I've been reading about Blockstream and Liquid but I was under the impression that sidechain was something that would require changes to the Bitcoin Core platform. Is that correct? I mean, is the bicoin blockchain already supporting a "peg" to another sidechain? Can I already launch my own sidechain like Blockstream did?
The seminal whitepaper on sidechains, "Enabling Blockchain Innovations with Pegged Sidechains," describes modifying Bitcoin's Script to support simplified payment validation (SPV):
To use Bitcoin as the parent chain, an extension to script which can recognise and validate such SPV proofs would be required. At the very least, such proofs would need to be made compact enough to fit in a Bitcoin transaction. However, this is just a soft-forking change⁹, without effect on transactions which do not use the new features.
⁹A soft-forking change is a change which only imposes further restrictions on what is valid inside the chain.
However, this is for a "two-way peg."