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.
|Title of host publication||Cyber Security Cryptography and Machine Learning - 1st International Conference, CSCML 2017, Proceedings|
|Editors||Shlomi Dolev, Sachin Lodha|
|Number of pages||10|
|State||Published - 2017|
|Event||1st International Conference on Cyber Security Cryptography and Machine Learning, CSCML 2017 - Beer-Sheva, Israel|
Duration: 29 Jun 2017 → 30 Jun 2017
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||1st International Conference on Cyber Security Cryptography and Machine Learning, CSCML 2017|
|Period||29/06/17 → 30/06/17|
Bibliographical noteFunding 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).
© Springer International Publishing AG 2017.
- General Pairing Inversion
- Pairing Inversion
- Self-bilinear map