Extended Galbraith’s test on the anonymity of IBE schemes from higher residuosity

Xiaopeng Zhao; Zhenfu Cao; Xiaolei Dong; Jun Shao

doi:10.1007/s10623-020-00816-w

Extended Galbraith’s test on the anonymity of IBE schemes from higher residuosity

Xiaopeng Zhao
, Zhenfu Cao^*
, Xiaolei Dong
, Jun Shao

^*Corresponding author for this work

Software Engineering Institute

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

At PKC 2019, Clear and McGoldrick presented the first identity-based encryption (IBE) scheme that is group homomorphic for 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 for F_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.

Original language	English
Pages (from-to)	241-253
Number of pages	13
Journal	Designs, Codes, and Cryptography
Volume	89
Issue number	2
DOIs	https://doi.org/10.1007/s10623-020-00816-w
State	Published - Feb 2021

Keywords

Anonymity
Galbraith’s test
Identity-based encryption
Reciprocity law for F[x]

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10.1007/s10623-020-00816-w

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title = "Extended Galbraith{\textquoteright}s test on the anonymity of IBE schemes from higher residuosity",

abstract = "At PKC 2019, Clear and McGoldrick presented the first identity-based encryption (IBE) scheme that is group homomorphic for 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{\textquoteright}s test on the anonymity of the first pairing-free IBE scheme due to Cocks. With the eye of the reciprocity law for Fq[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.",

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author = "Xiaopeng Zhao and Zhenfu Cao and Xiaolei Dong and Jun Shao",

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doi = "10.1007/s10623-020-00816-w",

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AU - Zhao, Xiaopeng

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AU - Shao, Jun

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Y1 - 2021/2

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AB - At PKC 2019, Clear and McGoldrick presented the first identity-based encryption (IBE) scheme that is group homomorphic for 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 for Fq[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.

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KW - Identity-based encryption

KW - Reciprocity law for F[x]

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DO - 10.1007/s10623-020-00816-w

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ER -

Extended Galbraith’s test on the anonymity of IBE schemes from higher residuosity

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Keywords

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