How to answer to this polite, but strange request? I am a young postgraduate researcher, and I have developed an algorithm to measure the blood flow from echographic signals in a novel manner. I currently only have one published paper from my pregraduate years, on which I am 4th author, and it is not about my current field of research.

Long story short, my algorithm is unpublished and works quite well... so well that recently a PhD in electrical engineering from the other side of the planet saw a summary about it on the net, and sent me an email asking for some data, so that one of his undergraduate students can reproduce my program. They assure me that they won't use it for publishing, and both the PhD and his supposed undergraduate sent me several emails already. When I asked for precisions about their project, they just in essence replied: "We don't really know yet, but we would like to reproduce your work"

I don't know what to answer... moreover, the data they are asking for (a video of an echographic exam) can be found in 10 seconds on Youtube. What should I do?
I agree with both previous commenters: publish your algorithm first and then point them to the YouTube video. If you cannot or don't want to go the traditional journal publishing route, at least, consider self-publishing a paper, describing your algorithm, at a preprint or e-print server, such as arXiv. At the same time, I don't see a problem with this request, IF it involves sharing only data, but not the algorithm itself.

If you see the value of and are serious about commercialization of your algorithm, consider filing a provisional patent application with USPTO and/or Swiss patent agency. I'm not sure about possibility and details of applying for provisional patent in Switzerland, therefore, I refer you to this page, which seems to be relevant. It might be easier to skip filing provisional patent application with USPTO and file a standard one in Europe to establish the priority right (for example, see this page). Should you be thinking about going the patent route, I would definitely recommend you to consult a legal professional, specializing in intellectual property (IP) domain.

Disclaimer: I'm not a lawyer and this answer does not represent legal advice.