In this article processor elements for the effective implementation of standard cell circuits based on Residue Number Systems (RNS) are presented. Two new processors are proposed helping to reduce the hardware requirements of the implementations. Following a new strategy for implementation a comparison between other circuits discussed in past prove the new method and cells to lead to faster and...

This paper presents a general architecture for designing efficient reverse converters based on the moduli set {2α, 22β+1-1, 2β-1}, where β ≺ α 2β, by using a parallel implementation of mixed-radix conversion (MRC) algorithm. The moduli set {2α, 22β+1-1, 2β-1} is free from modulo (2k+1)-type which can result in an efficient arithmetic unit for residue number system (RNS). The values of α and β c...

In this PhD thesis I propose coprocessors architectures for high performance computations of asymmetric primitives like RSA, Elliptic Curves and Pairing. Coprocessors have been implemented in FPGA, and propose the lowest latency ever showed in public litterature on such targets. The novelty of these architectures is the usage of the Residue Number System (RNS), an alternate way to represent big...

The operation of logarithmic addition was always eclipsed with heavy volumes of look-up tables. So with a goal to reduce the ROM size, an elegant and novel technique for logarithmic addition using RNS (Residue Number System) is demonstrated in this paper. To formulate this technique, the properties of Finite Fields and Finite Rings are exploited. A multiple base logarithm has been defined first...

This paper presents new structures of circuits: adders and D triggers based on the current mode gates – digital elements operating with constant, continuous power supply current. Current mode circuits do not perturb the analogue part of the chip integrated on the same die through the parasitic coupling across the substrate with the same strength as voltage mode circuits do. Designed circuits ar...

In last years, many modulus sets in the Residue Number System (RNS) for increasing Dynamic Range (DR) and parallelism are presented. Hence, for reach these purposes a new 5-Moduli Set for even n, and its efficient reverse converter design are introduced in this paper. This modulus set contains pair-wise relatively prime, and it offers the maximum feasible DR. New CRT-I and MRC are used to obtai...

today, optimal performance and cost advantages of using internet telephony are obvious. despite current standardized techniques, voice transferring through protocol (voip) has lower security than traditional telephony. one of the most important security issues which should be noticed in using voip is end -to-end user2 identity, i.e. when  there is a connection between user a and b, user a shoul...

The operation of logarithmic addition was always eclipsed with heavy volumes of look-up tables. So with a goal to reduce the ROM size, an elegant and novel technique for logarithmic addition using RNS (Residue Number System) is demonstrated in this paper. To formulate this technique, the properties of Finite Fields and Finite Rings are exploited. A multiple base logarithm has been defined first...

Lattice based cryptography is claimed as a serious candidate for post quantum cryptography, it recently became an essential tool of modern cryptography. Nevertheless, if lattice based cryptography has made theoretical progresses, its chances to be adopted in practice are still low due to the cost of the computation. If some approaches like RSA and ECC have been strongly optimized in particular ...

We identify a canonical parameter in the Chinese Remainder Theorem (CRT) and call it the ‘‘Reconstruction Coefficient’’, (denoted by ‘‘RC ’’); and introduce the notions of ‘‘Partial’’ and ‘‘Full’’ Reconstruction. If the RC can be determined efficiently, then arithmetic operations that are (relatively) harder to realize in RNS; including Sign Detection, Base change/extension and Scaling or divis...