Gaussian Fuzzy Commitment A.J. Han Vinck University of Duisburg-Essen Institute for Experimental Mathematics Essen, Germany Email: han.vinck@uni-due.de Aram Jivanyan American University of Armenia Yerevan College of Engineering Yerevan, Armenia Email: jivanyan@gmail.com Jonas Winzen University of Duisburg-Essen Duisburg, Germany Email: jonas.winzen@uni-due.de Abstract—We discuss the protection of Gaussian biometric templates. We first introduce the Juels-Wattenberg for binary biometrics, where the binary biometrics are a result of hard- quantized Gaussian biometrics. The Juels-Wattenberg scheme adds a random binary code word to the biometric for privacy reasons and to allow errors in the biometric at authentication. We modify the Juels- Wattenberg scheme in such a way that we do not have to quantize the biometrics. We investigate and compare the performance of both approaches. Introduction Authentication and identification systems based on biomet- rics, see [1], suffer from basic problems, like: • Leaking information about the biometrics of a person from the stored data; • Biometric measurements are often noisy or vary, which causes problems at authentication. We discuss biometric authentication schemes and their perfor- mance using linear error correcting codes. The biometrics are vectors B of length n where E [B i ]=0, σ 2 b = 1 n · E  n  i=1 (B i ) 2  . As input to the biometric schemes we use the DCT transform of the vector B, where b = B T , and for large values of n (≥ 256),b i is a Gaussian random variable N ( 0,σ 2 b ) . The vector b can be quantized and processed as a binary (0,1) input vector with equally probable inputs, or it can be used as a Gaussian biometric of length n with components N ( 0,σ 2 b ) . One of the popular schemes using error correcting codes is the Juels-Wattenberg (JW) scheme, [1]. The JW scheme adds a randomly selected binary code word c to a binary, in our case a binary quantized Gaussian, biometric for privacy reasons and to allow errors in the biometric at authentication. We use the JW scheme in such a way that we do not quantize the Gaussian biometrics. For this we add to the Gaussian biometric a randomly selected binary code word with components ± √ E. The value of √ E can be chosen at enrollment. We investigate and compare the performance of both approaches. The performance parameters that we use to evaluate and compare schemes are: • FAR, the false acceptance rate. We calculate the proba- bility that an arbitrary user is accepted as being authentic; Data Base b c h=H(c) b q b q c (a) Enrollment + b e b+e [b+e] q (b) Authentication Figure 1: The Juels-Wattenberg Scheme • FRR, the false rejection rate. We calculate the probability that we reject an authentic biometric at authentication; • SAR, the successful attack rate. We calculate the prob- ability that a guess gives the correct biometric or code word c and thus the secret. The contribution is organized as follows. We first describe the JW scheme and its performance in section 2. In section 3 we give a modification of the JW scheme for Gaussian inputs. In section 4 we extend the noise to include erasures. In section 5 we represent the schemes by a wiretap channel model and calculate the “secrecy capacity”. I. THE J UELS-WATTENBERG SCHEME The scheme that we work on is the JW scheme introduced in [1], see figure 1a. At enrollment, the Gaussian biometric vector b is quantized as a binary (0,1) vector b q and added modulo-2 component wise to a randomly selected binary code word c from a linear error correcting code. The result s = b q ⊕c is stored in the data base. At the same time we also store the result of a hashing function of c as H (c)= h. We assume that from h it is impossible to get information about c. At authentication a possibly “slightly” modified biometric b ′ =[b + e] q is added to s and we obtain a vector z = c ⊕ b q ⊕ [b + e] q . We assume that the components of e are N ( 0,σ 2 w ) .