This creates some difficulty with key exhange . Public key cryptography solved this problem. The public key is exactly what it says public. It can be freely distributed to anyone. Knowing a user's public key does not yield any information about his private key.
Private keys are much like credit cards.
They must be kept secure by the owner against lost and theft. In each case, the issuer places a block on the document. When an imposter attempts to use the card or private key, the bank or CA notifies the merchant or validator that the card or key has been revoked. Optionally, it could be possible to determine who is masquerading as the user. The validator then applies the public key to the data signed by the user's private key.