###### Abstract
In [25], a QPC protocol that relies on W triplets, and also uses a third party, was presented. Later, another QPC protocol using Bell states and a third party appeared in [26]. In [27; 28; 29; 30; 31], the authors proposed different QPC protocols, having as a common characteristic the fact that they utilize entangled states, such as \(\chi\), GHZ states, or highly entangled six-qubit states. The authors in [32] presented the first semi-quantum private comparison protocol for participants who compare their secrets without any quantum capability, and under an almost dishonest third-party. Similarly, in [33], an improved semi-quantum private comparison protocol was introduced, achieving a higher security level. There have also been different approaches, e.g., the authors in [34] do not use entanglement but still require a semi-honest third party as the QPC protocol proposed in [35] makes use of random rotation angles. Recently, a practical quantum-secure protocol for the socialist millionaires' problem based on single photons was introduced, with emphasis on the ease of implementation with current technology [36]. For more pointers on the subject, the interested reader may consult the comprehensive survey [37]. Sophisticated quantum protocols for magnitude comparison have also been proposed in [38; 39; 40; 41; 42; 43]; all these protocols envision \(d\)-level quantum systems and also require a third party. Typically, \(d\) is assumed to be greater than a certain threshold, which, in practice, considerably complicates their implementation on contemporary quantum computers based on qubits. [PERSON] et al. in [44] were the first to devise a clever generalization to \(n\) parties that requires \(|GHZ_{n}\rangle\)-class states and the prior distribution of a secret key to each of the \(n\) parties. This inspired researchers to design more multiparty quantum private comparison (MQPC for short) protocols. Along this direction, the authors in [45] proposed a different MQPC protocol based on a \(d\)-level quantum system. Similarly, the researchers in [46] introduced an MPQC protocol with an almost dishonest third party that requires a \(d\)-level quantum system, where also \(d\) is assumed greater than the largest number slated for comparison. Subsequently, in [47], an enhanced MQPC protocol was introduced that uses \(|GHZ_{n}\rangle\)-type states for \(n\) participants. [PERSON] and [PERSON] in [41] came up with a sophisticated MQPC protocol also based on a \(d\)-level quantum system. One of the novelties of their protocol was the creative utilization of two semi-honest third parties that eliminate the need for pre-shared keys between each pair. Other notable MQPC protocols were proposed in [42], relying on \(d\)-level \(|GHZ_{n}\rangle\) states; in [48], exploiting properties of quantum homomorphic encryption; and in [49; 50]. In constructing secure QPC protocols, there are certain obstacles. It has been shown in [51] that unconditionally secure classical computation involving two parties is not possible for certain categories of functions. Despite the fact that things are different in the quantum setting [52], [PERSON] has demonstrated that it is impossible to securely evaluate the equality function in a two-party scenario [53]. This has necessitated the introduction of further assumptions, typically in the form of a semi-honest third party. Given the current level of technology and the challenging issues that must still be overcome, today a hybrid approach, combining classical and quantum techniques to leverage the strengths of both paradigms, may be a fruitful solution. Toward this end, the sophisticated classical algebraic scheme introduced in [54] can offer many practical advantages. The new protocol we propose was designed from a computer scientist perspective that now or in the near future will be endowed with a quantum computer powerful enough to run a QMEP for a modest number of participants.