I am developing a windows desktop app where the clients applications need to download some data file from a public shared folder. in order to protect the data from tempering i would like to generate RSA private and public keys. keep the public key in my own machine at home and include the private key in all clients.
when i want to send a new file for the clients to download (at well) i hash the file and encrypt the hash with the public key and store it as .sig file alongside the data file in a public shared folder.
now if one of the client users is malicious he can steal the private key from his machine.
the question is : provided that the public key is secret and this is the only use of that key pair and i absolutely don't need any encryption on the data file. does stealing the private key from a client compromise my public key? i.e can the malicious user craft a file signature so that the data file appear to be coming from me?