Secure multiparty quantum computations for greatest common divisor and private set intersection. (arXiv:2303.17196v1 [quant-ph])

We present a secure multiparty quantum computation (MPQC) for computing
greatest common divisor (GCD) based on quantum multiparty private set union
(PSU) by Liu, Yang, and Li. As the first step, we improve the security of the
MPQC protocol for computing least common multiple (LCM) by Liu and Li by
constructing an efficient exact quantum period-finding algorithm (EQPA) as a
subroutine instead of the standard (probabilistic) Shor’s quantum
period-finding algorithm (QPA). The use of EQPA instead of the standard QPA
guarantees the correctness of the protocol without repetitions. The improvement
of LCM protocol also improves the private set union protocol which is based on
computing LCM. Finally, using the same idea of the PSU protocol, we construct a
quantum multiparty private set intersection (PSI) by transforming the PSI
problem into the problem of computing GCD. Performance analysis shows that the
correctness and the unconditional security in the semihonest model are
guaranteed directly from the correctness and the security of the subroutine
protocols (LCM and PSU protocols). Moreover, we show that the complexity of the
proposed protocols is polynomial in the size of the secret inputs and the
number of parties.