An RSA cryptographic method and system is provided in which a sender encrypts a message (m) using a public modulus n, and an encryption exponent e that is a function of a sender-chosen string. This function is such that the values of e generated by it will not be coprime. In a preferred embodiment, a recipient receives the encrypted message and subjects it to a modulo-n blinding operation. The resultant blinded encrypted message is then made available to a trusted authority which decrypts it using a decryption exponent d based on the sender-chosen string and private data associated with the public modulus; however, the blinding applied to the message prevents the trusted authority from reading the message. The decrypted, but still blinded, message is passed back to the recipient who cancels the blinding to recover the message.