The company’s CTO described the deduplication in a note posted in the “Bugs & Troubleshooting” section on the company’s web forum last year:

Woah! How did that 750MB file upload so quickly?

Dropbox tries to be very smart about minimizing the amount of bandwidth used. If we detect that a file you’re trying to upload has already been uploaded to Dropbox, we don’t make you upload it again. Similarly, if you make a change to a file that’s already on Dropbox, you’ll only have to upload the pieces of the file that changed.

This works across all data on Dropbox, not just your own account. There are no security implications [emphasis added] - your data is still kept logically separated and not affected by changes that other users make to their data.