Results 1 to 10 of about 4,862 (157)

Montgomery Reduction for Gaussian Integers [PDF]

Cryptography, 2021
Modular arithmetic over integers is required for many cryptography systems. Montgomery reduction is an efficient algorithm for the modulo reduction after a multiplication. Typically, Montgomery reduction is used for rings of ordinary integers.
Freudenberger Jürgen, Malek Safieh
exaly   +5 more sources

The group of primitive Pythagorean triples over Gaussian integers [PDF]

Heliyon, 2023
A group structure of the set of primitive Pythagorean triples over Gaussian integers is investigated. In addition, we show that it is a free abelian group.
Ekkasit Sangwisut
exaly   +4 more sources

SPN based RGB image encryption over Gaussian integers [PDF]

Heliyon
This research paper proposes a novel approach for constructing substitution boxes (S-boxes) over Gaussian integers, which are complex numbers with integer coefficients.
Bander Almutairi, Qin Xin, Tariq Shāh   +2 more
exaly   +4 more sources

Prime labeling of families of trees with Gaussian integers

AKCE International Journal of Graphs and Combinatorics, 2016
A graph on n vertices is said to admit a prime labeling if we can label its vertices with the first n natural numbers such that any two adjacent vertices have relatively prime labels.
Steven Klee
exaly   +3 more sources

ON THE DISTRIBUTION OF THE GREATEST COMMON DIVISOR OF GAUSSIAN INTEGERS. [PDF]

Involve, 2016
For a pair of random Gaussian integers chosen uniformly and independently from the set of Gaussian integers of norm $x$ or less as $x$ goes to infinity, we find asymptotics for the average norm of their greatest common divisor, with explicit error terms.
Bradley TD, Cheng YC, Luo YF.
europepmc   +6 more sources

Modeling Toroidal Networks with the Gaussian Integers

IEEE Transactions on Computers, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Esteban Stafford, Carmen Martinez, Miquel Moreto Planas   +2 more
exaly   +3 more sources

SRAM based Gaussian noise generation for post quantum cryptography [PDF]

Scientific Reports
As quantum computing progresses, conventional public-key cryptographic schemes such as RSA and ECC face increasing vulnerability to quantum attacks.
Moon-Seok Kim, Seung-Bae Jeon, Sungho Kim   +2 more
doaj   +2 more sources

The minimal Euclidean function on the Gaussian integers

Indagationes Mathematicae, 2023
In 1949, Motzkin proved that every Euclidean domain $R$ has a minimal Euclidean function, $ϕ_R$. He showed that when $R = \mathbb{Z}$, the minimal function is $ϕ_{\mathbb{Z}}(x) = \lfloor \log_2 |x| \rfloor$. For over seventy years, $ϕ_{\mathbb{Z}}$ has been the only example of an explictly-computed minimal function in a number field. We give the first
Hester Graves
exaly   +4 more sources

Multiple color images security by SPN over the residue classes of Gaussian integer $$\:Z{\left[i\right]}_{h}$$ [PDF]

Scientific Reports
In this paper, the authors present the design of a new pair of 8 × 8 S-boxes over the residue classes of Gaussian integers $$\:Z{\left[i\right]}_{h}$$ and their usage for the encryption of multiple RGB images using a three-stage Substitution-Permutation ...
Muhammad Sajjad, Tariq Shah, Rafik Hamza, Bander Almutairi, Robinson Julian Serna   +4 more
doaj   +2 more sources

Reliability-Based Decoding of Low-Density Lattice Codes Using Gaussian and Eisenstein Integers

IEEE Open Journal of the Communications Society
This paper proposes reliability-based decoding for complex low-density lattice codes (CLDLC) which can be applied to both Gaussian and Eisenstein integers.
Brian M Kurkoski, Warangrat Wiriya
exaly   +3 more sources