Generalized quasi-cyclic (GQC) codes with arbitrary lengths over the ring Fq + uFq, where u 2 = 0, q = p, n a positive integer and p a prime number, are investigated. By the Chinese Remainder Theorem, structural properties and the decomposition of GQC codes are given. For 1-generator GQC codes, minimal generating sets and lower bounds on the minimum distance are given. As a special class of GQC...

However, in cryptography, we are more interested in trap-door functions, which are easy to compute and hard to invert unless given trap-door information. In this class, we will go deeper into computational number theory, in particular, the Chinese Remainder theorem, then look at operations in Z n, and finally introduce RSA and Rabin assumptions which shed lights to the design of trap-door funct...

Generalized quasi-cyclic (GQC) codes with arbitrary lengths over the ring Fq + uFq, where u 2 = 0, q = p, n a positive integer and p a prime number, are investigated. By the Chinese Remainder Theorem, structural properties and the decomposition of GQC codes are given. For 1-generator GQC codes, minimal generating sets and lower bounds on the minimum distance are given. As a special class of GQC...

An algorithm is given for deciding existential formulas involving addition and the divisibility relation over the natural numbers. In this paper it will be shown that there is an algorithm for deciding formulas of the form k 0) 3x,.3x„6N A /,(*.,..., xn)\g¡(xx, ...,xtt) /-I in N (the natural numbers), where the / and g¡ are linear polynomials with integer coefficients. (a\b means "a divides b"....

In this paper, we will show a reduction of ideal arithmetic, or more generally, of arithmetic of ZZ{modules of full rank in orders of number elds to problems of linear algebra over ZZ=mZZ, where m is a possibly composite integer. The problems of linear algebra over ZZ=mZZ will be solved directly, instead of either \reducing" them to problems of linear algebra over ZZ or factoring m and working ...

The modular product computation A*B (mod N) is a bottleneck for some public-key encryption algorithms, as well as many exact computations implemented using the Chinese Remainder Theorem. We show how to compute A*B (mod N) efficiently, for single-precision A,B, and N, on a modern RISC architecture (Intel 80860) in ANSI C. On this architecture, our method computes A*B (mod N) faster than ANSI C c...

In this paper, we present a new class of linear multivariate PKC referred to as K(I)SE(1)PKC. We shall show that K(I)SE(1)PKC, a linear multivariate PKC, can be sufficiently secure against any linear transformation attack due to the probabilistic structure. We show that the probabilistic structure can be successfully introduced by the use of the Chinese Remainder Theorem.

The discrete Fourier-cosine transform (cos-DFT), the discrete Fourier-sine transform (sin-DFT) and the discrete cosine transform (DCT) are closely related to the discrete Fourier transform (DFT) of real-valued sequences. This paper describes a general method for constructing fast algorithms for the cos-DFT, the sin-DFT and the DCT, which is based on polynomial arithmetic with Chebyshev polynomi...

Abstract In this paper, we deal with the critical problem of performing non-modular operations in Residue Number System (RNS). The Chinese Remainder Theorem (CRT) is widely used many modern computer applications. Throughout article, an efficient approach for implementing CRT algorithm described. structure rank RNS number, a principal positional characteristic residue code, investigated. It show...