If you understand DH key exchange (the one where you multiply numbers modulo something) then you know what the discrete logarithm problem (DLP) is. All that EC

If you understand DH key exchange (the one where you multiply numbers modulo something) then you know what the discrete logarithm problem (DLP) is. All that EC crypto is, is a way of doing the same maths, but replacing integers with points on a curve. If you remember a bit of maths theory you know that you can define groups and things with multiplication and the like. It's that kind of idea. The advantage is that the known best approaches to solving the DLP for integers don't carry across to the points on a curve (because the points don't work like integers for all of maths - they support enough to the crypto, but not enough for the attack). So you can use smaller keys. AFAICT. IMHO. IANAM/C.