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How does Public and Private Key Cryptography work?

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How does Public and Private Key Cryptography work?

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In public key cryptography, a public and private key are created simultaneously using the same algorithm (a popular one is known as RSA) by a Certification Authority(CA). The private key is given only to the requesting party and the public key is made publicly available (as part of a digital certificate) in a directory that all parties can access. The private key is never shared with anyone or sent across the Internet but has to be kept secret. You use the private key to decrypt text that has been encrypted with your public key by someone else (who can find out what your public key is from a public directory). Thus, if I send you a message, I can find out your public key (but not your private key) from a central administrator and encrypt a message to you using your public key. When you receive it, you decrypt it with your private key. In addition to encrypting messages (which ensures privacy), you can authenticate yourself to me (so I know that it is really you who sent the message) by

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