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. The authors apply the idea of ECDSA on the solution space of Pell equation to design a digital signature scheme. In this paper, they compare the security of their signatures scheme to DSA and ECDSA. Their scheme is as secure as conventional DSA. They show that the signatures scheme based on Pell equation is more efficient than its analogue to elliptic curve i.e. ECDSA.