Paper 2026/883

Secure Two-Party Quantum Computation with Complete Fairness without Trusted Third Party

Goutam Paul, Indian Statistical Institute

Asim K. Pal, Indian Institute of Management Calcutta

Asmita Samanta, Indian Statistical Institute

Hridam Basu, Rump Labs

Abstract

In 1997, Lo proved that if one of the parties is malicious, it is not possible to achieve unconditional security in quantum bit-commitment (Phy. Rev. Lett, 1997) and hence in two-party quantum computation (Phy. Rev. A, 1997). However, restricting the computational power of the adversary, via assumptions like the existence of one-wayness, it has been shown that secure quantum bit-commitment is indeed possible by Dumais et al. (EUROCRYPT 2000). In their paper, they showed that with the assumption of a one-way permutation that is secure against any polynomial-time quantum adversary, one can achieve a secure quantum bit-commitment scheme. Although security is guaranteed, complete fairness remains an issue in quantum two-party computation for the real-world framework. In this paper, we show for the first time that there are some functions for which secure two-party quantum computation with complete fairness is achievable. This seems in sharp contrast with the impossibility result of Ben-Or et al. (FOCS, 2006). In Ben-Or et al.'s work, they have considered a malicious quantum adversary with unconditional computational power and used a broadcast channel. We have used the hybrid model idea of Gordon et al. (STOC 2008) using a non-simultaneous channel and the idea of composition of multiparty computations by Ran Canetti (Journal of Cryptology, 2000), to achieve complete fairness in the quantum domain, under the assumption of computationally bounded adversary. The functions we study are of two types (similar to Gordon et al.): one is any function without an embedded XOR, and the other is a particular function containing an embedded XOR. At first, we design secure two-party computation protocols in a hybrid model, using a trusted third party. Then we prove how these protocols achieve complete fairness in the hybrid model. Finally, we construct a secure two-party communication protocol and show how we can use this to remove the trusted third party of the hybrid model, and achieve both security and complete fairness in the real-world model.

@misc{cryptoeprint:2026/883,
      author = {Arpita Maitra and Goutam Paul and Asim K. Pal and Asmita Samanta and Hridam Basu},
      title = {Secure Two-Party Quantum Computation with Complete Fairness without Trusted Third Party},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/883},
      year = {2026},
      url = {https://eprint.iacr.org/2026/883}
}