# Methods of Generating Key Sequences Based on Parameters of Handwritten Passwords and Signatures

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## Abstract

**:**

## 1. Introduction

## 2. Building a Template Database for Open and Hidden Biometric Images for Investigation

## 3. Analysis of Test Persons’ Handwritten Passwords and Signatures and Features Space

- Discard the first and last values for all dots with zero pressure.
- Perform one-dimensional Fourier transform for x(t), y(t), and p(t).
- Perform the inverse transform of these functions, taking into account that the output dimension should correspond to the nearest minimum integer multiple of the 2nd power.

#### 3.1. The Distances between the Dots (Readings) of the Signature

- 4.
- Calculate the step: $\mathrm{h}=\frac{N}{{R}_{d}}$, where N is the number of dots resulting from the inverse Fourier transform, and R
_{d}is the desirable matrix dimension that is a multiple of the second power.

_{ij}is the distance between the ith and the jth coordinates obtained using the formula:

_{i}, y

_{i}, p

_{i}are the values of the x(t), y(t), p(t) functions at appropriate timing t

_{i}.

_{ij}is a normalized distance between the ith and the jth coordinates:

#### 3.2. Signature Appearance Characteristics

- The proportion of the length and the width of the signature.
- The center of the signature described by C
_{x}, C_{y}, and C_{p}coordinates. - An angle of slope for the signature. The angle of slope is a cosine of a mean angle of slope for a polygonal path of the signature to the X axis.$$\mathsf{\theta}=\frac{1}{n-1}{\sum}_{i=1}^{n}\frac{{x}_{i+1}-{x}_{i}}{\sqrt{{\left({x}_{i+1}-{x}_{i}\right)}^{2}+{\left({y}_{i+1}-{y}_{i}\right)}^{2}}}.$$
- An angle of slope between the centers of halves of the signature. After the center of the signature C
_{x}has been found, the set (X,Y,Z) = {(x_{i},y_{i},p_{i})} should be divided into two subsets L = {(x_{i},y_{i},p_{i})|𝑥_{𝑖}> C_{x}} and R = {(x_{i},y_{i},p_{i})|𝑥_{𝑖}> C_{x}}. Further, the centers of the obtained sets L and R should be found:$$\begin{array}{c}{C}_{{X}_{L}}=\frac{1}{\left|L\right|}{\sum}_{{x}_{j}\in L}^{n}{x}_{j},\text{}{C}_{{Y}_{L}}=\frac{1}{\left|L\right|}{\sum}_{{y}_{j}\in L}^{n}{y}_{j},\text{}{C}_{{P}_{L}}=\frac{1}{\left|L\right|}{\sum}_{{p}_{j}\in L}^{n}{p}_{j};\\ {C}_{{X}_{R}}=\frac{1}{\left|R\right|}{\sum}_{{x}_{j}\in R}^{n}{x}_{j},\text{}{C}_{{Y}_{R}}=\frac{1}{\left|R\right|}{\sum}_{{y}_{j}\in R}^{n}{y}_{j},\text{}{C}_{{P}_{R}}=\frac{1}{\left|R\right|}{\sum}_{{p}_{j}\in R}^{n}{p}_{j}.\end{array}$$

#### 3.3. Daubechies Wavelet Transform Coefficients

_{jk}that characterize a structure of the process to be analyzed in different scales (j). These studies considered different bases of Daubechies wavelets (from D4 to D10 [16]). To transit to a new analysis scale, the signal length must be multiple of 2

^{n}, where n is a number of factorization levels. If this requirement is not met, the numerical series may be added with deficient values using one of the following ways:

- Periodic addition, which means the beginning of the sequence is put at the end of the numerical series.
- Mirroring data at the ends of the sequence.
- The calculation of special scaling and wavelet functions that are applied to the beginning and the end of the sequence, presupposed by Gram–Schmidt orthogonalization.

#### 3.4. Fourier Wavelet Transform Coefficients

- Time normalization (resampling, described above).
- Fourier series function decomposition.
- Harmonics amplitude normalization based on power.

#### 3.5. Correlation Coefficients between Functions of the Signature

## 4. A Fuzzy Extractor Method

#### 4.1. On the Presenting of Attribute Values in the Form of a Bit Sequence

#### 4.2. Evaluation of Feature Informativeness Individually for each Subject

## 5. A Simulation Model of the Cryptographic Key Generation System

- a number of recording attributes (when the procedure of estimating the information content for the attribute is used);
- a number of signature (handwritten password) instances;
- an encryption algorithm;
- a block size (for Hadamard codes);
- the error-correcting ability (for BCH codes).

## 6. Results and Their Comparison with Early Achieved Results

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

IV | the procedure of estimation of informative value (stability) of features |

NoI | number of signature instances when forming the open string |

KL | the length of generated key in bits |

Code | error correction code name |

FAR1 | the probability of FAR for biometric unknown (secret) image |

FAR2 | the probability of FAR for biometric known image |

CI | confidence interval of FRR, FAR1, and FAR2 probabilities |

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**Figure 1.**Wavelet transform coefficients before scaled by the pen pressure function (onto a tablet) to the mean length of a signature instance for a signer.

**Figure 2.**Wavelet transform coefficients scaled by the pen pressure function (onto a tablet) to the mean length of a signature instance for a signer.

**Figure 3.**Wavelet transform coefficients scaled by the pen pressure function (onto a tablet) to the mean length of a signature instance for different signers.

No. | Attributes Group | Short Description | Number of Features |
---|---|---|---|

1.1 | Distances in 3d | Distances between some signature dots are normalized on the signature length in three-dimensional space (the third dimension is pen pressure on the tablet) | 120 |

1.2 | Distances in 2d | Distances between some signature dots are normalized on the signature length in two-dimensional space (the tablet surface without taking into account the pressure) | 120 |

2 | Static | Some characteristics of the static signature image | 5 |

3.1 | Daubechies D4 | Daubechies wavelet transform coefficient D4 | 74–392 |

3.2 | Daubechies D6 | Daubechies wavelet transform coefficient D6 | 68–369 |

3.3 | Daubechies D8 | Daubechies wavelet transform coefficient D8 | 68–369 |

3.4 | Daubechies D10 | Daubechies wavelet transform coefficient D10 | 58–369 |

4.1 | Fourier v(t) | The first 16 amplitudes (the most low frequency) of function v(t) harmonics | 16 |

4.2 | Fourier p(t) | The first 16 amplitudes (the most low frequency) of function p(t) harmonics | 16 |

5 | Correlation between x(t), y(t), p(t), x’(t), y’(t), p’(t) | Correlation coefficients between pairs of signature x(t), y(t), p(t) functions and their derivatives—x’(t), y’(t), p’(t) functions | 15 |

**Table 2.**The main results of generating key sequences using handwritten passwords and signatures.

**IV**—the procedure of estimation of informative value (stability) of features;

**NoI**—number of signature instances when forming the open string;

**KL**—the length of generated key in bits;

**Code**—error correction code name;

**FAR**—the probability of FAR for biometric unknown (secret) image;

_{1}**FAR**—the probability of FAR for biometric known image;

_{2}**CI**—confidence interval of

**FRR**,

**FAR1**, and

**FAR2**probabilities.

Attributes | IV | NoI | KL | Code | FRR | FAR1 | FAR2 | CI |
---|---|---|---|---|---|---|---|---|

Fourier v(t) and p(t) + correlation between x(t), y(t), p(t), x’(t), y’(t), p’(t) | + | 25 | 32 | BCH | 0.314 | 0.255 | 0.263 | 0.05/0.05/0.05 |

Fourier v(t) and p(t) + correlation between x(t), y(t), p(t), x’(t), y’(t), p’(t) | + | 25 | 32 | BCH | 0.31 | 0.315 | 0.325 | 0.05/0.05/0.05 |

Fourier v(t) and p(t) + correlation between x(t), y(t), p(t), x’(t), y’(t), p’(t) + static | + | 25 | 48 | BCH | 0.225 | 0.001 | 0.005 | 0.05/0.001/0.001 |

Fourier v(t) and p(t) + correlation between x(t), y(t), p(t), x’(t), y’(t), p’(t) + static | + | 25 | 48 | BCH | 0.225 | 0.004 | 0.044 | 0.05/0.002/0.01 |

Fourier v(t) and p(t) + correlation between x(t), y(t), p(t), x’(t), y’(t), p’(t) + static | − | 25 | 48 | BCH | 0.351 | 0.095 | 0.109 | 0.05/0.01/0.01 |

Fourier v(t) and p(t) + correlation between x(t), y(t), p(t), x’(t), y’(t), p’(t) + static | − | 25 | 48 | BCH | 0.357 | 0.215 | 0.251 | 0.05/0.05/0.05 |

Distances in 3d | − | 30 | 64 | BCH | 0.305 | 0.212 | 0.315 | 0.05/0.05/0.05 |

Distances in 2d | − | 30 | 64 | BCH | 0.226 | 0.237 | 0.338 | 0.05/0.05/0.05 |

Daubechies D4 | + | 20 | 168 | Hadamard | 0.343 | 0.33 | 0.35 | 0.05/0.05/0.05 |

Daubechies D6 | + | 20 | 180 | Hadamard | 0.34 | 0.323 | 0.325 | 0.05/0.05/0.05 |

Daubechies D8 | + | 20 | 172 | Hadamard | 0.36 | 0.34 | 0.345 | 0.05/0.05/0.05 |

Daubechies D10 | + | 20 | 160 | Hadamard | 0.349 | 0.33 | 0.34 | 0.05/0.05/0.05 |

Daubechies D4 | + | 20 | 160 | BCH | 0.11 | 0.105 | 0.11 | 0.01/0.01/0.01 |

Daubechies D6 | + | 20 | 168 | BCH | 0.105 | 0.095 | 0.013 | 0.01/0.01/0.01 |

Daubechies D8 | + | 20 | 160 | BCH | 0.115 | 0.11 | 0.122 | 0.01/0.01/0.01 |

Daubechies D10 | + | 20 | 152 | BCH | 0.121 | 0.115 | 0.129 | 0.01/0.01/0.01 |

Daubechies D4 + distances in 2d and 3d + static + Fourier v(t) and p(t) + correlation between x(t), y(t), p(t), x’(t), y’(t), p’(t) | + | 30 | 256 | BCH | 0.055 | 0.016 | 0.016 | 0.01/0.01/0.01 |

Daubechies D6 + distances in 2d and 3d + static + Fourier v(t) and p(t) + correlation between x(t), y(t), p(t), x’(t), y’(t), p’(t) | + | 30 | 264 | BCH | 0.045 | 0.015 | 0.015 | 0.01/0.002/0.002 |

Daubechies D8 + distances in 2d and 3d + static + Fourier v(t) and p(t) + correlation between x(t), y(t), p(t), x’(t), y’(t), p’(t) | + | 30 | 248 | BCH | 0.075 | 0.017 | 0.018 | 0.01/0.002/0.002 |

Daubechies D10 + distances in 2d and 3d + static + Fourier v(t) and p(t) + correlation between x(t), y(t), p(t), x’(t), y’(t), p’(t) | + | 30 | 248 | BCH | 0.08 | 0.019 | 0.02 | 0.01/0.002/0.002 |

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**MDPI and ACS Style**

Lozhnikov, P.; Sulavko, A.; Eremenko, A.; Volkov, D. Methods of Generating Key Sequences Based on Parameters of Handwritten Passwords and Signatures. *Information* **2016**, *7*, 59.
https://doi.org/10.3390/info7040059

**AMA Style**

Lozhnikov P, Sulavko A, Eremenko A, Volkov D. Methods of Generating Key Sequences Based on Parameters of Handwritten Passwords and Signatures. *Information*. 2016; 7(4):59.
https://doi.org/10.3390/info7040059

**Chicago/Turabian Style**

Lozhnikov, Pavel, Alexey Sulavko, Alexander Eremenko, and Danil Volkov. 2016. "Methods of Generating Key Sequences Based on Parameters of Handwritten Passwords and Signatures" *Information* 7, no. 4: 59.
https://doi.org/10.3390/info7040059