There are existing mechanisms of digital signing of emails/data/etc. involving public/private key encryption, but the technical complexity involved in setting it up is more then most who are even capable of doing so want to bother with individually.
But if you are interested, you should check out things like:
[What is Public Key Infrastructure (PKI)](https://www.digicert.com/what-is-pki)
[OpenPGP](https://www.openpgp.org/)
[The GNU Privacy Guard (GnuPG)](https://gnupg.org/)
[Gpg4win](https://www.gpg4win.org/)
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