Private Function Evaluation for Multi In- and Output-Gate Circuits

Bachelor Thesis

Published in 29. Advances in Cryptology – ASIACRYPT'23


The cryptographic protocol Private Function Evaluation (PFE) allows two parties to securely compute f(x), where x is the private data input of one party and f is a private function given by the other party without learning anything but the output. There are many applications for PFE like insurance rate calculation [1], credit checking [2], and software diagnosis [3]. It was recently shown that, for large function sizes, homomorphic encryption (HE)-based PFE [4] outperforms the more general approaches that use a universal circuit (UC) [5] as public function in a multi-party computation (MPC) protocol. However, UC-based PFE protocols are way more flexible as they are fully compatible to well-studied generic MPC protocols and can implement Boolean circuits consisting of any gates, while HE-based PFE cannot be easily implemented in existing MPC tools and is restricted to circuits of two input NAND gates. This thesis should investigate how the size of UCs can be reduced by replacing function blocks that implement, e.g., lookup tables or complex functionalities, with n-input, k-output gates (LUTs) [6], which can be easily included into universal circuits and evaluated with corresponding generic MPC protocols.


The goal of this thesis is to implement n-input, k-output gate (LUT) support into the UC implementation of Alhassan et al. [5]. This implementation then shall be used to compare the sizes of circuits optimized with n-input gates to equivalent circuits consisting of only 2-input, 1-output gates. Finally, the optimized UCs have to be benchmarked with an MPC protocol and compared to previous works.


  • Good programming skills in C++
  • At least basic knowledge of cryptography
  • High motivation + ability to work independently
  • Knowledge of the English language, Git, LaTeX, etc. goes without saying


  • [1] D. Günther, Á. Kiss, L. Scheidel, T. Schneider: Framework for Semi-Private Function Evaluation with Application to Secure Insurance Rate Calculation. In CCS Poster/Demo, 2019.
  • [2] K.B. Frikken, M.J. Atallah, C.Zhang: Privacy-preserving Credit Checking. In EC, 2005.
  • [3] J. Brickell, D. E. Porter, V. Shmatikov, E. Witchel: Privacy-preserving Remote Diagnostics. In CCS, 2007.
  • [4] M. Holz, Á. Kiss, D. Rathee, T. Schneider: Linear-Complexity Private Function Evaluation is practical. In ESORICS, 2020.
  • [5] M.Y. Alhassan, D. Günther, Á. Kiss, T. Schneider: Efficient and Scalable Universal Circuits. In JoC, 2020.
  • [6] A. Sadeghi and T.Schneider: Generalized Universal Circuits for Secure Evaluation of Private Functions with Application to Data Classification. In ICISC, 2008.