Piveteau signature scheme allows message recovery but the methodology differs from that of the Nyberg-Rueppel schemes. This paper analyzes the security of the Piveteau scheme by designing some attacks. Two improved methods to Piveteau signature scheme and Nyberg-Rueppel schemes were developed to avoid these weaknesses. Analyses of the security of the improved schemes prove that the improved methods can effectively handle the attacks proposed in this paper. Piveteau signature scheme allows message recovery but the methodology differs from that of the Nyberg-Rueppel schemes. The paper analyzes the security of the Piveteau scheme by designing some attacks. Two improved methods to Piveteau signature scheme and Nyberg-Rueppel schemes were developed to avoid these weaknesses. Analyzes of the security of the improved schemes prove that the improved methods can effectively handle the attacks proposed in this paper.