# From Iris Image to Embedded Code: System of Methods
## 6 Selecting the Embedding Method
One function is used for registration and recognition. The conditions must hold  
\[ \begin{split} T_{1},T_{2}\text{ taken from one person}& \implies K_{1}=K_{2}\,\\ T_{1},T_{2}\text{ taken from different persons}& \implies K_{1}\
eq K_{2}\.\end{split}  \tag{35}\]  
These conditions are closely related to (34); however, in (35) the task is to reproduce the sequence of bits. The results of the methods without supplementary data are not very hopeful for practical applications. Error level is generally very high in this approach. In [50] the authors report \(\text{FRR}=24\%\) at \(\text{FAR}=0.07\%\) even for homogeneous high-quality images [32]. In [51], the idea is based on assumption that two iris codes can be mapped to some \"closest\" prime number and this number will be the same for the codes from one person. Considering the variability of iris codes even for ideal conditions this is unlikely to happen. The authors do not report the study of recognition errors. Scenario with _helper code_ demonstrates much better performance. During registration the encoder takes the template \(T_{1}\), computes the key \(K_{1}=K(T_{1})\), encrypts the message \(M\) with \(K_{1}\) and additionally outputs some helper code \(h=\Phi(T_{1})\). Immediately after this the original \(T_{1}\), \(M\), and \(K_{1}\) are destroyed, leaving only encoded message \(M^{\prime}\) and helper code \(h\). The original template \(T_{1}\) or key \(T_{1}\) cannot be recovered from \(M^{\prime}\) and \(h\). During presentation another set of biometric traits \(T_{2}\) is obtained and the key \(K_{2}=\Psi(T_{2},h)\) is calculated. Functions \(\Phi\) and \(\Psi\) are designed so as to satisfy (35). Thus, by providing biometrics and helper code, the registered user can obtain the original key \(K_{2}=K_{1}\), and hence the message \(M\). At the same time, the intruder, even knowing \(h\), will not be able to obtain \(K_{1}\)[52], so the helper code \(h\) can be made non-secret. The biometric data itself may be used as a key: \(K\equiv T\). In this case, at the stage of presentation, original biometrics \(T_{1}\) is restored from presented \(T_{2}\). This scenario is called _secure sketch_[53]. However, the works based on secure sketches and available in the literature show rather modest results. For example, the system [54] is workable under the assumption that intraclass variability of features is below \(10\%\). In practice, the variability is more than \(20\%\). This conditions the inoperability of the proposed method. The _key binding_ scheme in the above terms looks like a pair of encoder function \(C=\Phi(K_{1},T_{1})\) and decoder function \(K_{2}=\Psi(C,T_{2})\), which holds the (35) condition. The advantage is that \(K_{1}\) is set externally, rather than created by the developed algorithm. From this point of view, \(K_{1}\) can be perceived as a message \(M\), which is external to the encryption system. This immediately simplifies the biometric cryptosystem to a symmetric encryption scenario. The difference is that the secret key \(K\) must be the same in encoding and decoding in symmetric encryption, whereas the biometric features (also secret) differ: \(T_{1}\
eq T_{2}\). This scenario is called _fuzzy extractor_[53]. If \(\Psi\) is an inverse of \(\Phi\) and biometric data are composed of real numbers the scenario is referred to as _shielding functions_[55]. So-called _fuzzy vault_[43] is another popular method of key embedding. It is founded on [PERSON]'s secret separation scheme [56]. Here rather low, practically meaningful error values are obtained: [57] reports \(\text{FRR}=0.78\%\) and [58] reports \(\text{FRR}=4.8\%\) at zero FAR. However, both results are shown using a single small image database (less than 1000 samples). The most promising for use in iris biometry is _fuzzy commitment_ scenario [59]. In [60], a simple algorithm is proposed. The basic idea is to use employ the _error correcting coding_ (ECC) [61]. ECC is widely used in data transmission over noisy channels.