Privacy–Preserving Text Similarity via Non-Prefix-Free Codes

Abstract

Many methods have been proposed to compute the similarity score $\alpha \leftarrow S(\mathcal {A},\mathcal {B})$ in between two plain documents $\mathcal {A}$ and $\mathcal {B}$. However, when their contents are confidential, special processing is required to protect privacy. A great extent of the solutions offered to date is mostly based on homomorphic encryption or secure multi-party computation techniques, where their computational cost inhibits the practical usage, especially on massive sets. In this study we propose an alternative by encoding the documents with non-prefix-free (NPF) coding before applying the preferred similarity metric S(). The NPF coding simply represents the symbols with variable-length codewords, where the codeword set is generated without the prefix-free restriction. Thus, a codeword may be a prefix of another, and without the explicit codeword boundary information, retrieving the original data from the encoded stream becomes hard due to the lack of unique decodability in non-prefix-free codes. We provide the combinatorial analysis of this hardness, and experimentally compare the similarity scores obtained on NPF encoded documents and on original plain text versions. We have considered normalized compression distance (NCD) and Jaccard coefficient (JC) for the similarity metric S(). When $\mathcal {A^\prime }$ and $\mathcal {B^\prime }$ denote the NPF-encoded documents, experiments conducted on METER corpus revealed that the difference between $\alpha ^\prime \leftarrow S(\mathcal {A^\prime },\mathcal {B^\prime })$ and $\alpha \leftarrow S(\mathcal {A},\mathcal {B})$ lie in the range of $0.5\%$ and $3\%$ for both NCD and JC.

This work has been supported by the TÜBİTAK grant number 117E865.