1 ) A system directed at a digital signatures scheme capable of averting 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 scheme being operable by the at least one computer for application to the message, said digital signatures scheme being operable to keep a generator utilized by the digital signatures scheme secret; wherein attacks upon the security of the message are averted through the application of the digital signatures scheme.