More precisely it can be shown that computing discrete logarithms takes exponential time, except when some particular extra structure is present. In the case of elliptic curve discrete logarithms, no such extra structure is known except in a few special cases. Thus it appears that ECDLs are difficult in general. This alone makes them very interesting for mathematician-programmers. We are constantly searching for better algorithms or implementation methods and expanding the set of special cases.
Cryptographers also base the security of codes on the difficulty of computing ECDLs.
By solving ECC2-97 we are not looking for a secret message but we are looking for a secret key by solving a mathematical problem. In doing so we are also demonstrating what codes can be broken in practice. The discrete logarithm can be defined very generally as follows. There can be several solutions n , but any one will do. Remind me what a finite group is.