Public key cryptosystems were invented in the late 1970's, with some help from the development of complexity theory around that time. It was observed that based on a problem so difficult that it would need thousands of years to solve, and with some luck, a cryptosystem could be developed which would have two keys, a secret key and a public key. With the public key one could encrypt messages, and decrypt them with the private key. Thus the owner of the private key would be the only one who could decrypt the messages, but anyone knowing the public key could send them in privacy.
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