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2020 | OriginalPaper | Chapter

Homomorphic Data Concealment Powered by Clifford Geometric Algebra

Authors : David W. H. A. da Silva, Marcelo A. Xavier, Philip N. Brown, Edward Chow, Carlos Paz de Araujo

Published in: Advances in Computer Graphics

Publisher: Springer International Publishing

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Abstract

We propose general-purpose methods for data representation and data concealment via multivector decompositions and a small subset of functions in the three dimensional Clifford geometric algebra. We demonstrate mechanisms that can be explored for purposes from plain data manipulation to homomorphic data processing with multivectors. The wide variety of algebraic representations in Clifford geometric algebra allow us to explore concepts from integer, complex, vector and matrix arithmetic within a single, compact, flexible and yet powerful algebraic structure in order to propose novel homomorphisms. Our constructions can be incorporated into existing applications as add-ons as well as used to provide standalone data-centric algorithms. We implement our representation and concealment mechanisms in the Ruby programming language to demonstrate the ideas discussed in this work.

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Title: Homomorphic Data Concealment Powered by Clifford Geometric Algebra
Authors: David W. H. A. da Silva
Marcelo A. Xavier
Philip N. Brown
Edward Chow
Carlos Paz de Araujo
Publisher: Springer International Publishing
Book: Advances in Computer Graphics
Print ISBN: 978-3-030-61863-6

Electronic ISBN: 978-3-030-61864-3

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-61864-3_44

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