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Secure online storage? [Imwebhost]

I have a client that wants to make large files available to subcontractors, and their e-mail server is dropping files larger than 20MB. This client is not technically inclined, and I'm not sure about the security of FTP uploads to blind links on a Web server.

I guess my main question is: Do most hosting services have online storage for large files that allow sharing of those large files securely?