Cryptanalysis of ECC

To make sure that your cryptosystem is secure, then you have to do cryptanalysis.

The known attacks for ECC are:

* The Pohlig-Hellman algorithm (which reduces the problem to subgroups of prime order)

* Shanks’ baby-step-giant-step method

* Pollard’s methods, the rho method and the kangaroo method, both of which have parallel versions due to van Oorschot and Wiener

* The Menezes-Okamoto-Vanstone (MOV) attack using the Weil pairing

* The Frey-Rueck attack using the Tate pairing

* The attacks on anomalous elliptic curves (i.e., elliptic curves over F_p which have p points) due to Semaev, Satoh-Araki and Smart

* Weil descent (for some special finite fields)

* Algebro-geometric attack

Next step will be to choose which attacks to be used for measuring the level of security of ECC.