Abstract: In this paper, the VCA interaction scheme for VE presented by Liu and Pan (for short, L-P scheme) is firstly analyzed, and it is found that a plain secret sharing method was directly used to construct the threshold RSA signature and the key distribution algorithms in the ring Z\-φ(N), which inevitably causes some algebraic construction flaws, i.e. incalculableness of elements’ inverses, unexpected decomposition of the module N, and the leakage of system secrets. In order to remedy L-P scheme’s drawbacks, a new improved scheme is then presented, in which a new parameter π is introduced to avoid computing of some particular elements’ inverses in the ring Z\-φ(N) since it is the multiple of these elements. And consequently the important parameter exp can be computed in the integer ring Z other than the residue ring Z\-φ(N) since it is the exponential component in the function of SIG which is in Z\-N. Analysis shows that the new scheme can effectively avoid any inverse’s computing in any ring, and can furthermore avoid the unexpected decomposition of the module N and the leakage of secret parameters. In addition, the proposed scheme is more efficient than the L-P scheme in the VCA sub-keys redistribution stage. Therefore, the new improved scheme provides a correct and feasible VCA interaction model for VE based on RSA threshold signature mechanism.