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"A private Ethereum-based network that had a linkage allowing ether to be securely moved from the public Ethereum main chain onto it and back would be considered to be a sidechain of the public network"
What are the main steps for the "linkage" and how secure would it be? For example, are there any concerns about the sidechain being attacked (like there would be if it involved merge mining)?
One would need to deploy contracts on both public and private chain, which are able to verify the tokens of one another. That could be, of course, tricky since EtHash's (POW algorithm) implementation in Ethereum VM would be inefficient. It is potentially much more plausible to implement such a thing in Proof-Of-Stake phase (after Serenity), since mutual verification would be much simpler.
If the private chain is mined by much smaller hash power, it is indeed more susceptible to an attack. However, this does not have any implications for the public chain. The private chain's tokens would be known to have weaker security and, consequently, treated as such, with extra caution and suspicion.
