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In public-key cryptography - one of the basis of cryptocurrency, digital keys are generated from a large random number through a cryptograhic key generation program to produce a private key and public key. In such a system, anyone can encrypt a message using the receiver's public key, but that encrypted message can only be decrypted with the receiver's private key.
Public keys can be disseminated freely as the receving address for your cryptocurrency.
A cryptocurrency is said to be "mineable" when it has the system thrugh which miners can be rewarded with newly-created cryptocurrencies for creating blocks.
It is the "second layer" or an off-chain of payment protocol that operates on top of a blockchain. Payments on this network do not need block confirmation and it will be instant.