Thales UK has been investigating the use of Homomorphic Encryption (HE) in satellite scenarios. In particular, our assessment has focused on the data processing of imaging products; one of the many types of signal processing applications which could have been chosen.
It is relatively simple to find signal processing satellite applications where HE could, in theory at least, provide real benefit. In particular, to provide end-to-end security of data from the sensor on the satellite to the end user, while allowing the potentially complex and specialised signal processing to be performed on shared (and less trusted from the end user’s point of view) infrastructure. The real challenge has been to find such applications that are potentially practical in the near term, using Somewhat Homomorphic Encryption (SHE).
Consider the Sentinel 2 Multi Spectral Imager which is a representative example of an earth observation satellite (in this case designed for environmental monitoring). In order to be suitable for the application of HE to provide sensor to end user security, all the signal processing algorithms would have to be amenable to HE. It turns out that many of them potentially are, in particular the deconvolution algorithms that use Fourier Transforms. However, other parts of the processing are more difficult to deal with in HE. For example, processing to deal with imperfections such as:
- saturated pixels
- no data pixels and partially corrected pixels (crosstalk correction)
- defective pixels
These are very simple algorithms, but involve a lot of conditional operators (<, >, etc. to test pixel values) that would be expensive when implemented on HE encrypted data.
A much more promising candidate is Synthetic Aperture Radar (SAR) (e.g. Envisat). SAR is used to provide high precision, and often 3D, imaging for applications such as sea ice and glacier monitoring, vegetation coverage analysis, disaster monitoring and traffic surveillance. Being a radio-based technique, it is not affected by weather or the lack of daylight. The raw data collected by the satellite consists of a series of radar echoes, and these must be processed to form an image. On examining the details of this processing, it can be seen that the core functionality consists of a series of:
- Fourier Transforms (and their inverses)
- Hadamard products of matrices
These can be implemented, in theory at least, with a low multiplicative depth, and without the need for conditional operators. This is therefore a good candidate application for SHE, but much work needs to be done to demonstrate its practicality.