Theoretical Framework for Constructing Matching Algorithms in Biometric Authentication Systems

Abstract

In this paper, we propose a theoretical framework to construct matching algorithms for any biometric authentication systems. Conventional matching algorithms are not necessarily secure against strong intentional impersonation attacks such as wolf attacks. The wolf attack is an attempt to impersonate a genuine user by presenting a “wolf” to a biometric authentication system without the knowledge of a genuine user’s biometric sample. A “wolf” is a sample which can be accepted as a match with multiple templates. The wolf attack probability (WAP) is the maximum success probability of the wolf attack, which was proposed by Une, Otsuka, Imai as a measure for evaluating security of biometric authentication systems [UOI1], [UOI2]. We present a principle for construction of secure matching algorithms against the wolf attack for any biometric authentication systems. The ideal matching algorithm determines a threshold for each input value depending on the entropy of the probability distribution of the (Hamming) distances. Then we show that if the information about the probability distribution for each input value is perfectly given, then our matching algorithm is secure against the wolf attack. Our generalized matching algorithm gives a theoretical framework to construct secure matching algorithms. How lower WAP is achievable depends on how accurately the entropy is estimated. Then there is a trade-off between the efficiency and the achievable WAP. Almost every conventional matching algorithm employs a fixed threshold and hence it can be regarded as an efficient but insecure instance of our theoretical framework. Daugman’s algorithm proposed in [Da2] can also be regarded as a non-optimal instance of our framework.

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