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Privacy in Biometrics

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A (M, m, l, t, )-fuzzy extractor is a pair of procedures that generate Gen and Rep, where: r Gen is a randomized generation function that on input w M extracts a private

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string R {0, 1}l and public string P such that for all random variable W over M with min-entropy H (W) m, it holds that r is close to uniform even for observers P, that is, the statistical distance D(R, P)(Ul , P) . r Rep is a regeneration function that, given a word w H and a public string P, outputs a string S such that if d(w, w ) t and (R, P) = Gen(w), it holds that Rep(w , P) = R = S.

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The rst property (security) guarantees the uniformity of the extracted secret string R (remember that the min-entropy, the second property (correctness), guarantees the correctness of the reproduction. In this setting it is possible to show that the fuzzy commitment construction of Juels and Wattenberg is a (M = n , n, k, t, 0)-fuzzy extractor when a binary linear code C of length n, dimension k, and correction capacity t (i.e., with parameters [n, k, 2t + 1]) is used and when W is uniform (i.e., m = n). In this case, Gen(w), where s = w C(x), returns R = x and P = s. To execute Rep(w , P), decode w P to obtain C(x) and apply the decoding function to obtain x. Notice that s is random when also w is random, and if W is not uniform, s would leak information about x. In general, it is possible to obtain for a given code C with parameters [n, k, 2t + 1] and any m and a (M, m, l, t, ) fuzzy extractor with = m + k n 2 log(1/ ) + 2, by using in the extraction phase pairwise independent hashing. In a successive work, Boyen [28], pointed out how multiple use of the same fuzzy secret can cause some security problem, introducing outsider and insider attack scenarios, where an adversary tries to obtain information on the secret by performing repeatedly extractions and regenerations of the fuzzy secret. In such scenarios, with some limitations, it is possible to show that information-theoretic security can be achieved and existing constructions can be adapted to satisfy the additional requirements. More general attack models and constructions to achieve secure remote biometric authentication are proposed in reference 33. 25.3.2.4 Fuzzy-Based Authentication Schemes

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Since the introduction of the fuzzy primitives, many researchers have proposed several authentication schemes based on the applications of such techniques. A general framework to design and analyze a secure sketch for biometric templates is presented in reference 12, where the face biometrics have been used as an example. Interestingly, the paper shows that theoretical bounds have their limitations in practical schemes. In particular, it has been shown that the entropy loss of the template cannot be considered a complete description of the robustness level of the scheme in practical application, while the analysis of the FAR and FRR should be always envisioned. In reference 34 a near-optimal error-correcting code is discussed (based on a two-dimensional iterative min-sum decoding algorithm) for application with iris biometrics in a fuzzy sketches scheme. The paper produces also an explicit estimation of the upper bounds

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25.4 Privacy in Multimodal Systems

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on the correction capacity of fuzzy sketches on iris-based biometrics. A fuzzy-based construction for ngerprint biometrics has been discussed in reference 13, where the string representation of the biometric templates relays on Fingercodes.

PRIVACY IN MULTIMODAL SYSTEMS

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Humans beings typically identify other individuals using a biometric approach that encompasses more than a single biometric trait. For example, we can recognize a person watching his face, but the nal decision is often integrated using other biometric traits such as the voice, the stature, the gait, or the behavior. In a similar way, a multimodal biometric system uses different biometric traits and combines them ef ciently [35]. More in detail, in the literature the term multibiometric system is used when different approaches are considerd. In particular, the term is used when one or more of the following setups are present: multiple sensors (e.g., solid state and optical ngerprint sensors), multiple acquisitions (e.g., different frames/poses of the face), multiple traits (e.g., an eye and a ngerprint), multiple instances of the same trait kind (e.g., left eye, and right eye), multiple algorithm (e.g., different preprocessing and/or matching techniques). In this framework, a multimodal system is a case of a multibiometric system. The usage of multimodal systems has an heavier impact on the privacy of the user since the amount of the involved personal information is greater. This issue can be better understood taking into account the speci c peculiarities of multimodal systems.

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