[ Changed 29th October 1997 ]
In recent years the use of elliptic curves in cryptography has become something of a "hot topic". This is because the discrete logarithm problem on elliptic curves is in general harder than the associated problem in the more traditional finite fields. In this talk I shall outline how one should choose one's elliptic curve by showing how certain attacks work. In particular I shall concentrate on the recent attack on "trace one curves".