  The original two-way continuous-variable quantum-key-distribution (CV QKD)
protocols [S. Pirandola, S. Mancini, S. Lloyd, and S. L. Braunstein, Nature
Physics 4, 726 (2008)] give the security against the collective attack on the
condition of the tomography of the quantum channels. We propose a family of new
two-way CV QKD protocols and prove their security against collective entangling
cloner attacks without the tomography of the quantum channels. The simulation
result indicates that the new protocols maintain the same advantage as the
original two-way protocols whose tolerable excess noise surpasses that of the
one-way CV-QKD protocol. We also show that all sub-protocols within the family
have higher secret key rate and much longer transmission distance than the
one-way CV-QKD protocol for the noisy channel.
