Continuous variable controlled quantum dialogue and secure multiparty quantum computation

Abstract

A continuous variable (CV) controlled quantum dialogue (QD) scheme is proposed. The scheme is further modified to obtain two other protocols of (CV) secure multiparty computation. The first one of these protocols provides a solution of two-party socialist millionaire problem, while the second protocol provides a solution for a special type of multi-party socialist millionaire problem which can be viewed as a protocol for multiparty quantum private comparison. It is shown that the proposed scheme of (CV) controlled (QD) can be performed using bipartite entanglement and can be reduced to obtain several other two- and three-party cryptographic schemes in the limiting cases. The security of the proposed scheme and its advantage over corresponding discrete variable (DV) counterpart are also discussed. Specifically, the ignorance of an eavesdropper, i.e., information encoded by Alice/Bob, in the proposed scheme is shown to be more than that in the corresponding (DV) scheme, and thus the present scheme is less prone to information leakage inherent with the (DV) (QD) based schemes. It is further established that the proposed scheme can be viewed as a (CV) counterpart of quantum cryptographic switch which allows a supervisor to control the information transferred between the two legitimate parties to a continuously varying degree.