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A Digital Signature Scheme Based on Pell Equation

Aditya Mani Mishra

Elliptic curve digital signature algorithm (ECDSA) is well established digital signature scheme based on the discrete logarithms problems. On the other hand, many cryptosystem has been designed using the Pell Equation. We apply the idea of ECDSA on the solution space of Pell equation to design a digital signature scheme. In this paper we compare the security of our signatures scheme to DSA and ECDSA. Our scheme is as secure as conventional DSA. We show that the signatures scheme based on Pell equation is more efficient than its analogue to elliptic curve i.e. ECDSA.