Cryptology ePrint Archive: Report 2019/557

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

Xiaopeng Zhao and Zhenfu Cao and Xiaolei Dong and Jun Shao

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.

Category / Keywords: public-key cryptography / identity-based encryption; Galbraith's test; anonymity

Date: received 24 May 2019, last revised 20 Sep 2020

Contact author: 1306062147 at qq com

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Version: 20200920:194127 (All versions of this report)

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