I want to allow users to store some videos on YouTube using my website. These videos are personal videos for the person storing them. The videos would presumably be transferred from my site to the YouTube site using the APIs. I would imagine all the videos would be stored in a single account (that I make as the site operator). It is important to note that the videos correspond to the individuals that save them - i.e. all users can't see all videos. The security access is done by my server and should not be accessible by anyone on the Internet.
A user must go through my website, enter his password, etc. (that I validate) and then I provide him access to his videos and once he is successfully authenticated, he can see his videos - that he views on my website.
Is this possible using YouTube or Vimeo APIs?
YouTube Direct API seems to be something similar to Your needs. Have a look at it.
Edit: Link, thanks @Simon.