It is a different system. An encryption system that uses the public key and the private key. The public key can be widely distributed and the private key is known only to the owner. The encryption algorithm is designed to produce a one-way function. Distributed public key does not compromise security.
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Thus, the encryption of a message can be done using the public key of the receiver, but the decryption of the encrypted message can only be done with the recipient's private key. This cryptographic system has privacy, robust authentication, data storage etc.
Therefore, the most popular use of asymmetric cryptography is public key encryption and digital signatures. In the case of digital signatures, a message is signed with the sender's private key and can be verified by anyone who has access to the sender's public key.
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This verification proves that the sender is able to access the private key and is therefore the person who is connected to the public key.
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