This paper proposes a Fault-Tolerant Linear Convolution architecture using Residue Number Systems (RNS) and Polynomial Residue Number Systems (PRNS). The RNS and PRNS are both given error-detection capability by the addition of redundant residue channels, and the combined redundancy enables errors to be corrected without explicit error-decoding. The method is simple, fast, and amenable to VLSI ...

The purpose of this master's thesis was to explore the circuit design space (speed, area, power) of conventional binary arithmetic and to suggest improvements or alternatives to this arithmetic. The alternatives to the binary arithmetic focused on was the Signed-Digit (SD) number system, the Residue Number System (RNS) and the combination of these two systems (RNS+SD). The work resulted in new ...

This paper studies the effect of the moduli number within a moduli set on the overall speed of the residue number system (RNS). Choosing a proper moduli set greatly affects the performance of the whole system. The widely known issue is that as the number of moduli increases the speed of the residue arithmetic units (RAUs) increases, whereas the residue-to-binary converters (RCs) become slower a...

The Residue Number System (RNS) is an efficient alternative number system which has been attracted researchers for over three decades. In RNS, arithmetic operations such as addition and multiplication can be performed on residues without carry-propagation between them; resulting in parallel arithmetic and high-speed hardware implementations (Parhami, 2000; Mohan, 2002; Omondi & Premkumar, 2007)...

Scaling is one of the complex operations in Residue Number System (RNS). This operation necessary for RNS-based implementations deep neural networks (DNNs) to prevent overflow. However, state-of-the-art RNS scalers special moduli sets consider 2k modulo as scaling factor, which results a high-precision output with high area and delay. Therefore, low-precision based on multi-moduli factors shoul...

This contribution to the ongoing discussion of division algorithms for residue number systems (RNS) is based on Newton iteration for computing the reciprocal. An extended RNS with twice the number of moduli provides the range required for multiplication and scaling. Separation of the algorithm description from its RNS implementation achieves a high level of modularity, and makes the complexity ...

Performing RSA public and private key operations fast is increasingly important. In this paper I describe an eecient implementation of RSA for a highly parallel computer. I present a new algorithm for modular multiplication using a residue number system (RNS) and a variation of Montgomery's method. The heart of the algorithm is a new method for converting from one RNS to another.

The RNS has been considered as an interesting area for researchers in recent year. This paper presents memoryless and area efficient RNS converters for moduli set with dynamic ranges up to 6n-bit. Residue number system (RNS) has mainly targeted parallelism and larger dynamic ranges. In this paper, we start from the moduli sets {2, 2 1, 2 + 1, 2 – 2 + 1, 2 + 2 + 1} with dynamic range of 5n-bit a...

We present a method to increase the dynamical range of a Residue Number System (RNS) by adding virtual RNS layers on top of the original RNS, where the required modular arithmetic for a modulus on any non-bottom layer is implemented by means of an RNS Montgomery multiplication algorithm that uses the RNS on the layer below. As a result, the actual arithmetic is deferred to the bottom layer. The...

The quick growth of easy communication technologies concluded the last several decades has led in establishment strict standards for functioning productive systems. system execution is improved by reducing computation time with “Residue Number System (RNS)”. It extensively castoff “signal processing” “numeral analysis”, and “cryptoanalysis”, an exact graph-based technique designing perfect conv...