Actively Secure Two-Party Evaluation of Any Quantum Operation

  • Frédéric Dupuis
  • Jesper Buus Nielsen
  • Louis Salvail
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7417)


We provide the first two-party protocol allowing Alice and Bob to evaluate privately even against active adversaries any completely positive, trace-preserving map \(\mathscr {F} \in \mathrm {L}(\mathcal {A}_{{{\mathrm{in}}}} \otimes \mathcal {B}_{{{\mathrm{in}}}}) \rightarrow \)\(\mathrm {L}(\mathcal {A}_{{{\mathrm{out}}}} \otimes \mathcal {B}_{{{\mathrm{out}}}})\), given as a quantum circuit, upon their joint quantum input state \(\rho _{\mathrm {in}}\in \mathrm{D}({\mathcal {A}_{{{\mathrm{in}}}} \otimes \mathcal {B}_{{{\mathrm{in}}}}})\). Our protocol leaks no more to any active adversary than an ideal functionality for \(\mathscr {F}\) provided Alice and Bob have the cryptographic resources for active secure two-party classical computation. Our protocol is constructed from the protocol for the same task secure against specious adversaries presented in [4].


  1. 1.
    Aharonov, D., Ben-Or, M., Eban, E.: Interactive proofs for quantum computations. In: Proceedings of Innovations in Computer Science (2008),
  2. 2.
    Barnum, H., Crépeau, C., Gottesman, D., Smith, A., Tapp, A.: Authentication of quantum messages. In: 43rd Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 449–458 (2002)Google Scholar
  3. 3.
    Bravyi, S., Kitaev, A.: Universal quantum computation with ideal clifford gates and noisy ancillas. Physical Review A 71, 022316 (2005), quant-ph/0403025MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Dupuis, F., Nielsen, J.B., Salvail, L.: Secure Two-Party Quantum Evaluation of Unitaries against Specious Adversaries. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 685–706. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Dupuis, F., Nielsen, J.B., Salvail, L.: Actively secure two-party evaluation of any quantum operation. Cryptology ePrint Archive, record 2012/304 (2012),
  6. 6.
    Gottesman, D.: Stabilizer codes and quantum error correction. PhD thesis, California Institute of Technology (1997)Google Scholar
  7. 7.
    Gottesman, D.: An introduction to quantum error correction and fault-tolerant quantum computation. In: Lomonaco Jr., S.J. (ed.) Quantum Information Science and Its Contributions to Mathematics. Proceedings of Symposia in Applied Mathematics, vol. 68, pp. 13–60 (April 2010),
  8. 8.
    Gottesman, D., Chuang, I.L.: Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations. Nature 402, 390–393 (1999)CrossRefGoogle Scholar
  9. 9.
    Gottesman, D., Chuang, I.L.: Quantum teleportation is a universal computational primitive (August 1999),
  10. 10.
    Gutoski, G., Watrous, J.: Toward a general theory of quantum games. In: 39th Annual ACM Symposium on Theory of Computing (STOC), pp. 565–574 (2007)Google Scholar
  11. 11.
    Hallgren, S., Smith, A., Song, F.: Classical Cryptographic Protocols in a Quantum World. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 411–428. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. 12.
    Lunemann, C., Nielsen, J.B.: Fully Simulatable Quantum-Secure Coin-Flipping and Applications. In: Nitaj, A., Pointcheval, D. (eds.) AFRICACRYPT 2011. LNCS, vol. 6737, pp. 21–40. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  13. 13.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: 37th Annual ACM Symposium on Theory of Computing (STOC), pp. 84–93 (2005)Google Scholar
  14. 14.
    Shor, P.W.: Fault-tolerant quantum computation. In: 37th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 56–65 (1996)Google Scholar

Copyright information

© International Association for Cryptologic Research 2012 2012

Authors and Affiliations

  • Frédéric Dupuis
    • 1
  • Jesper Buus Nielsen
    • 2
  • Louis Salvail
    • 3
  1. 1.Institute for Theoretical PhysicsETH ZurichZürichSwitzerland
  2. 2.Department of Computer ScienceAarhus UniversityAarhus CDenmark
  3. 3.Université de (DIRO)MontrealCanada

Personalised recommendations