A novel circular two-party semiquantum private comparison of size relationship based on d-level single-particle state without any preshared key

Abstract In order to cut down the resource expended by the preshared key, this paper uses <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>d</mml:mi> </mml:mrow> </mml:math> -level single-particle states to design a novel circular two-party semiquantum private comparison scheme with a quantum semi-honest third party who does not need any preshared key. This scheme is capable of determining the size relationship of two integer sequences from two semiquantum communicants. The traveling particles are transmitted in a circular way. This protocol does not use quantum entangled states, quantum entanglement swapping, unitary operations or delay lines. This protocol does not require the semiquantum communicants to use any quantum memory either. Its security toward external attacks and internal attacks is fairly good.