Abstract
Image/video compression is a widely used operation in our everyday life. Such an operation usually proceeds independantly on small rectangular portions, so-called macroblocks, and is mainly divided into four operations: color conversion, Discrete Cosine Transform (DCT), quantization and entropic encoding. This operation is carried out easily on non-encrypted image. In this paper, we consider the case where such an execution is done in the encrypted domain. In fact, this is today one central question related to individuals’ privacy since such image/video compression is most of the time done on the premises of a service provider data center, and pictures are potentially sensitive personal data. Thus, the capacity for such entity to perform an action “blindfolded”, that is not knowing the underlying input in plain, is an important topic since it permits to obtain both individual privacy and data usability.
In this context, one of the main cryptographic tool is (fully) homomorphic encryption (FHE), that permits to perform operations while keeping the data encrypted. We here consider two different instantiations of FHE, one for which the plaintext space is binary (\(\mathbb {Z}_2\)) and the other a modular space (\(\mathbb {Z}_p\) for an integer \(p> 2 \)), and compare them when running the well-known H264 and HEVC macroblock processing pipelines.
Our contribution is twofold. On one hand, we provide an exhaustive comparison between FHEs over \(\mathbb {Z}_2\) and FHEs over \(\mathbb {Z}_p\) (\(p>2\)) in terms of functional capabilities, multiplicative depth and real performances using several existing FHE implementations, over libraries such as Cingulata, SEAL and TFHE. On the other hand, we apply this to image compression in the encrypted domain, being the first to “crypto-compress” a full encrypted photograph with practically relevant performances.
This work was supported in part by projects PerSoCLoud (for the two first authors) and CRYPTOCOMP (for the third author).
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Notes
- 1.
Cingulata transforms a C++ program in the boolean circuit and execute it over bitewise encrypted data. It also enables to choose the underground FHE which encrypts input data. The current version is based on the FV FHE scheme.
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Nokam Kuate, D., Canard, S., Sirdey, R. (2018). Towards Video Compression in the Encrypted Domain: A Case-Study on the H264 and HEVC Macroblock Processing Pipeline. In: Camenisch, J., Papadimitratos, P. (eds) Cryptology and Network Security. CANS 2018. Lecture Notes in Computer Science(), vol 11124. Springer, Cham. https://doi.org/10.1007/978-3-030-00434-7_6
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