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Remarks on Quaternions/Octonion Based Diffie-Hellman Key Exchange Protocol Submitted to NIST PQC Project
Diffie-Hellman key agreement NIST PQC Project
2018/1/2
In November 2017, Juan edro Hecht and Jorge Alejandro Kamlofsky submitted a quaternions/octonions based Diffie-Hellman key agreement protocol HK17 to NIST post quantum cryptography project. Daniel J. ...
Impurity and quaternions in nonrelativistic scattering from a quantum memory
Impurity and quaternions nonrelativistic scattering quantum memory
2015/10/16
Models of quantum computing rely on transformations of the states of a quantum memory. We study mathematical aspects of a model proposed by Wu in which the memory state is changed via the scattering o...
Factorization of Matrices of Quaternions
Factorization Matrices Quaternions Operator Algebras
2011/8/24
Abstract: We review known factorization results in quaternion matrices. Specifically, we derive the Jordan canonical form, polar decomposition, singular value decomposition, the QR factorization. We p...
Branching of the W(H4) Polytopes and Their Dual Polytopes under the Coxeter Groups W(A4) and W(H3) Represented by Quaternions
Dual Polytopes the W(H4) Polytopes Quaternions
2011/7/26
Abstract: 4-dimensional H4 polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group W(H4) where the group elements and the vertices of the polytopes are represe...
Minimal Polynomials of Some Matrices Via Quaternions
Minimal Polynomials Matrices Quaternions
2010/12/16
This work provides explicit characterizations and formulae for the minimal polynomials of
a wide variety of structured 4 × 4 matrices. These include symmetric, Hamiltonian and orthogonal matrices. Ap...
Minimal Polynomials of Some Matrices Via Quaternions
Minimal Polynomials Some Matrices Via Quaternions
2010/11/26
This work provides explicit characterizations and formulae for the minimal polynomials of
a wide variety of structured 4 × 4 matrices. These include symmetric, Hamiltonian and
orthogonal matrices. A...
Minimal Polynomials of Some Matrices Via Quaternions
Minimal Polynomials Matrices Quaternions
2010/12/16
This work provides explicit characterizations and formulae for the minimal polynomials of
a wide variety of structured 4 × 4 matrices. These include symmetric, Hamiltonian and
orthogonal matrices. A...
Dual Quaternions in Spatial Kinematics in an Algebraic Sense
Dual quaternions Hamilton operators Lie algebras
2010/2/25
This paper presents the finite spatial displacements and spatial screw motions by using dual quaternions and Hamilton operators. The representations are considered as 4 \times 4 matrices and the relat...