[Resource Topic] 2019/557: Extended Galbraith's Test on the Anonymity of IBEs from Higher Residuosity

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Extended Galbraith’s Test on the Anonymity of IBEs from Higher Residuosity

Authors: Xiaopeng Zhao, Zhenfu Cao, Xiaolei Dong, Jun Shao


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.

ePrint: https://eprint.iacr.org/2019/557

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