelfandNaimark duality between finit...