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Secure multiparty computation of a comparison problem.

Xin Liu1, Shundong Li2, Jian Liu3

  • 1School of Computer Science, Shaanxi Normal University, Xi'an, 710062 China ; School of Information Engineering, Inner Mongolia University of Science and Technology, Baotou, 014010 China.

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Summary

This study introduces new secure multiparty computation protocols for private comparison of integers and rational numbers. These novel methods offer enhanced efficiency and information-theoretical security in semi-honest models.

Keywords:
Comparison problemGM encryption schemeSecure multiparty computationVector encoding method

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Area of Science:

  • Cryptography
  • Secure Multiparty Computation
  • Computational Number Theory

Background:

  • Private comparison is a critical primitive in secure multiparty computation (SMC).
  • Existing protocols often lack efficiency or comprehensive security guarantees for diverse number types.
  • The need for robust and efficient private comparison methods persists in secure data analysis.

Purpose of the Study:

  • To develop novel protocols for private comparison of integers and rational numbers within a single secure multiparty computation execution.
  • To enhance the efficiency and security of private comparison protocols compared to existing solutions.
  • To rigorously prove the privacy-preserving properties of the proposed protocols.

Main Methods:

  • A 0-1-vector encoding method is introduced to represent numbers for private integer comparison.
  • The Goldwasser-Micali encryption scheme is utilized for secure integer comparison.
  • A geometric method is employed for the information-theoretical secure private comparison of rational numbers.
  • The simulation paradigm is used to prove privacy in the semi-honest model.

Main Results:

  • Novel protocols for private determination of [Formula: see text] and [Formula: see text] are presented.
  • The proposed integer comparison protocol leverages Goldwasser-Micali encryption.
  • The rational number comparison protocol achieves information-theoretical security.
  • Protocols are proven to be privacy-preserving under the simulation paradigm in the semi-honest model.
  • Complexity analysis indicates improved efficiency over prior art.

Conclusions:

  • The developed protocols offer efficient and secure solutions for private comparison of integers and rational numbers.
  • The use of 0-1-vector encoding and geometric methods provides novel approaches to private number comparison.
  • The findings contribute to advancing the field of secure multiparty computation with practical and secure primitives.