Quantum secure multi-party summation based on entanglement swapping

Quantum secure multi-party summation is a specific primitive of classical secure multi-party computation. Compared with classical secure multi-party summation based on mathematical difficulty problems such as integer factorization and discrete logarithm which has been threatened by potential quantum computers, the quantum version can provide unconditional security for the computing tasks. A quantum protocol based on the entanglement swapping between d-level Bell state and d-level cat state is constructed to perform secure multi-party summation. With the aid of a semi-honest third party who does not conspire with any participant, the proposed protocol can calculate the non-modular sum of the secret integers held by the participants who do not trust each other. Not only can the protocol resist the attacks from both outside and semi-honest third party, but also resist participants’ attack, even though there are at most $$n-2$$ participants colluding together. (n is the number of participants.) This protocol only needs $$O(\log M)$$ (M is the maximum value of all secret integers) quantum resources to complete the computing task. Specially, under the condition of computing the sum of larger integers for a small number of participants, this protocol utilizes fewer quantum resources and has higher efficiency than other proposed protocols.