Cryptology ePrint Archive: Report 2019/1069

Efficient Private PEZ Protocols for Symmetric Functions

Yoshiki Abe and Mitsugu Iwamoto and Kazuo Ohta

Abstract: 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.

Category / Keywords: cryptographic protocols / Private PEZ protocol, Multiparty computation, Symmetric functions, Threshold functions

Original Publication (with minor differences): IACR-TCC-2019

Date: received 20 Sep 2019, last revised 20 Sep 2019

Contact author: yoshiki at uec ac jp

Available format(s): PDF | BibTeX Citation

Version: 20190923:071437 (All versions of this report)

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