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On the Invisibility and Anonymity of Undeniable
Signature Schemes 1Faculty
of Information Science and Technology, Multimedia University, Melaka, Malaysia jasonlohjc@gmail.com, shheng@mmu.edu.my 2School
of Computing, Newcastle University,
Newcastle upon Tyne, United Kingdom syh-yuan.tan@newcastle.ac.uk 3Department
of Computer and Information Sciences, Ibaraki University, Hitachi, Ibaraki 316-8511,
Japan kaoru.kurosawa.kk@vc.ibaraki.ac.jp Abstract Undeniable signature is a special featured digital
signature which can only be verified with the help of the signer. Undeniable
signature should satisfy invisibility which implies the inability of a user
to determine the validity of a message and signature pair as introduced by
Chaum et al. Galbraith and Mao later proposed the notion of anonymity which
implies the infeasibility to determine which user has issued the signature.
They also proved that the notions of invisibility and anonymity are
equivalent when the signers possess the same signature space, such that if an
undeniable signature possesses invisibility, then it also possesses
anonymity, and vice versa. In this paper, we show that in contradiction to the
equivalency result established by Galbraith and Mao, there exist some
undeniable signature schemes that possess invisibility but not anonymity.
This motivates us to find out whether there is a limitation on Galbraith and
Mao’s equivalency result or the schemes are actually flawed. Our analysis
shows that the anonymity property requires all signers to possess the same
signature space but the invisibility property does not. This conforms to the
equivalency result and implies that an undeniable signature scheme can be
invisible but not anonymous if the signers possess the different signature
space. Our result invalidates two past cryptanalyses on undeniable signature
schemes. We also provide a generic solution to solve the above problem. Keywords: anonymity, invisibility,
undeniable signature +: Corresponding author: Swee-Huay
Heng Faculty
of Information Science and Technology, Multimedia University, Jalan Ayer
Keroh Lama, 75450 Melaka, Malaysia, Tel: +60-(0)6-2523600 Journal of Wireless
Mobile Networks, Ubiquitous Computing, and Dependable Applications (JoWUA) Vol. 11, No. 1, pp. 18-34, March 2020
[pdf] Received:
January 23, 2020; Accepted: March 6, 2020; Published: March 31, 2020 DOI: 10.22667/JOWUA.2020.03.31.018 |