Modular arithmetic operations (inversion, multiplication and exponentiation) are used in several cryptography applications. RSA and elliptic curve cryptography (ECC) are two of the most well established and widely used public key cryptographic (PKC) algorithms. The encryption and decryption of these PKC algorithms are performed by repeated modulo multiplications. These multiplications differ fr...

Residue Number Systems (RNS) allow the distribution of large dynamic range computations over small modular rings, which allows the speed up of computations. This feature is well known, and already used in both DSP and cryptography. Most of implementations use RNS bases of three elements to reduce the complexity of conversions, but if can increase the number of RNS modular computational channels...

The FPL implementation of an 8×8 Two Dimensional Discrete Cosine Transform (2D-DCT) processor based on the Residue Number System (RNS) is presented in this paper. It makes use of a Fast Cosine Transform (FCT) algorithm that requires a single multiplication stage for each signal path, while most other algorithms include paths with more than one multiplication. The row-column decomposition techni...

High speed execution of arithmetic operations and high degree of precision in real time system are of major concern in any digital signal processing (DSP). Speed of DSP depends on speed of multiplier and algorithm used. In this paper we propose Residue Number System method for fast “carry free” floating point arithmetic operations. Floating Point RNS units have obvious advantages over tradition...

Title of Thesis: Fast Modular Exponentiation Using Residue Domain Representation: A Hardware Implementation and Analysis Christopher Dinh Nguyen, Master of Science, 2013 Thesis directed by: Alan T. Sherman, Associate Professor Department of Computer Science and Electrical Engineering Dhananjay S. Phatak, Associate Professor Department of Computer Science and Electrical Engineering Using modular...

The super-Poincaré covariant formalism for the superstring is used to compute mass-less four-point two-loop amplitudes in ten-dimensional superspace. The computations are much simpler than in the RNS formalism and include both external bosons and fermions.

In this paper, a new method is introduced for improving the efficiency of the Residue Number System, which uses both binary and residue representations in order to represent a number. A residue number system uses the remainder of the division in several different modules. Conversion of a number to smaller ones and carrying out parallel calculations on these numbers greatly increase the speed of...

In this paper optimized Residue Number System (RNS) arithmetic blocks to better exploit some of the architectural characteristics of the last generation FPGAs are presented. The implementation of modulo m adders, constant and general multipliers, input and output converters is presented. These architectures are based on moduli sets chosen in order to optimally use the six inputs Look-Up Tables ...