[plopilop]

Big mistake in the article: the discrete log is not a trapdoor function, as far as we know, and elliptic curve crypto does not rely on trapdoors.

A trapdoor function is when you have a function hard to invert (for any x, given y = f(x), find x), which inversion becomes very easy once you know some additional info. For instance in RSA, given c = m^e mod N, it is hard to find m. Unless you know d such that e*d = 1 mod phi(N), then you can easily find m by computing m = c^d mod N.

There is no known way of easily inverting exponentiation on finite groups.

To quote Wikipedia, "Functions related to the hardness of the discrete logarithm problem [...] are not known to be trapdoor functions, because there is no known "trapdoor" information about the group that enables the efficient computation of discrete logarithms. "

[lanecwagner]

Author here, thanks for bringing this up. I'll be looking into this and updating the article

[curyous]

Doesn't elliptic curve crypto rely on trap doors because it uses finite fields? The wrap around caused by the finite field is a trap door, isn't it?