Non-interactive and fully output expressive private comparison

Yu Ishimaki*, Hayato Yamana

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Citations (Scopus)


Private comparison protocols are fundamental to the field of secure computation. Recently, Lu et al. (ASIACCS 2018) proposed a new protocol, XCMP,, which is based on a ring-based fully homomorphic encryption (FHE) scheme. In that scheme, two μ-bit integers a and b are compared in encrypted form without revealing the plaintext to an evaluator. The protocol outputs a bit in encrypted form, which indicates whether a > b. XCMP has the following three advantages: the output can be reused for further processing, the evaluation is performed without any interactions with a decryptor having a secret key, and the required multiplicative depth is only 1. However, XCMP has two potential disadvantages. First, the protocol result preserves both additive and multiplicative homomorphisms over ℤ t only, whereas the underlying FHE scheme can support a much larger plaintext space of (Formula Presented) for a prime t and a power-of-two N; this restricts the functionality of applications using the comparison result. Second, the bit length μ of the integers to be compared is no more than log N (typically 16 bits, at most). Thus, it is difficult for XCMP to handle larger integers. In this paper, we propose a non-interactive private comparison protocol that solves the aforementioned problems and outputs an additively and multiplicatively reusable comparison result over the ring without adding an extremely large computational overhead over XCMP. Moreover, by regarding a μ (>16 -bit integer as a sequence of chunks, we show that the multiplicative depth required for our comparison protocol is logarithmic in the number of chunks. This value is much smaller than the naïve solution with a multiplicative depth of log μ. Experiment results demonstrate that our protocol introduces a subtle overhead over XCMP. Remarkably, we experimentally demonstrate that our protocol for a larger domain is comparable to the construction given by one of the state-of-the-art bitwise FHE schemes.

Original languageEnglish
Title of host publicationProgress in Cryptology – INDOCRYPT 2018 - 19th International Conference on Cryptology in India, Proceedings
EditorsDebrup Chakraborty, Tetsu Iwata
PublisherSpringer Verlag
Number of pages20
ISBN (Print)9783030053772
Publication statusPublished - 2018
Event19th International Conference on Cryptology in India, INDOCRYPT 2018 - New Delhi, India
Duration: 2018 Dec 92018 Dec 12

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11356 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other19th International Conference on Cryptology in India, INDOCRYPT 2018
CityNew Delhi


  • Homomorphic encryption
  • Non-interactive private comparison
  • Secure computation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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