scholarly journals A Generalised Approach on Generation of Commutative Matrix

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Biswanath Rath ◽  
Keyword(s):  
Commutative Matrix

scholarly journals Non-Commutative Key Exchange Protocol

2021 ◽  
Author(s):  
Luis Adrián Lizama-Pérez ◽  
José Mauricio López Romero
Keyword(s):  
Discrete Logarithm ◽  
Matrix Multiplication ◽  
Key Exchange ◽  
Security Level ◽  
Search Problem ◽  
Key Exchange Protocol ◽  
Secret Communication ◽  
Perfect Forward Secrecy ◽  
Iot Devices ◽  
Commutative Matrix

We introduce a novel key exchange protocol based on non-commutative matrix multiplication defined in $\mathbb{Z}_p^{n \times n}$. The security of our method does not rely on computational problems as integer factorization or discrete logarithm whose difficulty is conjectured. We claim that the unique eavesdropper's opportunity to get the secret/private key is by means of an exhaustive search which is equivalent to the unsorted database search problem. Furthermore, we show that the secret/private keys become indistinguishable to the eavesdropper. Remarkably, to achieve a 512-bit security level, the keys (public/private) are of the same size when matrix multiplication is done over a reduced 8-bit size modulo. Also, we discuss how to achieve key certification and Perfect Forward Secrecy (PFS). Therefore, Lizama's algorithm becomes a promising candidate to establish shared keys and secret communication between (IoT) devices in the quantum era.

Simulating the scalar field using the fuzzy sphere

2003 ◽  
Vol 18 (33n35) ◽  
pp. 2389-2396 ◽  
Author(s):  
XAVIER MARTIN
Keyword(s):  
Scalar Field ◽  
Numerical Scheme ◽  
Approximation Scheme ◽  
Fuzzy Sphere ◽  
Continuous Space ◽  
The Real ◽  
Matrix Algebras ◽  
Real Scalar ◽  
Fuzzy Space ◽  
Commutative Matrix

Fuzzy spaces provide a new approximation scheme using (non–commutative) matrix algebras to approximate the algebra of function of the continuous space. This paper describes how to implement a numerical scheme based on a fuzzy space approximation. In this first attempt, the simplest fuzzy space and field theory, respectively the fuzzy two–sphere and the real scalar field, are used to simulate the real scalar field on the plane. Along the way, this method is compared to its traditional lattice discretisation equivalent.

scholarly journals Karakteristik Matriks sebagai Daerah Asal Suatu Logaritma

2018 ◽  
Vol 6 (1) ◽  
pp. 60
Author(s):  
Era Dewi Kartika
Keyword(s):  
Positive Characteristic ◽  
Identity Matrix ◽  
Singular Matrix ◽  
Natural Logarithm ◽  
The Matrix ◽  
Characteristic Values ◽  
Commutative Matrix ◽  
Jordan Matrix ◽  
Logarithm Function ◽  
Square Matrix

Abstrak Rumus umum fungsi logaritma asli dengan daerah asal suatu matriks adalah ln⁡A=T S_((J_A ) ) {ln⁡〖(λ_1 I^((p_1 ) )+H^((p_1 ) ) ),ln⁡(λ_2 I^((p_2 ) )+H^((p_2 ) ) ),…,ln⁡(λ_u I^((p_u ) )+H^((p_u ) ) ) 〗 } 〖S_((J_A ) )〗^(-1) T^(-1) dengan T adalah matriks non-singular dimana A=TJ_A T^(-1), S_((J_A ) )adalah sebarang matriks yang komutatif dengan J_A, J_A adalah matriks Jordan dari matriks A, λ_i adalah nilai karakteristik dari pembagi elementer A, I adalah matriks identitas dan H^((p)) adalah matriks berukuran p×p yang mempunyai 1 sebagai anggota pada superdiagonal pertama dan 0 untuk lainnya. Karakteristik matriks A sebagai daerah asal suatu fungsi logaritma adalah matriks persegi yang non-singular dengan nilai-nilai karakteristik real positif Kata Kunci: matriks, daerah asal, logaritma asli Abstract The general formula of the natural logarithm function with domain of a matrix is ln⁡A=T S_((J_A ) ) {ln⁡〖(λ_1 I^((p_1 ) )+H^((p_1 ) ) ),ln⁡(λ_2 I^((p_2 ) )+H^((p_2 ) ) ),…,ln⁡(λ_u I^((p_u ) )+H^((p_u ) ) ) 〗 } 〖S_((J_A ) )〗^(-1) T^(-1) with T is the non-singular matrix which A=TJ_A T^(-1), S_((J_A ) ) is any commutative matrix with J_A, J_Ais the Jordan matrix of the matrix A, λ_i is the characteristic value of the elementary divider A, I is the identity matrix and H^((p)) is a square matrix which has 1 as a member of the first superdiagonal and 0 for other. The characteristic of matrix A as domain of a natural logarithm function is a non-singular square matrix with real positive characteristic values Keywords: matrix, domain, natural logarithm

A Maximality Criterion for Nilpotent Commutative Matrix Algebras

1974 ◽  
Vol 17 (1) ◽  
pp. 125-126
Author(s):  
D. Handelman ◽  
P. Selick
Keyword(s):  
Commutative Algebra ◽  
Nilpotency Class ◽  
Matrix Algebras ◽  
Commutative Subalgebra ◽  
Commutative Matrix

Let A be a commutative algebra contained in Mn(F), F a field. Then A is nilpotent if there exists v such that Av=(0), and is said to have nilpotency class k (denoted Cl(A)=k) if Ak=(0), but Ak-1≠(0). A well known result asserts that matrix algebras are nilpotent if and only if every element is nilpotent. Let N = {A | A is a nilpotent commutative subalgebra of Mn(F)}.

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