Secure Authentication using a Garbled Circuit Variant for Arithmetic Circuits

Abstract

Biometric template security is an important issue given that biometric features, in their naiive form, are not revocable and provide a one-to-one link to the registered users. In this paper, we propose a new garbled circuit variant for arithmetic circuits along with the python implementation of them for two popular similarity metrics, namely Euclidean Distance and Cosine Similarity. We show that biometric matchers don’t suffer any accuracy losses under this template security scheme. Further, unlike other solutions, our proposed method is compatible with both binary and non-binary templates and all match metrics. Garbled Circuit is used to convert a Boolean circuit $\mathcal{C}$ to a garbled circuit $\mathcal{C}^{\prime}$. Our scheme converts an arithmetic circuit $\mathcal{C}:\mathbb{Z}^{n}\rightarrow\mathbb{Z}^{m}$ into an arithmetic garbled circuit $\mathcal{C}^{\prime}$ by the introduction of b-gates with two inputs $I_{1},I_{2}:I_{1},I_{2}\in[\mathbb{Z}]_{b}$ and two outputs. We design addition and multiplication circuits using our new gates and then garble them using garbled circuit techniques. Improvements to a garbled circuit such as point and permute and free XOR are added to our approach so that our garbled circuit version of each b-circuit is faster than its equivalent Boolean garbled circuit by a factor of $(\log_{2}b)/2$. The python implementation of a 10-gate garbled circuit for any arbitrary arithmetic circuit is given.