Abstract
Biometric Authentication Protocols (\(\mathsf {BAP}\)s) have increasingly been employed to guarantee reliable access control to places and services. However, it is well-known that biometric traits contain sensitive information of individuals and if compromised could lead to serious security and privacy breaches. Yasuda et al. [23] proposed a distributed privacy-preserving \(\mathsf {BAP}\) which Abidin et al. [1] have shown to be vulnerable to biometric template recovery attacks under the presence of a malicious computational server. In this paper, we fix the weaknesses of Yasuda et al.’s \(\mathsf {BAP}\) and present a detailed instantiation of a distributed privacy-preserving \(\mathsf {BAP}\) which is resilient against the attack presented in [1]. Our solution employs Backes et al.’s [4] verifiable computation scheme to limit the possible misbehaviours of a malicious computational server.
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Notes
- 1.
The same leakage of information could happen if a \(\mathsf {SHE}\) scheme is used.
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Acknowledgements
This work was partially supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no 608743; the VR grant PRECIS no 621-2014-4845 and the STINT grant “Secure, Private & Efficient Healthcare with wearable computing” no IB2015-6001.
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A Details in the Correctness Analysis
A Details in the Correctness Analysis
In this section, we show the intermediate steps of the calculation.
The derived tags are:
The homomorphic bilinear map calculation results are:
To prove that \(W = {\mathbf {GroupEval}}(f,R_{\alpha }, R_{\beta })\) satisfies Eq. (4), we start by analysing the three factors that made up the righthand of the equation, namely: \(e(g, g)^{y_{0}^{{\mathsf {HD}}}}\cdot e(Y_{1}^{{\mathsf {HD}}}, g)^{\theta }\cdot (\hat{Y}_{2}^{({\mathsf {HD}})})^{\theta ^{2}}\).We in turn expand each one of the factors and finally compute the product of the results, evaluating it against W.
The first factor can be expanded as:
The second factor is expanded as:
The third factor is expanded as:
Here we need to prove the right hand side is equal to W. We use a temporary variable \(P = e(g, g)^{y_{0}^{{\mathsf {HD}}}}\cdot e(Y_{1}^{{\mathsf {HD}}}, g)^{\theta }\cdot (\hat{Y}_{2}^{({\mathsf {HD}})})^{\theta ^{2}}\) to denote the expansion result of the righthand-side. The expression below proves the correctness of the second verification Eq. (4).
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Pagnin, E., Liu, J., Mitrokotsa, A. (2018). Revisiting Yasuda et al.’s Biometric Authentication Protocol: Are You Private Enough?. In: Capkun, S., Chow, S. (eds) Cryptology and Network Security. CANS 2017. Lecture Notes in Computer Science(), vol 11261. Springer, Cham. https://doi.org/10.1007/978-3-030-02641-7_8
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