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Definition
Public-key cryptography is a form of cryptography which generally allows users to communicate securely without having prior access to a shared secret key, by using a pair of cryptographic keys, designated as public key and private key, which are related mathematically.
In public key cryptography, the private key is generally kept secret, while the public key may be widely distributed. In a sense, one key "locks" a lock; while the other is required to unlock it. It should not be possible to deduce the private key of a pair given the public key.
References
Public Key Cryptography Wikipedia Entry