Public-key cryptosystems based on elliptic curves

Abstract

We discuss the use of elliptic curves in cryptography. Compared to the difficulty of solving the classical discrete logarithm problem, it appears that the elliptic curve analog of the discrete logarithm problem is at least as difficult to solve, especially over GF (2/sup m/). Furthermore, elliptic curve cryptosystems might prove to have a higher bit-rate operation than conventional cryptosystems.<>