Doesn't http progressive download (over https) achieve this? I could be wrong, but I think if you just configure nginx with SSL and have the webcam dump to some sort of a raw file format, you should be able to download the file and since you're using SSL now it's encrypted. It won't be a true streaming server, but should be close enough.

You may need to have the client send a byte range header with each request to ensure you always start near the end of the stream so it's closer to realtime.