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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.
Private keys must be stored securely to maintain the safety of one's cryptocurrency. "not your keys, not your coins".
It is number of transactions done per second. For example, there are 10 transactions of Bitcoin done in 1-minute. The TPS would be 10 transactions/60 seconds = ~0.17 TPS.
