What is "fed-peg" and "predefined functionaries" with sidechains? I am reading about side-chains, and what I read in this article is:


  The initial sidechain included in Sidechain Elements works on a
  federated security model; while it’s still peer-to-peer and
  consensus-based, security for the blockchain is provided by a set of
  predefined functionaries in an arrangement called a Fed-Peg. A number
  of academic groups and individual contributors have agreed to run the
  Sidechain Elements Fed-Peg, including blockchain groups at Stanford,
  MIT, and Princeton. The sidechain does not include mining or
  proof-of-work at this point.


I have no idea what that means. What is "fed-peg"? Why is that needed? Does it change in any way the security of the main chain? How does it differ from decentralized PoW?
I have no idea what that means. What is "fed-peg"? Why is that needed?


When you're creating a sidechain, you need a way to move Bitcoins from the main network to your sidechain. This is pretty straightforward. Counterparty, Ethereum, and NXT had various ways of doing this. (Admittedly, none of these allowed people to turn Bitcoin into the assets on these networks after they started, but I suspect that's due to economic reasons rather than technical ones.)

The more complicated, and more important issue, is how you move Bitcoins that are on the sidechain back into the main network. I've heard multiple proposals on how to do this, but all of them are either  


insecure,
centralized,
or require very complicated changes to the Bitcoin protocol. 


This approach is centralized.

The idea with that you have several authorities, each of whom has a private key. Those private keys together control a multisignature account. When you move Bitcoins onto the sidechain, you deposit them into the multisignature account. When you want to move them back to the main chain, you do so on the sidechain; those federated authorities will independently validate that transaction. Then, all of them sign a withdrawal from the multisignature account to the main network address you specified in your sidechain transaction.

The blockstream paper suggests a 3 of 5 multisignature account. The issue with this is that if 3 of those keys are compromised (or if 3 of them collude) then they can take all of the money out of the multisignature account.


  Does it change in any way the security of the main chain?


No. It doesn't modify the main network. Future incarnations might, though. There's not enough detail about those possible future systems to answer that at present.


  How does it differ from decentralized PoW?


The federated authorities have two roles in this system: gating transactions into the system by producing timestamped blocks, (something normally done by miners) and the previously mentioned multisignature account.