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Homomorphic Data Concealment Powered by Clifford Geometric Algebra

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

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.

Keywords

  • Data concealment
  • Data hiding
  • Homomorphisms
  • Multivector packing
  • Clifford geometric algebra

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

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

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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: , 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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