Homomorphic lattice cryptosystems for secure signal processing

Resumo

Signal processing has become ubiquitous in our daily lives, being present in everyday digital appliances and applications. Actually, although apparently it is hard to be aware of its presence, it does have a great influence on our everyday life and the list of applications and science fields which make use of signal processing tools is accordingly huge: it encompasses communication and entertainment technologies, from speech and audio processing to image and video analysis (e.g., biometric processing of faces, fingerprints, iris, etc.), with a strong impact on emerging applications such as smart grids, autonomous driving, tele-diagnosis and analysis of medical signals (like Electrocardiograms or DNA), among others. This is especially relevant because, although in our everyday life we are not really conscious of the possible risks, many of the previous scenarios involve the use of very privacy-sensitive data (e.g., a service which depends on the use of personal information). This becomes even worse in many of the most prominent signal processing applications, where the involved signals have to be processed by untrusted parties (i.e., the service provider requires the use of the personal information for the correct operation of the service), and the user must trust the service provider. The field of Secure Signal Processing (SSP) was born to address these challenges, by devising efficient solutions stemming from the collaborative efforts of cryptography and signal processing. Due to its inherent multidisciplinary grounds, it can effectively combine and take advantage of the advances and technologies from the two disciplines. Additionally, numerous applications have been already proposed based on the use of different cryptographic techniques. This thesis proposes novel methods for privacy protection when dealing with highly privacy-sensitive signals in untrustworthy environments. With this goal in mind, the thesis was originally motivated by the following two research lines: (1) privacy protection when dealing with multidimensional signals, and (2) design of new primitives and protocols for encrypted signal processing. In particular, the work presented in this thesis introduces a secure framework for outsourced and unattended (multidimensional) signal processing; that is, the proposed solutions do not need the intervention of the secret key owner in the middle of the process. The contributions are numerous and their outcomes range from low-level cryptographic primitives to more concrete high-level practical applications. Next, we briefly enumerate the main contributions: (1) We formalize a lattice hard problem denoted as multivariate RLWE (Ring Learning with Errors). Due to its particular structure, it is especially useful to work with multidimensional signals. It also brings about efficiency improvements on current RLWE-based cryptographic primitives. (2) Building on modern lattice-based primitives, we present a toolbox for unattended secure signal processing (e.g., filtering, generalized convolutions, error correcting codes or matrix-based processing, among others). (3) We exemplify the use of the proposed tools on several concrete signal processing scenarios (going from genomics to multimedia applications), where we face the additional difficulties which arise in each specific application due to the nature of the used signals.