On pairing inversion of the self-bilinear map on unknown order groups
- 주제(키워드) General Pairing Inversion , Pairing Inversion , Self-bilinear map
- 지원기관 Ministry of Science, ICT and Future Planning
- 관리정보기술 faculty
- 등재 SCOPUS
- 발행기관 Springer Verlag
- 발행년도 2017
- URI http://www.dcollection.net/handler/ewha/000000155673
- ISBN 9783319600796
- 본문언어 영어
- Published As http://dx.doi.org/10.1007/978-3-319-60080-2_6
초록/요약
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. © Springer International Publishing AG 2017.
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