  Intrinsic symmetry of the existing protocols of quantum dialogue are
explored. It is shown that if we have a set of mutually orthogonal $n$-qubit
states {\normalsize
$\{|\phi_{0}>,|\phi_{1}>,....,|\phi_{i}<,...,|\phi_{2^{n}-1}>\}$ and a set of
$m-qubit$ ($m\leq n$) unitary operators
$\{U_{0},U_{2},...,U_{2^{n}-1}\}:U_{i}|\phi_{0}>=|\phi_{i}>$ and
$\{U_{0},U_{2},...,U_{2^{n}-1}\}$ forms a group under multiplication then it
would be sufficient to construct a quantum dialogue protocol using this set of
quantum states and this group of unitary operators}. The sufficiency condition
is used to provide a generalized protocol of quantum dialogue. Further the
basic concepts of group theory and quantum mechanics are used here to
systematically generate several examples of possible groups of unitary
operators that may be used for implementation of quantum dialogue. A large
number of examples of quantum states that may be used to implement the
generalized quantum dialogue protocol using these groups of unitary operators
are also obtained. For example, it is shown that GHZ state, GHZ-like state, W
state, 4 and 5 qubit Cluster states, Omega state, Brown state, $Q_{4}$ state
and $Q_{5}$ state can be used for implementation of quantum dialogue protocol.
The security and efficiency of the proposed protocol is appropriately analyzed.
It is also shown that if a group of unitary operators and a set of mutually
orthogonal states are found to be suitable for quantum dialogue then they can
be used to provide solutions of socialist millionaire problem.
