# From Iris Image to Embedded Code: System of Methods
## 6 Selecting the Embedding Method  
There are many works, where biometry is used in combination in combination with other security measures such as usual secured passwords, for instance [41; 42]. Here, we intend to develop a system that uses only data transmitted insecurely--the only protection is the iris of the owner. We also limit ourselves to the case of symmetric encryption. During encoding the _message_\(M\) and the secret _key_\(K\) are combined into the _code_ by the _encoder_ function \(\Phi\): \(C=\Phi(M,K)\), and during decoding the message is reconstructed from code and key by _decoder_ functions \(\Psi\): \(M=\Psi(C,K)\). If key \(K\) is not present, it is impossible to obtain \(M\) from \(C\), thus the code \(C\) can be made public. Symmetric encryption requires that \(K\) is repeated exactly. Not a single bit of it can be changed. The central problem in automatic biometry systems can be put as developing the optimal classifier. The classifier consists of a distance function between two biometric data samples \(\rho(D_{1},D_{2})\) and a threshold \(\theta\) (34). The function \(\rho\) can be treated as a superposition of two sub-functions. The first one is the calculation of the biometric template \(T\) from source data \(T=T(D)\), Second sub-function is the calculation of the distance itself \(\rho(T_{1},T_{2})\). Features should be selected, which are stably close for the same person and stably far for different persons with respect to function \(\rho\). As a rule, the elements of biometric templates are highly correlated. On the contrary, cryptographic keys are deliberately developed so as to have uncorrelated bits. However, the entropy (information amount) of an iris template is comparable to that of currently used cryptographic keys [43]. This suggests that it is possible to implement a cryptographic key in biometrics without reducing its robustness. It should be noted that most of the works presenting the application of cryptographic methods to biometrics, develop the scenario of _cancelable biometrics_[44]. Its essence is producing such biometric templates that source biometric data cannot be extracted or guessed anyhow from any number of templates. Cancelable biometrics is nothing but a kind of fuzzy hashing [45]. Formally, an additional step is introduced in the calculation of the distance function \(\rho\). Distance \(\rho(S_{1},S_{2})\) is calculated, \(S=S(T)\) is the hash function. Obviously, the recognition problem is still being solved here. Thus, cancelable biometrics is just a remake of identification and cannot be used for our purposes. There are two approaches to how to process volatile biometrics, leading them to an unchanging cryptographic key. The first approach employs already computed biometric features constituting the template \(T\), which are supplemented with error correction usingdifferent variants of redundant coding. This approach is used here. In the second approach [46] biometric features are not obtained in explicit form. Instead, a neural network is trained, which directly produces a target key from raw biometric data \(D\). The advantage of this approach is said to be less coding redundancy by using continuous data at all stages and quantization only at the end. Disadvantages are the unpredictability of neural network training, lack of guaranteed quality of performance, including uncertainty in retaining quality in a wider set of data than that used in training. The task of reproducing a cryptographic key is accomplished by _biometric cryptosystems_ (BC) [45; 47], also called _biometric encryption_[48]. There are two classes of BCs, which implement different approaches: _key generation_ and _key binding_. Methods of key generation, i.e., direct production of the key from raw biometry or template without using supplementary code are studied in [49; 50; 51]. Biometric template \(T\) is mapped into the space of cryptographic keys (usually bit strings) by a special function: \(K(T):T\rightarrow\left\{0,1\right\}^{n}\), where \(n\) is the length of the key.