  Nonlocality inequalities for multi-party systems act as contextuality
inequalities for single qudit systems of suitable dimensions. In this paper, we
propose the procedure for adaptation of nonlocality-based quantum conferencing
protocols (QCPs) to contextuality-based QCPs. Unlike the nonlocality-based
protocols, the proposed protocols do not involve nonlocal states. These
protocols can also be implemented in a class of noisy channels without any
compromise in the key generation rate. As an illustration of the procedure, we
present a QCP based on Mermin's contextuality inequality. As a significant
improvement, we propose a QCP based on CHSH contextuality inequality involving
only four-dimensional states irrespective of the number of parties sharing the
key. The key generation rate of the latter is twice that of the former.
Although these QCPs allow for an eavesdropping attack which has no analog in
nonlocality-based QCPs, a way out of this attack is demonstrated. Finally, we
show the feasibility of experimental implementation of these protocols with
orbital angular momentum (OAM) states.
