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Ideal Private Simultaneous Messages Schemes and Their Applications

Authors Keitaro Hiwatashi, Reo Eriguchi

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LIPIcs.ITCS.2026.76.pdf
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ACM Subject Classification
  • Theory of computation → Cryptographic primitives
Keywords
  • secure computation
  • private simultaneous messages
  • communication complexity

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Abstract

Private Simultaneous Messages (PSM) is a minimal model for secure computation, where two parties, Alice and Bob, have private inputs x,y and a shared random string. Each of them sends a single message to an external party, Charlie, who can compute f(x,y) for a public function f but learns nothing else. The problem of narrowing the gap between upper and lower bounds on the communication complexity of PSM has been widely studied, but the gap still remains exponential. In this work, we study the communication complexity of PSM from a different perspective and introduce a special class of PSM, referred to as ideal PSM, in which each party’s message length attains the minimum, that is, their messages are taken from the same domain as inputs. We initiate a systematic study of ideal PSM with a complete characterization, several positive results, and applications. First, we provide a characterization of the class of functions that admit ideal PSM, based on permutation groups acting on the input domain. This characterization allows us to derive asymptotic upper bounds on the total number of such functions and a complete list for small domains. We also present several infinite families of functions of practical interest that admit ideal PSM. Interestingly, by simply restricting the input domains of these ideal PSM schemes, we can recover most of the existing PSM schemes that achieve the best known communication complexity in various computation models. As applications, we show that these ideal PSM schemes yield novel communication-efficient PSM schemes for functions with sparse or dense truth-tables and those with low-rank truth-tables. Furthermore, we obtain a PSM scheme for general functions that improves the constant factor in the dominant term of the best known communication complexity. An additional advantage is that our scheme simplifies the existing construction by avoiding the hierarchical design of internally invoking PSM schemes for smaller functions.

Cite As Get BibTex

Keitaro Hiwatashi and Reo Eriguchi. Ideal Private Simultaneous Messages Schemes and Their Applications. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 76:1-76:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ITCS.2026.76

Author Details

Keitaro Hiwatashi
  • National Institute of Advanced Industrial Science and Technology, Tokyo, Japan
Reo Eriguchi
  • National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

Funding

This work was supported in part by JST CREST Grant Number JPMJCR22M1, JST K Program Grant Number JPMJKP24U3, and JSPS KAKENHI Grant Numbers 24K20775.

Acknowledgements

We would like to thank Koji Nuida for his helpful comments.

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