You are probably talking about detecting Tor relay nodes IP addresses that the sender connects to or patterns in the traffic.
So you could use a VPN, or a chain of VPNs to hide the IP.
And to escape traffic analysis you could switch the entry VPN automatically (that would require quite a few VPNs for large files or many receivers).
Still, connecting to unknown IPs from a corporate network can be detected.
Then you could use some public service that stores data like Github (repos / gists / ...) and somehow communicate between your computer and a relay server through Github.
Still not foolproof, there could be timing attacks to detect when data is transmitted when the receiver requests the file, so introducing delays along the nodes would help.
Systemic solution to this problem: NNTP (Usenet). I can't recall the specific newsgroup, but there are Usenet "numbers stations" groups for the upload of anonymous encrypted binaries. They get store-and-forward-ed like anything else, at arbitrary times.
Alice dumps an encrypted document into the NNTP network on one side of the world; Bob later downloads the entire newsgroup's contents (not just the stuff he wants—because there's no metadata to even determine that!) from his local NNTP server, and then attempts to decrypt everything he downloaded until he hits on something that works.
But wouldn't that have the same problem that GP mentioned, that this traffic would be easily identifiable as NNTP? If you were the only person using NNTP, then whammo...
One part of this scheme that I forgot about, which the link in the sibling reply mentions, is MixMaster (http://mixmaster.sourceforge.net/faq.shtml#1.2), a self-hostable service for “mixing” SMTP traffic (including SMTP>NNTP gateway traffic) around. Many people host these, even today. It’s a bit like Mailinator with all its alias domains, but for the other end of the connection, and distributed.
So, to get all the security features at the same time:
1. Using Tor to hide your IP,
2. Connect to a MixMaster node (using TLS), and
3. Send an encrypted NNTP message through it,
4. To an SMTP>NNTP gateway,
5. With the embedded NNTP message’s Recipient being alt.messages.anonymous.
Kinda complicated, but you could wrap all that up into a nice GUI program if you wanted.
MixMaster doesn’t do the Tor part for you, though. My suggestion would be to run AAM Direct in a https://tails.boum.org session, which will automatically force the connection through Tor without any configuration needed.
An additional boost to security would be for there to be .onion MixMaster nodes, so that the traffic doesn’t have to traverse the public internet (and thus probably force you to rely on the only-kind-of-secure SMTP STARTTLS extension for security between the Tor exit node and the MixMaster node.)
So you could use a VPN, or a chain of VPNs to hide the IP.
And to escape traffic analysis you could switch the entry VPN automatically (that would require quite a few VPNs for large files or many receivers).
Still, connecting to unknown IPs from a corporate network can be detected.
Then you could use some public service that stores data like Github (repos / gists / ...) and somehow communicate between your computer and a relay server through Github.
Still not foolproof, there could be timing attacks to detect when data is transmitted when the receiver requests the file, so introducing delays along the nodes would help.