Paper 2019/557 Original: eprint.iacr.org/2019/557 ↗
Extended Galbraith's Test on the Anonymity of IBEs from Higher Residuosity
Abstract
At PKC 2019, Clear and McGoldrick presented the first identity-based encryption (IBE) scheme that supports homomorphic addition modulo a poly-sized prime $e$. Assuming that deciding solvability of a special system of multivariate polynomial equations is hard, they proved that their scheme for $e>2$ is anonymous. In this paper, we review the classical Galbraith's test on the anonymity of the first pairing-free IBE scheme due to Cocks. With the eye of the reciprocity law over $\mathbb{F}_\mathtt{q}[x]$, we can have a profound understanding of the test and naturally extend it to give a practical attack on the anonymity of the Clear-McGoldrick IBE scheme. Furthermore, we believe that our technique plays a crucial role in anonymizing IBE schemes from higher residuosity.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2020-09-20: last updated
- 2019-05-25: published
- Short URL
- https://ia.cr/2019/557
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2019/557,
author = {Xiaopeng Zhao and Zhenfu Cao and Xiaolei Dong and Jun Shao},
title = {Extended Galbraith's Test on the Anonymity of IBEs from Higher Residuosity},
howpublished = {Cryptology {ePrint} Archive, Paper 2019/557},
year = {2019},
url = {https://eprint.iacr.org/2019/557}
}