Basic question about crypto algorithms

Hello,

I'm new in here and in cryptography, and I'd like some help about a general doubt I have.

What I want to do is encrypt a message in a way that the following holds:

(a) The message can be split after being encrypted, routed (over a network), regrouped and decrypted. Ideally the routing information would be encrypted too, and routing devices would be able to decipher the routing information of the data (this is easy, but the following make it more difficult -- I guess).

(b) If the encrypted message is broken in "n" pieces, capturing any "n-1" peaces won't give you any hint of the message (making brute force either unfeasible or impossible).

(c) Even if you manage to get the deciphering key, you won't be able to decrypt unless you have all "n" peaces.

(d) It shouldn't offer statistical regularities (although, I guess I could use a salt here).

Is there any cryptographic algorithm/crypto system/scheme which can offer me these properties?

Sorry about the silly question.

Thank you in advance,
Rodro

Here are two links that might help get you started. I think what you're trying to do is possible, but I've never done much work with this particular branch of cryptography.

All-or-nothing transform
Secret sharing

Thank you for the reply, it certainly helped me understand more about the problem.

Nice signature btw .