An Efficient Homomorphic Data Encoding with Multiple Secret Hensel Codes

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.