1. A system directed at a digital signatures system configured to avert attacks upon messages, comprising: a. at least one computer; b. a message sent by a sender by way of the at least one computer; c. the digital signatures system being configured to operate by the at least one computer for application to the message, said digital signatures system being configured to keep a generator utilized by the digital signatures system secret; wherein attacks upon the security of the message are averted through the application of the digital signatures system, wherein the digital signatures system comprises a signing procedure and verification procedure that utilize at least the following: a. the generator; b. a private key; c. one or more public keys; and d. a sessional number, and wherein the digital signatures system generates two public keys.