# Elliptic curve cryptosystems

@article{Koblitz1987EllipticCC, title={Elliptic curve cryptosystems}, author={Neal Koblitz}, journal={Mathematics of Computation}, year={1987}, volume={48}, pages={203-209} }

We discuss analogs based on elliptic curves over finite fields of public key cryptosystems which use the multiplicative group of a finite field. These elliptic curve cryptosystems may be more secure, because the analog of the discrete logarithm problem on elliptic curves is likely to be harder than the classical discrete logarithm problem, especially over GF(2'). We discuss the question of primitive points on an elliptic curve modulo p, and give a theorem on nonsmoothness of the order of the…

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