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Securing electronic signature gives the contracting parties, especially the consumer, safety and security, which positively reflects on trade exchange. Digital-signature algorithms can be categorized based on the type of security suppositions, for example discrete logarithm, factorization of hard-problems, and elliptic-curve cryptography, which are all currently believed to be unsolvable in a reasonable time period. In recent years, a variety of chaotic cryptographic schemes have been proposed. The idea of chaotic systems with applications to cryptography has received a great deal of attention from researchers from a variety of disciplines. Therefore, in this paper, we propose a new signature scheme based on two hard number theoretic problems, Chaotic Maps (CM) and Quadratic Residue (QR). Our performance analysis shows that compared, to other associated schemes, our scheme not only improves the efficiency level but also ensures security . We also give a proof that the security of the proposed scheme can protect against the known key attacks.

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