Multivariate Cryptosystems for Secure Processing of Multidimensional Signals
This work addresses privacy-preserving processing of sensitive multidimensional signals in untrustworthy environments, representing a domain-specific advancement.
The paper tackles the challenge of efficiently processing encrypted multidimensional signals like images and videos by introducing a new cryptographic hard problem called m-RLWE and related techniques, resulting in a cryptosystem that outperforms RLWE in security, efficiency, and cipher expansion for encrypted image processing.
Multidimensional signals like 2-D and 3-D images or videos are inherently sensitive signals which require privacy-preserving solutions when processed in untrustworthy environments, but their efficient encrypted processing is particularly challenging due to their structure, dimensionality and size. This work introduces a new cryptographic hard problem denoted m-RLWE (multivariate Ring Learning with Errors) which generalizes RLWE, and proposes several relinearization-based techniques to efficiently convert signals with different structures and dimensionalities. The proposed hard problem and the developed techniques give support to lattice cryptosystems that enable encrypted processing of multidimensional signals and efficient conversion between different structures. We show an example cryptosystem and prove that it outperforms its RLWE counterpart in terms of security against basis-reduction attacks, efficiency and cipher expansion for encrypted image processing, and we exemplify some of the proposed transformation techniques in critical and ubiquitous block-based processing applications