Homomorphic Data Concealment Powered by Clifford Geometric Algebra

被引：1

作者：

da Silva, David W. H. A. ^{[1
]}

Xavier, Marcelo A. ^{[2
]}

Brown, Philip N. ^{[1
]}

Chow, Edward ^{[1
]}

de Araujo, Carlos Paz ^{[1
]}

机构：

[1] Univ Colorado Colorado Springs, Colorado Springs, CO 80918 USA

[2] Ford Motor Co, Dearborn, MI 48124 USA

来源：

ADVANCES IN COMPUTER GRAPHICS, CGI 2020 | 2020年 / 12221卷

关键词：

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

D O I：

10.1007/978-3-030-61864-3_44

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

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.

引用

页码：513 / 525

页数：13

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