The present invention is a digital signatures scheme method and system that permits the generation of a digital signature in a manner whereby the generator is kept secret. The inclusion of a secret generator in the digital signatures scheme may reduce the potential for an attack upon the scheme to be successful. The present invention may incorporate a signing procedure and a verification procedure. The signing procedure may facilitate the determination of a group, and the identification of the generator from the group. The signing procedure may also keep the generator secret and may generate a digital signature of a message. The generator may be kept secret by one or more conditions, and one or more public keys may be utilized by the digital signatures scheme. The verification procedure may be a verification procedure operable to obtain the message and the digital signature and to verify the digital signature. Embodiments of the present invention may achieve processing of the signing procedure and/or verification procedure at a fast rate of speed, which may further diminish the chance of a successful attack upon the digital signatures scheme. Embodiments of the present invention may further generate variations of digital signatures.