Hi Prabhat,
Private key not shared under any circumstances. It is maintained in the system to de-crypt the data encrypted with your public key.
Say in above scenario, you have given your public key to SystemA so SystemA will encrypt the data with your public key and then send it to you. After you receive the the data, it is de-crypted using your private key.
The benefit of sharing the public key is in case the data sent by SystemA is received by some intruder then it cannot be decrypted as he won't be having your private key.
So always remember not share your private key in any circumstances.
Regards
VJ
