  We consider the security of the BB84, six-state and SARG04 quantum key
distribution protocols when the eavesdropper doesn't have access to a quantum
memory. In this case, Eve's most general strategy is to measure her ancilla
with an appropriate POVM designed to take advantage of the post-measurement
information that will be released during the sifting phase of the protocol.
After an optimization on all the parameters accessible to Eve, our method
provides us with new bounds for the security of six-state and SARG04 against a
memoryless adversary. In particular, for the six-state protocol we show that
the maximum QBER for which a secure key can be extracted is increased from
12.6% (for collective attacks) to 20.4% with the memoryless assumption.
