Overview of UB Technologies in .NET

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26.5 Overview of UB Technologies
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the other hand, the attacker chooses to cryptographically test (i.e., to run them through the hash function) all possible keys, the number would be 2k . The requirement (26.6) means, in fact, that the FAR attack must be made more dif cult for the attacker than the cryptographic brute force search! However, it is obvious that the latter method (i.e., inverting the hash) is much more available and attractive to an ordinary attacker, and the requirement (26.6) just invites him to do so. There is a signi cant difference between FAR attack and a cryptographic brute force attack. The FAR attack does not have an exact analogue in conventional cryptography and requires collection or generation of a large database of biometric samples that must be compatible with the samples used in the real BE system. Second, the BE algorithm is usually much slower than simply hashing the key. Image processing, features extraction, and ECC decoding parts may take longer (by six orders of magnitude or more) than hashing. Note that six orders of magnitude are equivalent to extra 20 bits of security. Taking into account the cost factor, CF, of collecting and maintaining the interoperable biometric database,3 and the speed factor, SF, we will turn the over-restrictive requirement 26.6 right-side up: k log2 (FAR) + log2 (CF) + log2 (SF) . (26.7)
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In other words, the key should be long enough to make the cryptographic brute force search less feasible than the FAR attack.
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26.5 26.5.1
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OVERVIEW OF UB TECHNOLOGIES Biometric Encryption
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Bodo
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The prior art of BE is a German patent to Bodo [51]. It suggests deriving a cryptographic key directly from a biometric (e.g., ngerprint minutiae) template without storing any helper data. The patent does not actually disclose a method for deriving a key. Although it may be tempting to map any biometric to a unique key, there are two major problems with this approach [15, 52]: r It is very hard to accommodate for biometric variability; and r The key would not be revocable; that is, if compromised, this particular biometric would be lost forever. The dif culties of handling errors in the biometric without helper data can be illustrated by the following simple example: Let us assume that the biometric template is a random binary string, such as 100101110100100110. . .. We will try to use an ECC in a decoding mode in order to map parts of that string to the nearest codeword. For example, we can choose a (9, 1)
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cost factor is de ned from the attacker s perspective on feasibility of the attack.
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Biometric Encryption: The New Breed of Untraceable Biometrics
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repetition code. The rst 9 bits, 100101110, will be mapped to 1, because there are 5 ones and 4 zeros; and by the majority rule, the nearest codeword is 111111111. The second chunk, 100100110, is mapped to 0. However, on veri cation, this scheme will not tolerate even a single bit error that would change the 5:4 score to 4:5. If, on the contrary, we use a BE fuzzy commitment scheme, then the codeword 111111111000000000 . . . is XOR-ed with the template, and the result is stored as helper data. This scheme tolerates up to 4 arbitrary bit errors in each chunk (note that a repetition code is not a good choice for BE in general, because it creates many security problems detailed in Section 26.6, and this simple example is used for the sake of clarity only). Key generation without helper data is more likely to succeed if the biometric is condensed to a few very robust biometric features, and the key size is small (see references 21 and 53). DNA testing is, probably, the only biometric of the future that could generate long keys with this technique. 26.5.1.2 Mytec1
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The rst BE scheme, which we call Mytec1,4 now holds only a historical signi cance. Nevertheless, we think it is worth describing to illustrate major concepts and problems with BE. The method used optical correlation and was implemented in a hardware (see references 25, 54, and 55 for details). A Fourier transform of a ngerprint image was performed in an analog way using the properties of a coherent light passing through an optical system. It is important to point out that the optical hardware did not serve an obscuration purpose; therefore, the system could be implemented digitally, as follows: Let f(x) be the input ngerprint pattern signal and let s(x) be the output signal, which is designed to have the form of the sum of n delta functions in the positions x1 , x2 , . . . , xn and relative intensities g1 , g2 , . . . , gn : (26.8) s(x) = g1 (x x1 ) + g2 (x x2 ) + gn (x xn ). The Fourier lter function, H(u), is stored as a ratio of the output signal Fourier transform, S(u), and the ngerprint Fourier transform F(u) = |F(u)|exp(i (u)): H(u) = exp( i (u)) S(u) = |F (u)| F (u) g1 exp( i2 ux1 ) + g2 exp( i2 ux2 ) + .
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(26.9)
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Thus, the stored lter, H(u), is a ratio of a complex pseudo-random function (the sum of complex exponents), which is related to the key, and a ngerprint Fourier transform. At the rst glance, it is impossible to derive either the key or the ngerprint from this ratio. If a correct ngerprint is submitted on veri cation, its Fourier
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