Abstract—Data encoding is widely used for a variety of
reasons. Encoding schemes in general serve to convert one form
of data to another in order to enhance the efficiency of data
storage, transmission, computation and privacy, to name just a
few. When it comes to privacy, data may be encoded to hide its
meaning from direct access or encrypted to attain a certain
security level. If the encoding scheme preserves additive and
multiplicative homomorphisms, then operations on encoded
data may be performed without prior decoding, which improves
the utility of such mechanism. We introduce a probabilistic fully
homomorphic encoding scheme that is practical as a
stand-alone entry-level solution to data privacy or as an added
component of existing encryption schemes, especially those that
are deterministic. We demonstrate how the finite segment of
p-adic numbers can be explored to derive probabilistic multiple
secret Hensel codes which yields multiple layers of obscurity in
an efficient way. Our encoding scheme is compact, ultra
lightweight and suitable for applications ranging from edge to
cloud computing. Without significant changes in its
mathematical foundation, as a proposed continuation of this
present work, further investigation can take place in order to
confirm if the same encoding scheme can be extended to be a
standalone secure instance of a fully homomorphic encryption
scheme.
Index Terms—Data encoding, p-adic numbers, g-adic
numbers, hensel code, secret Hensel codes, homomorphic
encoding.
David W. H. A. da Silva, Carlos Paz de Araujo, and Edward Chow are
with are the University of Colorado at Colorado Springs, CO 80918 USA
(e-mail: dhonorio@uccs.edu, cpazdear@uccs.edu, cchow@uccs.edu).
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Cite:David W. H. A. da Silva, Carlos Paz de Araujo, and Edward Chow, "An Efficient Homomorphic Data Encoding with Multiple Secret Hensel Codes," International Journal of Information and Electronics Engineering vol. 10, no. 1, pp. 5-15, 2020.
