Results 21 to 30 of about 391,951 (282)

Towards quantized complex numbers: $q$-deformed Gaussian integers and the Picard group [PDF]

Open Communications in Nonlinear Mathematical Physics, 2021
This work is a first step towards a theory of "$q$-deformed complex numbers". Assuming the invariance of the $q$-deformation under the action of the modular group I prove the existence and uniqueness of the operator of translations by~$i$ compatible with
Valentin Ovsienko
doaj   +1 more source

An asymmetric cryptography using Gaussian integers

Engineering and Applied Science Research, 2020
In this paper, the already strong McEliece cryptosystem is enhanced with atwo-dimensional finite Gaussian integer. By substituting the one-dimensional linear code with atwo-dimensional code employing afinite Gaussian integer, anew system ...
Wanarat Juraphanthong, Suradet Jitprapaikulsarn   +1 more
doaj   +1 more source

On Generation of the Groups $SL_n(\mathbb{Z}+i\mathbb{Z})$ and $PSL_n(\mathbb{Z}+i\mathbb{Z})$ by Three Involutions, Two of Which Commute

Известия Иркутского государственного университета: Серия "Математика", 2022
M. C. Tamburini and P. Zucca proved that the special linear group of dimension greater than 13 over the ring of Gaussian integers is generated by three involutions, two of which commute (J. of Algebra, 1997).
R. I. Gvozdev, Ya.N. Nuzhin, T. B. Shaipova   +2 more
doaj   +1 more source

Improved Bernoulli Sampling for Discrete Gaussian Distributions over the Integers

Mathematics, 2021
Discrete Gaussian sampling is one of the fundamental mathematical tools for lattice-based cryptography. In this paper, we revisit the Bernoulli(-type) sampling for centered discrete Gaussian distributions over the integers, which was proposed by Ducas et
Shaohao Xie, Shaohua Zhuang, Yusong Du
doaj   +1 more source

Generic, efficient and isochronous Gaussian sampling over the integers

Cybersecurity, 2022
Gaussian sampling over the integers is one of the fundamental building blocks of lattice-based cryptography. Among the extensively used trapdoor sampling algorithms, it is ineluctable until now. Under the influence of numerous side-channel attacks, it is
Shuo Sun, Yongbin Zhou, Yunfeng Ji, Rui Zhang, Yang Tao   +4 more
doaj   +1 more source

Code-Based Cryptography With Generalized Concatenated Codes for Restricted Error Values

IEEE Open Journal of the Communications Society, 2022
Code-based cryptosystems are promising candidates for post-quantum cryptography. Recently, generalized concatenated codes over Gaussian and Eisenstein integers were proposed for those systems. For a channel model with errors of restricted weight, those q-
Johann-Philipp Thiers, Jurgen Freudenberger   +1 more
doaj   +1 more source

On automatic subsets of the Gaussian integers [PDF]

Indagationes Mathematicae, 2017
Suppose that $a$ and $b$ are multiplicatively independent Gaussian integers, that are both of modulus~$\geq \sqrt 5$. We prove that there exist a $X\subset \mathbb Z[i]$ which is $a$-automatic but not $b$-automatic. This settles a problem of Allouche, Cateland, Gilbert, Peitgen, Shallit, and Skordev.
Bosma, W., Fokkink, R., Krebs, T.
openaire   +3 more sources

An Algorithm for Finding Self-Orthogonal and Self-Dual Codes Over Gaussian and Eisenstein Integer Residue Rings Via Chinese Remainder Theorem

IEEE Access, 2023
A code over Gaussian or Eisenstein integer residue ring is an additive group of vectors with entries in this integer residue ring which is closed under the action of constant multiplication by the Gaussian or Eisenstein integers. In this paper, we define
Hajime Matsui
doaj   +1 more source

An objective representation of the Gaussian integers

Journal of Symbolic Computation, 2004
A rig is a ring without negatives. We analyse the free rig on a generator x subject to the equivalence x∼1+x+x2, showing that in it the non-constant polynomials form a ring. This ring can be identified with the Gaussian integers, which thus acquire objective meaning.
Fiore, Marcelo, Leinster, Tom
openaire   +3 more sources

Gaussian integers: an introductory approach to arithmetic aspects compared to the set of integers [PDF]

, 2023
In this research, the set of Gaussian integers is presented with a comparative basis to the set of integers. Thus, the aim of the research is to understand the set of Gaussian integers by presenting the arithmetical theory through an analogy with the ...
Lima, Elias da Silva
core   +1 more source