Two hardware implementations for modular multiplication in the AMNS: Sequential and semi-parallel

Chaouch, Asma; Didier, Laurent-Stéphane; Dosso, Fangan Yssouf; Mrabet, Nadia El; Bouallègue, Belgacem; Ouni, Bouraoui

doi:10.1016/j.jisa.2021.102770

Cited by 5 publications

(3 citation statements)

References 11 publications

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“…This paper employs virtual instruments to develop a complete system, which offers several advantages. First, the hardware is modular [10], and the program is designed using flow block diagrams and linear nodes, which are more concise than traditional programming languages. Second, when debugging the program, The software architecture is designed to be modular and scalable, allowing for easy integration of new hardware components or software modules as figure 18.…”

Section: Virtual Instrument-based System Implementationmentioning

confidence: 99%

Design and Implementation of a Virtual Instrument-Based Seismic Reflection Wave Imaging System

Zhang

2023

Preprint

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This paper presents a seismic reflection wave imaging system that uses virtual instrumentation technology to process seismic wave data. The system employs a modular approach to image reflection waves in a medium velocity hierarchy. The study investigates the time and frequency domain characteristics of seismic sub-waves transmitted in the reflection system and establishes and simulates the propagation model of seismic reflection waves in horizontally stratified media. Algorithms are proposed for implementing the overall system, including amplitude compensation, digital filtering, velocity analysis, and offset imaging. The effectiveness of 2D FK filtering in the filtering process is tested, which confirms its ability to filter out velocity domain interference waves. The hardware and software development solutions for the overall system are developed based on the architecture of virtual instrumentation technology. Seismic reflection wave imaging experiments are conducted in several scenarios, and the experimental results meet the application requirements. The experiments demonstrate that the system can accurately image the velocity of subsurface media using seismic reflection waves and virtual instrumentation hardware and software systems.

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Section: Virtual Instrument-based System Implementationmentioning

confidence: 99%

Design and Implementation of a Virtual Instrument-Based Seismic Reflection Wave Imaging System

Zhang

2023

Preprint

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“…In [14], the authors extend the AMNS representation system to F p k and show how it can be used in order to improve the performances of SIKE [35], one of the alternate KEM candidate of the NIST post-quantum standardization process [46]. A first hardware implementation of the AMNS is described in [17]. To end, it is shown in [22,49] that some "random steps" can be injected in AMNS multiplication in order to resist to a side channel analysis.…”

Section: Introductionmentioning

confidence: 99%

On Polynomial Modular Number Systems over $ \mathbb{Z}/{p}\mathbb{Z} $

Bajard

Marrez

Plantard

et al. 2024

AMC

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<p style='text-indent:20px;'>Since their introduction in 2004, Polynomial Modular Number Systems (PMNS) have become a very interesting tool for implementing cryptosystems relying on modular arithmetic in a secure and efficient way. However, while their implementation is simple, their parameterization is not trivial and relies on a suitable choice of the polynomial on which the PMNS operates. The initial proposals were based on particular binomials and trinomials. But these polynomials do not always provide systems with interesting characteristics such as small digits, fast reduction, etc.</p><p style='text-indent:20px;'>In this work, we study a larger family of polynomials that can be exploited to design a safe and efficient PMNS. To do so, we first state a complete existence theorem for PMNS which provides bounds on the size of the digits for a generic polynomial, significantly improving previous bounds. Then, we present classes of suitable polynomials which provide numerous PMNS for safe and efficient arithmetic.</p>

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“…Several hardware implementations illustrate that those representations can be more efficient than the classical one [18]- [20]. However, no software comparison exists.…”

Section: Introductionmentioning

confidence: 99%

A software comparison of RNS and PMNS

Didier

Robert

Dosso

et al. 2022

2022 IEEE 29th Symposium on Computer Arithmetic (ARITH)

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The Polynomial Modular Number System (PMNS) and the Residue Number System (RNS) are integer number systems which aim to speed up modular arithmetic. Their parallel properties make them suitable for the implementation of cryptographic applications on modern processors with SIMD instructions. In this work, we will show the implementation choices made for the modular multiplication in both systems and compare their implementation performances for several sizes of moduli. We target the Intel 64-bit sequential instruction set and the Intel AVX-512 vector instruction set. This instruction set allows significant speed-ups up to 1 621 bit size moduli, while the vectorized PMNS implementation is up to 2.5 times faster than the vectorized RNS, though the vectorized RNS becomes slightly better for 3 251 bits, due to the difficulty to find a PMNS with a suitable parameter n. The vectorized RNS implementations reach performance levels close the state-of-the-art GMP library, while the retired instruction counts are lower for sizes between 401 and 3 251 bits.

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Two hardware implementations for modular multiplication in the AMNS: Sequential and semi-parallel

Cited by 5 publications

References 11 publications

Design and Implementation of a Virtual Instrument-Based Seismic Reflection Wave Imaging System

Design and Implementation of a Virtual Instrument-Based Seismic Reflection Wave Imaging System

On Polynomial Modular Number Systems over $ \mathbb{Z}/{p}\mathbb{Z} $

A software comparison of RNS and PMNS

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