n ±1 are the most popular moduli in Residue Number Systems (RNS), a large variety of modulo 2 n ±1 adder designs have been proposed based on different number representations. However, in most of the cases, these encodings do not allow the implementation of a unified adder for all the moduli of the form 2 n-1, 2 n , and 2 n +1. In this paper, we address the modular addition issue by introducing ...

Data integrity has tremendous effects on any data communication system’s performance. Communication systems are probabilistic in nature and may fail due to errors generated during the transmission process. These errors are generated due to various factors as noise, heat and other disturbance from neighboring systems. In this paper, an error detection and correction scheme based on redundant res...

In this paper, we study the problem of factoring an RSA modulus N = pq in polynomial time, when p is a weak prime, that is, p can be expressed as ap = u0 + M1u1 + . . . + Mkuk for some k integers M1, . . . ,Mk and k+2 suitably small parameters a, u0, . . . uk. We further compute a lower bound for the set of weak moduli, that is, moduli made of at least one weak prime, in the interval [2, 2] and...

We show that local and semilocal strings in Abelian and non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex moduli parameters. Our analysis of generic geodesic motion in terms of those shows right-angle scattering in head-on collision ...

Fix a ruled surface S obtained as the projective completion of a line bundle L on a complex elliptic curve C; we study the moduli problem of parametrizing certain pairs consisting of a sheaf E on S and a map of E to a fixed reference sheaf on S. We prove that the full moduli stack for this problem is representable by a scheme in some cases. Moreover, the moduli stack admits an action by the gro...

Architecture of binary to residue number system encoder based on the moduli set {2 1,2 ,2 1} n n n   , and architecture of encoder with modulo 2 1 n  channel in the diminished-1 representation instead of the standard modulo 2 1 n  channel are presented. We consider the binary numbers with dynamic range of proposed moduli set which is 3 2 2 n n  . Within this dynamic range, 3n -bit binary n...

The supersymmetric flow equations describing the flow of moduli from infinity to the black hole horizon, and vice versa, are derived in the five-dimensional theories where the moduli space of the very special geometry has disjoint branches. The multiple solutions are derived from the ‘off the horizon’ attractor equation. Within each branch, the black hole entropy, as usual, depends only on the ...

In this paper, a novel ROM-less RNS-to-binary converter is proposed, using a new balanced moduli set {22n − 1, 2 + 1, 2 − 3, 2 + 3} for n even. The proposed converter is implemented with a two stage ROM-less approach, which computes the value of X based only in arithmetic operations, without using lookup tables. Experimental results for 24 to 120 bits of Dynamic Range, show that the proposed co...