We investigate password authenticated key exchange (PAKE) protocols in low resource environments, such as smartcards or mobile devices. In such environments, particularly in the future, it may be that the cryptosystems available for signatures and/or encryptions will be based on elliptic curves, because of their well-known advantages with regard to processing and size constraints. As a result, any PAKE protocols which the device requires should also preferably be implemented over elliptic curves. We show that the direct elliptic curve (EC) analogs of some PAKE protocols are insecure against partition attacks. We go on to propose a new EC based PAKE protocol. A modified version of the protocol for highly constrained devices, such as smartcards, is also presented.