For each pair of integers n = ∏r i=1 p ei i and k ≥ 2, a digraph G(n, k) is one with vertex set {0, 1, . . . , n − 1} and for which there exists a directed edge from x to y if x ≡ y (mod n). Using the Chinese Remainder Theorem, the digraph G(n, k) can be written as a direct product of digraphs G(pi i , k) for all i such that 1 ≤ i ≤ r. A fundamental constituent GP (n, k), where P ⊆ Q = {p1, p2,...

We show that the Cao-Li cryptosystem proposed in [1] is not secure. Its private key can be reconstructed from its public key using elementary means such as LU-decomposition and Euclidean algorithm. The Cao-Li public key cryptosystem was first proposed in [1]. It encrypts messages using a bilinear form that is chosen to permit easy decryption by the Chinese remainder theorem. Public key cryptosy...

The conference-key agreement protocol is a mechanism for generating a common session key among the authorized conference members. The common session key is used to encrypt communication messages transmitted over an open network. Inspired by traditional key agreement protocols and threshold cryptosystems, we have proposed a novel threshold conference-key agreement protocol in this paper. In the ...

We note that the Chinese remainder theorem implies that this group is isomorphic with the cylic group of order 30, Z30. 31 is prime so the only abelian group of order 31 is Z31. 32 = 2. So there are many possibilities corresponding to all of the ways we can write m1 +m2 + ...+mr = 5 with m1 ≥ m2 ≥ ... ≥ mr. The solutions are 5 = 5 which corresponds to Z32, 4 ≥ 1 giving Z16 ×Z2, 3 ≥ 2 giving Z8 ...

In this work, we study a class of generalized quasi-cyclic (GQC) codes called skew GQC codes. By the factorization theory of ideals, we give the Chinese Remainder Theorem over the skew polynomial ring, which leads to a canonical decomposition of skew GQC codes. We also focus on some characteristics of skew GQC codes in details. For a 1-generator skew GQC code, we define the parity-check polynom...

This study proposes a novel multi-image threshold sharing scheme based on Chinese remainder theorem and Lagrange interpolation. The exceptional property of the scheme is its ability to retrieve any secret image without recovering all the other images. Therefore, it works efficiently and reduces computation cost in case it needs to recover only one image from shares. In term of capacity, the sch...

In this note we describe a security weakness in pairingbased protocols when the group order is composite and the imbedding degree k is greater than 2. In pairing-based protocols, as in elliptic curve cryptography more generally, one usually works in a prime-order subgroup of an elliptic curve E(Fq). However, starting in 2005 with work of Boneh, Goh, and Nissim [1], composite-order groups have b...

We study minimal sets on continua X with a dense free interval J and locally connected remainder. This class of includes important spaces such as the topologist's sine curve or Warsaw circle. In case when remainder are known is connected, we obtain full characterization topological structure sets. particular, given in X∖J local dendrite.