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The secure electronic signature provides contracting parties, particularly the consumer, with safety and reassurance which has a favorable impact on business transactions due to the strong legal authority supplied by this signature, which is based on a method for its formation. Therefore, researchers are rushing to design safe and performance electronic signature schemes at the same time. We offer a novel signature technique based on two hard number theory issues in this work, Quadratic Residue (QR) and Chaotic Maps (CM). Several fields of study including mathematics, physics, and computer science have taken an interest in chaotic systems as a potential tool for cryptography. Analysis demonstrates that our strategy is more secure and efficient than other connected schemes, compared to other schemes. A proof of the proposed scheme's security against known key attacks is also provided in this article. [ABSTRACT FROM AUTHOR]