[KNYGA][B] Residue number systems

PVA Mohan, PVA Mohan - 2016 - Springer
The design of algorithms and hardware implementation for signal processing systems has
received considerable attention over the last few decades. The primary area of application …

High-throughput modular multiplication and exponentiation algorithms using multibit-scan–multibit-shift technique

A Rezai, P Keshavarzi - IEEE Transactions on Very Large Scale …, 2014 - ieeexplore.ieee.org
Modular exponentiation with a large modulus and exponent is a fundamental operation in
many public-key cryptosystems. This operation is usually accomplished by repeating …

Error-correction coding using polynomial residue number system

IA Kalmykov, VP Pashintsev, KT Tyncherov… - Applied Sciences, 2022 - mdpi.com
There has been a tendency to use the theory of finite Galois fields, or GF (2n), in
cryptographic ciphers (AES, Kuznyechik) and digital signal processing (DSP) systems. It is …

Residue arithmetic systems in cryptography: a survey on modern security applications

D Schoinianakis - Journal of Cryptographic Engineering, 2020 - Springer
In the last few years, the ancient residue number system has gained renewed scientific
interest and has emerged as an interesting alternative in the field of secure hardware …

Multifunction residue architectures for cryptography

D Schinianakis, T Stouraitis - IEEE Transactions on Circuits and …, 2014 - ieeexplore.ieee.org
A design methodology for incorporating Residue Number System (RNS) and Polynomial
Residue Number System (PRNS) in Montgomery modular multiplication in GF (p) or GF (2 n) …

Montgomery-friendly primes and applications to cryptography

JC Bajard, S Duquesne - Journal of Cryptographic Engineering, 2021 - Springer
This paper deals with Montgomery-friendly primes designed for the modular reduction
algorithm of Montgomery. These numbers are scattered in the literature and their properties …

Signature gateway: Offloading signature generation to IoT gateway accelerated by GPU

CC Chang, WK Lee, Y Liu, BM Goi… - IEEE Internet of Things …, 2018 - ieeexplore.ieee.org
The emergence of Internet of Things (IoT) brings us the possibility to form a well connected
network for ubiquitous sensing, intelligent analysis, and timely actuation, which opens up …

Single base modular multiplication for efficient hardware RNS implementations of ECC

K Bigou, A Tisserand - … Hardware and Embedded Systems--CHES 2015 …, 2015 - Springer
The paper describes a new RNS modular multiplication algorithm for efficient
implementations of ECC over F _P FP. Thanks to the proposition of RNS-friendly Mersenne …

RNS montgomery reduction algorithms using quadratic residuosity

S Kawamura, Y Komano, H Shimizu… - Journal of Cryptographic …, 2019 - Springer
The residue number system (RNS) is a method for representing an integer as an n-tuple of
its residues with respect to a given base. Since RNS has inherent parallelism, it is actively …

Efficient cryptographic hardware for safety message verification in internet of connected vehicles

MA Mehrabi, A Jolfaei - ACM Transactions on Internet Technology, 2022 - dl.acm.org
An important security requirement in automotive networks is to authenticate, sign, and verify
thousands of short messages per second by each vehicle. This requirement mandates the …