# Continuous variable controlled quantum dialogue and secure multiparty quantum computation

## TL;DR

This paper introduces a continuous variable quantum dialogue scheme and extends it to secure multiparty quantum computation protocols, demonstrating high security and versatility over discrete variable schemes.

## Contribution

It proposes a novel continuous variable controlled quantum dialogue scheme and its extensions for multiparty quantum computation, including solutions for socialist millionaire problems and quantum private comparison.

## Key findings

- High eavesdropper ignorance compared to discrete schemes
- Scheme can be implemented with bipartite entanglement
- Versatile in reducing to multi-party cryptographic protocols

## Abstract

A continuous variable controlled quantum dialogue scheme is proposed. The scheme is further modified to obtain two other protocols of continuous variable 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 continuous variable controlled quantum dialogue 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 counterpart are also discussed. Specifically, the ignorance of an eavesdropper in the proposed scheme is shown to be very high compared with corresponding discrete variable scheme and thus the present scheme is less prone to information leakage inherent with the discrete variable quantum dialogue based schemes.It is further established that the proposed scheme can be viewed as a continuous variable counterpart of quantum cryptographic switch which allows a supervisor to control the information transferred between the two legitimate parties to a continuously varying degree.