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Homomorphic Data Concealment Powered by Clifford Geometric Algebra

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Advances in Computer Graphics (CGI 2020)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12221))

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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.

Originally with University of Colorado Colorado Springs and is now with Ford Motor Company.

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Author information

Authors and Affiliations

  1. University of Colorado at Colorado Springs, Colorado Springs, CO, 80918, USA

    David W. H. A. da Silva, Philip N. Brown, Edward Chow & Carlos Paz de Araujo

  2. Ford Motor Company, Dearborn, MI, 48124, USA

    Marcelo A. Xavier

Authors
  1. David W. H. A. da Silva
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  2. Marcelo A. Xavier
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  3. Philip N. Brown
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  4. Edward Chow
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  5. Carlos Paz de Araujo
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Corresponding author

Correspondence to David W. H. A. da Silva .

Editor information

Editors and Affiliations

  1. University of Geneva, Geneva, Switzerland

    Nadia Magnenat-Thalmann

  2. University of Crete, Heraklion, Greece

    Constantine Stephanidis

  3. University of Macau, Macau, China

    Enhua Wu

  4. Swiss Federal Institute of Technology, Lausanne, Switzerland

    Daniel Thalmann

  5. Shanghai Jiao Tong University, Shanghai, China

    Bin Sheng

  6. University of Sydney, Sydney, Australia

    Jinman Kim

  7. University of Crete, Heraklion, Greece

    George Papagiannakis

  8. University of Calgary, Calgary, AB, Canada

    Marina Gavrilova

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da Silva, D.W.H.A., Xavier, M.A., Brown, P.N., Chow, E., de Araujo, C.P. (2020). Homomorphic Data Concealment Powered by Clifford Geometric Algebra. In: Magnenat-Thalmann, N., et al. Advances in Computer Graphics. CGI 2020. Lecture Notes in Computer Science(), vol 12221. Springer, Cham. https://doi.org/10.1007/978-3-030-61864-3_44

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  • DOI: https://doi.org/10.1007/978-3-030-61864-3_44

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-61863-6

  • Online ISBN: 978-3-030-61864-3

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