Tools Do Not Equal Security
Security is a function of your assets you want to protect (sensitive information, life and limb), your adversaries' resources, and the tools and methods you use to adequately protect your assets from your adversaries' resources.
For instance, your restricted network is unspecified but may be monitoring all client machines' keystrokes (or simply yours if you are a specific target) rather than your network packets. If this is the case, the Tor Browser Bundle is not keeping your activities confidential nor protecting your anonymity with respect to those activities.
Tor is extremely secure but it is not magic
In comparison to any other tools you might use to separate your person and identity from otherwise non-identifying Internet browser reading and publishing, all Tor Browser Bundle traffic intercepted between your machine and the last Tor relay (exit relay) is robustly secure because, if I understand correctly, Tor encrypts this traffic using "128-bit AES in counter mode, with an IV of all 0 bytes" for a stream cipher and using "RSA with 1024-bit keys and a fixed exponent of 65537" for a public-key cipher.
- Note, however, that Tor does not "magically encrypt all traffic throughout the Internet" and once your sensitive traffic is decrypted by the Tor network's exit relay you are relying on extra-Tor encryption or your traffic is cleartext that any adversary can read including the exit relay operator, etc.
A good place to find more information is: Tor Project FAQ
More Details
"We've already got an improved circuit extension handshake protocol that uses curve25519 in place of RSA1024, and we're using (where supported) P256 ECDHE in our TLS handshakes, but there are more uses of RSA1024 to replace, including:
- Router identity keys
- TLS link keys
- Hidden service keys"
"Ed25519 (specifically, Ed25519-SHA-512 as described and specified at http://ed25519.cr.yp.to/)."