Advances in Cryptology – CRYPTO 2012

Volume 7417 of the series Lecture Notes in Computer Science pp 794-811

Actively Secure Two-Party Evaluation of Any Quantum Operation

  • Frédéric DupuisAffiliated withInstitute for Theoretical Physics, ETH Zurich Email author 
  • , Jesper Buus NielsenAffiliated withDepartment of Computer Science, Aarhus University
  • , Louis SalvailAffiliated withUniversité de (DIRO)


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].