How secure are elliptic curves over composite extension fields?N. P. smart, How secure are elliptic curves over composite extension fields?. CSTR-00-017, Department of Computer Science, University of Bristol. November 2000. PDF, 198 Kbytes.
We compare the method of Weil descent for solving the ECDLP against the standard method of parallelised Pollard rho. We give details of a theoretical and practical comparison and then use this to analyse the difficulty of actually solving the ECDLP for curves of the size needed in a practical cryptographic systems. In particular we examine the elliptic curves proposed in the Oakley key determination protocol.