Results 1 to 10 of about 2,777,888 (247)

Degree of the Product of Two Algebraic Numbers One of Which Is of Prime Degree

Mathematics, 2023
Let α and β be two algebraic numbers such that deg(α)=m and deg(β)=p, where p is a prime number not dividing m. This research is focused on the following two objectives: to discover new conditions under which deg(αβ)=mp; to determine the complete list of
Paulius Virbalas
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Influence of the Linear Layer on the Algebraic Degree in SP-Networks

IACR Transactions on Symmetric Cryptology, 2022
We consider SPN schemes, i.e., schemes whose non-linear layer is defined as the parallel application of t ≥ 1 independent S-Boxes over F2n and whose linear layer is defined by the multiplication with a (n · t) × (n · t) matrix over F2.
Carlos Cid, Lorenzo Grassi, Aldo Gunsing, Reinhard Lüftenegger, Christian Rechberger, Markus Schofnegger   +5 more
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On the Degree of Product of Two Algebraic Numbers

Mathematics, 2023
A triplet (a,b,c) of positive integers is said to be product-feasible if there exist algebraic numbers α, β and γ of degrees (over Q) a, b and c, respectively, such that αβγ=1.
Lukas Maciulevičius
doaj   +1 more source

Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve

Journal of Mathematical Sciences and Modelling, 2021
In this paper, we give a parametrization of algebraic points of degree at most $4$ over $\mathbb{Q}$ on the schaeffer curve $\mathcal{C}$ of affine equation : $ y^{2}=x^{5}+1 $. The result extends our previous result which describes in [5] ( Afr.
Moussa Fall
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Creation of Problems by Prospective Teachers to Develop Proportional and Algebraic Reasonings in a Probabilistic Context

Education Sciences, 2023
To promote optimal learning in their students, mathematics teachers must be proficient in problem posing, making this skill a cornerstone in teacher training programs.
Nicolás Tizón-Escamilla, María Burgos
doaj   +1 more source

New Constructions of balanced Boolean functions with maximum algebraic immunity, high nonlinearity and optimal algebraic degree

Walailak Journal of Science and Technology, 2019
This paper consists of proposal of two constructions of balanced Boolean functions by using powers of primitive elements ...
Dheeraj Kumar Sharma, Rajoo Pandey
doaj   +1 more source

Constructing Odd-Variable Rotation Symmetric Boolean Functions With Optimal AI and Higher Nonlinearity

IEEE Access, 2019
As a part of the field of cryptography, rotation symmetric Boolean functions have rich cryptographic significance. In this paper, based on the knowledge of integer compositions, we present a new construction of odd-variable rotation symmetric Boolean ...
Yindong Chen, Lumin Liao, Fei Guo, Weihong Cai   +3 more
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On the Generalization of Butterfly Structure

IACR Transactions on Symmetric Cryptology, 2018
Butterfly structure was proposed in CRYPTO 2016 [PUB16], and it can generate permutations ...
Yongqiang Li, Shizhu Tian, Yuyin Yu, Mingsheng Wang   +3 more
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Constructing Higher Nonlinear Odd-Variable RSBFs With Optimal AI and Almost Optimal FAI

IEEE Access, 2019
Rotation symmetric Boolean functions (RSBFs) are nowadays studied a lot because of its easy operations and good performance in cryptosystem. This paper constructs a new class of odd-variable RSBFs with optimal algebraic immunity (AI). The nonlinearity of
Yindong Chen, Limin Lin, Lumin Liao, Jie Ruan, Fei Guo, Weihong Cai   +5 more
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Point counting for foliations over number fields

Forum of Mathematics, Pi, 2022
Let${\mathbb M}$ be an affine variety equipped with a foliation, both defined over a number field ${\mathbb K}$. For an algebraic $V\subset {\mathbb M}$ over ${\mathbb K}$, write $\delta _{V}$ for the maximum of the degree and log-height of V.
Gal Binyamini
doaj   +1 more source