At it's core, you are signing a message using elliptic curve cryptography. This is a methodology used for many things, not just Ethereum. On top of that, you have an add'l layer of Ethereum stuff—like Ethereum addresses, Ethereum encrypted specifications and formats, etc.
Your best bet for unlocking a wallet is going to be the ethereum-js wallet. From there, there are a lot of other moving pieces:
Constructing transactions manually (offline, not via an account in geth/parity): https://github.com/ethereumjs/ethereumjs-tx
AWS stuff: https://github.com/MyEtherWallet/docker-geth-lb
Infura's API: https://blog.infura.io/infrastructure-means-apis-introducing-the-infura-api-49f2951bb6ba
Etherscan's API: https://etherscan.io/apis
Due to how complex MEW has become, it may be in your best interest to poke around the very earliest versions of MEW. You shouldn't use the code in this version because its severely out of date, but I have found that conceptually it has helped people wrap their heads around what is happening: https://github.com/kvhnuke/etherwallet/tree/mew1.0