  Quantum dialogue is a process of two way secure and simultaneous
communication using a single channel. Recently, a Measurement Device
Independent Quantum Dialogue (MDI-QD) protocol has been proposed (Quantum
Information Processing 16.12 (2017): 305). To make the protocol secure against
information leakage, the authors have discarded almost half of the qubits
remaining after the error estimation phase. In this paper, we propose two
modified versions of the MDI-QD protocol such that the number of discarded
qubits is reduced to almost one-fourth of the remaining qubits after the error
estimation phase. We use almost half of their discarded qubits along with their
used qubits to make our protocol more efficient in qubits count. We show that
both of our protocols are secure under the same adversarial model given in
MDI-QD protocol.
