Paper 2019/1069

Efficient Private PEZ Protocols for Symmetric Functions

Yoshiki Abe, Mitsugu Iwamoto, and Kazuo Ohta


A private PEZ protocol is a variant of secure multi-party computation performed using a (long) PEZ dispenser. The original paper by Balogh et al. presented a private PEZ protocol for computing an arbitrary function with n inputs. This result is interesting, but no follow-up work has been presented since then, to the best of our knowledge. We show herein that it is possible to shorten the initial string (the sequence of candies filled in a PEZ dispenser) and the number of moves (a player pops out a specified number of candies in each move) drastically if the function is symmetric. Concretely, it turns out that the length of the initial string is reduced from O((2^n)!) for general functions in Balogh et al.'s results to O(n * n!) for symmetric functions, and 2^n moves for general functions are reduced to n^2 moves for symmetric functions. Our main idea is to utilize the recursive structure of symmetric functions to construct the protocol recursively. This idea originates from a new initial string we found for a private PEZ protocol for the three-input majority function, which is different from the one with the same length given by Balogh et al. without describing how they derived it.

Available format(s)
Cryptographic protocols
Publication info
A minor revision of an IACR publication in TCC 2019
Private PEZ protocolMultiparty computationSymmetric functionsThreshold functions
Contact author(s)
yoshiki @ uec ac jp
2019-09-23: received
Short URL
Creative Commons Attribution


      author = {Yoshiki Abe and Mitsugu Iwamoto and Kazuo Ohta},
      title = {Efficient Private PEZ Protocols for Symmetric Functions},
      howpublished = {Cryptology ePrint Archive, Paper 2019/1069},
      year = {2019},
      note = {\url{}},
      url = {}
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