@inproceedings{e3c683bb7df641459f4eebba03e76080,
title = "On pairing inversion of the self-bilinear map on unknown order groups",
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.",
keywords = "General Pairing Inversion, Pairing Inversion, Self-bilinear map",
author = "Lee, {Hyang Sook} and Seongan Lim and Ikkwon Yie",
note = "Funding Information: We thank the anonymous reviewers for useful comments. Hyang-Sook Lee was supported by Basic Science Research Programs through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (Grant Number: 2015R1A2A1A15054564). Seongan Lim was also supported by Basic Science Research Programs through the NRF (Grant Number: 2016R1D1A1B01008562). Publisher Copyright: {\textcopyright} Springer International Publishing AG 2017.; null ; Conference date: 29-06-2017 Through 30-06-2017",
year = "2017",
doi = "10.1007/978-3-319-60080-2_6",
language = "English",
isbn = "9783319600796",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "86--95",
editor = "Shlomi Dolev and Sachin Lodha",
booktitle = "Cyber Security Cryptography and Machine Learning - 1st International Conference, CSCML 2017, Proceedings",
}