Exceptional Curves

An elliptic curve $E$ defined over $F_p$ whose cardinality (or order) is also $p$ is an anomalous curve, and the discrete logarithm becomes trivial. We can employ Smart’s attack, which allows us to perform the discrete log of the curve in linear time. This paper by Novotney goes over the details of why the attack works. At the time of writing, I wish I understand what’s in the paper - some very topics into group theory....