Based on an algorithm derived from the New Chinese Remainder Theorem I, we present three new residue-to-binary converters for the residue number system (2 1 2 2 + 1) designed using 2 -bit or -bit adders with improvements on speed, area, or dynamic range compared with various previous converters. The 2 -bit adder based converter is faster and requires about half the hardware required by previous...

In this work, we are interested in arithmetic in large prime field and their extensions of small degree. We explain why it is very interesting to use RNS arithmetic for the base field Fp when computations in Fpk have to be done, essentially thanks to lazy reduction. This is for example the case for pairing computations on ordinary curves (as MNT or BN curves). We prove that using RNS can consid...

The massless 4-point one-loop amplitude computation in the pure spinor formalism is shown to agree with the computation in the RNS formalism.

A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter. In Part I, we compute the Levi-Civita connection for these metrics. The connection and curvature forms take values in pseudodifferential operators (ΨDOs), and we compute the top symbols of these forms. In Part II, we develop a theory of Chern-Simons classes CS ...

A special moduli set Residue Number System (RNS) of high Dynamic Range (DR) can speed up the execution of verylarge word-length repetitive multiplications found in applications like public key cryptography. The modulo 2n-1 multiplier is usually the noncritical datapath among all modulo multipliers in such high-DR RNS multiplier. This timing slack can be exploited to reduce the system area and p...

Modulo 2 ÿ 1 adders as fast as n-bit 2’s complement adders have been recently proposed in the open literature. This makes a Residue Number System (RNS) adder with channels based on the moduli 2, 2 ÿ 1, and any other of the form 2 ÿ 1, with k < n, faster than RNS adders based on other moduli. In this paper, we formally derive a parametric, with respect to the adder size, test set, for parallel t...

The Residue Number System (RNS) is suitable for DSP architectures because of its ability to perform fast carry-free arithmetic. However, this advantage is over-shadowed by the complexity involved in the conversion of numbers between binary to RNS representations and have prevented the widespread use of RNS. Converting a number from a binary representation to its RNS equivalent is known as forwa...

This paper investigates the conversion of Residue Number System (RNS) operands to decimal, which is an important issue concerning the utilization of RNS numbers in digital signal processing applications. We present a Mixed Radix Conversion (MRC) technique for efficient RNS to decimal conversion using the moduli set {2n + 2, 2n + 1, 2n}, which has a common factor of 2. First, we provide two impo...

This paper assesses the arithmetic benefits provided by the Residue Number System (RNS) for building Digital Signal Processing (DSP) systems with Field Programmable Logic (FPL) technology. The quantifiable benefits of this approach are studied in the context of a new Fast Cosine Transform (FCT) architecture enhanced by using the Quadratic Residue Number System (QRNS). The system reduces the num...