Circular semiquantum private comparison protocol for equality without a preshared key based on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>χ</mml:mi></mml:math>-type states

In this paper, we adopt $\ensuremath{\chi}$-type states to design an alternative circular semiquantum private comparison (SQPC) protocol, which can determine the equality of private inputs from two semiquantum users within one round implementation under the help of a semihonest third party (TP) who possesses complete quantum capabilities. Here, it is assumed that the semihonest TP has the abilities to launch all possible attacks to steal useful information about two semiquantum users' private inputs but cannot conspire with anyone else. The traveling particles go from TP to Alice, then from Alice to Bob, and back from Bob to TP. The security analysis turns out the proposed SQPC protocol can resist both the outside attacks and the inside attacks. Furthermore, it has been proven to be information-theoretically secure in the asymptotic scenario. Compared with some existing SQPC protocols of equality with quantum entangled states, the proposed SQPC protocol has some advantages: $◯\phantom{\rule{-9pt}{0ex}}1$ it requires no preshared key among different participants; $◯\phantom{\rule{-9pt}{0ex}}2$ it does not need quantum entanglement swapping; $◯\phantom{\rule{-9pt}{0ex}}3$ it employs no delay lines; $◯\phantom{\rule{-9pt}{0ex}}4$ it adopts no unitary operations; and $◯\phantom{\rule{-9pt}{0ex}}5$ it has fewer qubits transmitted and fewer classical modulo 2 addition computations.