Conceptual review on number theoretic transform and comprehensive review on its implementations

A Satriawan, I Syafalni, R Mareta, I Anshori… - IEEE …, 2023 - ieeexplore.ieee.org
The Number Theoretic Transform (NTT) is a powerful mathematical tool that has become
increasingly important in developing Post Quantum Cryptography (PQC) and Homomorphic …

[图书][B] 17 Lectures on Fermat numbers: from number theory to geometry

M Krizek, F Luca, L Somer - 2013 - books.google.com
The pioneering work of French mathematician Pierre de Fermat has attracted the attention of
mathematicians for over 350 years. This book was written in honor of the 400th anniversary …

Video filtering with Fermat number theoretic transforms using residue number system

T Toivonen, J Heikkila - … on Circuits and Systems for Video …, 2005 - ieeexplore.ieee.org
We investigate image and video convolutions based on Fermat number transform (FNT)
modulo q= 2/sup M/+ 1 where M is an integer power of two. These transforms are found to …

Exploring the Advantages and Challenges of Fermat NTT in FHE Acceleration

A Kim, AC Mert, A Mukherjee, A Aikata… - Annual International …, 2024 - Springer
Recognizing the importance of a fast and resource-efficient polynomial multiplication in
homomorphic encryption, in this paper, we design a multiplier-less number theoretic …

A Complete Beginner Guide to the Number Theoretic Transform (NTT)

A Satriawan, R Mareta, H Lee - Cryptology ePrint Archive, 2024 - eprint.iacr.org
Abstract The Number Theoretic Transform (NTT) is a powerful mathematical tool that has
become increasingly important in developing Post Quantum Cryptography (PQC) and …

[图书][B] From great discoveries in number theory to applications

M Křížek, L Somer, A Šolcová - 2021 - Springer
We encounter integer numbers daily, and they are literally everywhere around us. It is not
possible to avoid them, ignore them, or to be indifferent to them. So let us take together a …

SOME IDENTITIES OF k-MERSENNE NUMBERS.

K Uslu, V Deniz - Advances & Applications in Discrete …, 2017 - search.ebscohost.com
SOME IDENTITIES OF k-MERSENNE NUMBERS Page 1 Advances and Applications in
Discrete Mathematics © 2017 Pushpa Publishing House, Allahabad, India http://www.pphmj.com …

Efficient SIMD arithmetic modulo a Mersenne number

JW Bos, T Kleinjung, AK Lenstra… - 2011 IEEE 20th …, 2011 - ieeexplore.ieee.org
This paper describes carry-less arithmetic operations modulo an integer 2^ M-1 in the
thousand-bit range, targeted at single instruction multiple data platforms and applications …

Fragile watermarking using finite field trigonometrical transforms

RJ Cintra, VS Dimitrov, HM de Oliveira… - Signal Processing …, 2009 - Elsevier
Fragile digital watermarking has been applied for authentication and alteration detection in
images. Utilizing the cosine and Hartley transforms over finite fields, a new transform domain …

Theory of filter banks over finite fields

T Cooklev, A Nishihara… - Proceedings of APCCAS' …, 1994 - ieeexplore.ieee.org
The theory of digital filter banks for subband coding is well developed. The purpose of this
paper is to develop an analogous framework for the multiresolution analysis of sequences of …