On pairing inversion of the self-bilinear map on unknown order groups

Hyang Sook Lee, Seongan Lim, Ikkwon Yie

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

A secure self-bilinear map is attractive since it can be naturally extended to a secure multi-linear map which has versatile applications in cryptography. However, it was known that a self-bilinear map on a cyclic group of a known order cannot be cryptographically secure. In 2014, Yamakawa et al. presented a self-bilinear map, the YYHK pairing, on unknown order groups by using an indistinguishability obfuscator as a building block. In this paper, we prove that the Pairing Inversion (PI) of the YYHK pairing is equivalently hard to the factorization of RSA modulus N as long as iO in the scheme is an indistinguishability obfuscator. First, we prove that the General Pairing Inversion (GPI) of the YYHK pairing e: G×G → G is always solvable. By using the solvability of GPI, we prove that PI and BDHP for the YYHK-pairing e are equivalently hard to CDHP in the cyclic group G. This equivalence concludes that PI for the YYHK-pairing is equivalently hard to the factorization of N.

Original languageEnglish
Title of host publicationCyber Security Cryptography and Machine Learning - 1st International Conference, CSCML 2017, Proceedings
EditorsShlomi Dolev, Sachin Lodha
PublisherSpringer Verlag
Pages86-95
Number of pages10
ISBN (Print)9783319600796
DOIs
StatePublished - 2017
Event1st International Conference on Cyber Security Cryptography and Machine Learning, CSCML 2017 - Beer-Sheva, Israel
Duration: 29 Jun 201730 Jun 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10332 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference1st International Conference on Cyber Security Cryptography and Machine Learning, CSCML 2017
Country/TerritoryIsrael
CityBeer-Sheva
Period29/06/1730/06/17

Keywords

  • General Pairing Inversion
  • Pairing Inversion
  • Self-bilinear map

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