Find out what a cryptographic software and RSA are.
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RSA is used mostly in hybrid encryption schemes and digital signatures.
In the former it is used to encrypt a symmetric key and send it to a second party who has requested it.
This is because RSA is comparatively slow so you would never use it to encrypt a whole file.
Instead the file is encrypted symmetrically and only the key is encrypted by RSA directly.
For Digital signatures one can use the private key to sign a message or file (or better: sign the cryptographic hash of the message/file, much faster). If a second party has the corresponding public key he can verify that the file is authentic and has not been altered or damaged.
By that same logic it is trivially possible to build nonrepudiation schemes.
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