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How to achieve encryption at single source and decryption at multiple locations using asymmetric scheme

I need an encryption scheme where a single source/location can encrypt using their private key and while anyone with access to the corresponding public key can decrypt it. It has to be asymmetric to avoid any one else deriving that private key and pretending to become that source. For example, government issues an encrypted document that any one authorized with the issued public key can decrypt it. But no one else should be able to mimic the government issued document. So confidentiality and integrity are both solved.

If GPG can address it, how secure is it and is it possible to use HSM or is it supported pcks