Field of Invention

The present invention relates to an identity and license verification system for accessing and working with highly sensitive data which is bound by selective or paid access. The proposed system is primarily designed for working with highly sensitive data such as military or police software, authorization of banking transactions, software licensing, building access security and other analogous applications.

Background of the Invention

Used and known file protection, client authentication and licensing systems are based, e.g., on the Digital Signature Algorithm (DSA), qualified certificates and the like. These systems mostly use asymmetric cryptography methods utilizing a discrete logarithm or large number factorization. The use of polynomials in the standard form applies

Standard polynomials are unsuitable for high p values (the number of users or licenses), given the fact that the number of terms, values of polynomial coefficients as well as the values of individual exponents grow rapidly. This greatly increases the demand for computing power and the response time required for comprehensive security. Another negative consequence of using polynomials of high degrees is the space complexity caused by the necessity to keep these polynomials in the persistent memory of computing resources.

There are two typical methods used to eliminate or reduce these problems. One of them is the effort to speed up the polynomial calculation using the so-called Horner’s rule. While this solution leads to the partial acceleration of the authentication/authorization process, it does not eliminate the problem related to a large number of parameters.

The other suggested way to simplify and accelerate the verification process is to reduce the polynomial to a much lower degree. This allows to achieve the time and capacity improvement of the whole process but at the same time, there is a higher risk of unauthorized entry since the coefficients of such a reduced polynomial can be estimated, for example, by the Newton interpolation.

The task of this invention is to create the identity and license verification system for working with highly sensitive data that, at a high security level, provides the required response speed even for a large number of users and/or licenses (for high p values) without significantly increasing the space/memory requirements of computing resources.

Summary of the Invention

The above mentioned disadvantages and drawbacks of well-known security systems are largely eliminated according to the invention - Identity and License Verification System for Working with Highly Sensitive Data. The principle of the invention is that the system has a unique identifier stored in the client’s hardware; the said unique identifier is coupled to a server via the transfer environment using a higher layer protocol, the said unique identifier is in the evaluation module of the server further connected to the substitution and calculation module. At the same time, a w polynomial system stored in the persistent memory of the server is also connected to the substitution and calculation module, the output of which is a calculated key. At the same time, the client's hardware stores a local key which is via the transfer environment using the higher layer protocol connected to a key comparison module to which the calculated key is also connected. Positive output as well as negative output from the said key comparison module are both connected via the transfer environment using the higher layer protocol to a response processing module which is also stored in the client's hardware.

The advantage is that in the evaluation module, the identity and license verification system, according to the invention, has a search module in front of the substitution and calculation module. Furthermore, the x-mat matrix module, stored in the persistent memory of the server, is connected to the said search module together with the unique identifier. At the same time, the search module, together with the w polynomial system, is connected to the substitution and calculation module.

The advantage is that the identity and license verification system, according to the invention, has a p permutation stored in the persistent memory of the server, where both the p permutation and the x-mat matrix module are connected to the calculated key.

According to the invention, the main advantage of the Identity and License Verification System for Working with Highly Sensitive Data is the exceptional simplification of the calculation/processing of the user’s input data and the associated very fast yet secure login to the protected highly sensitive data system. This is enabled by the character of the polynomial used here. Another consequence and significant benefit of the achieved lightening computation capacity of the security system is the possibility of virtually any increase in the number of users/licenses - even in millions - without any significant impact on the system response time. Moreover, the system security, according to the invention, is enhanced by the fact that the keys representing licenses are divided into two parts and the verification takes place remotely on the server. The security of the system is further enhanced by the fact that any attempt to tamper with one column of the matrix in the x-mat matrix module will result in blocking several other local keys.

Brief Description of the Drawings

The accompanying drawings illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention.

- Fig. 1 - scheme of the system, according to Example 1 - basic embodiment,

- Fig. 2 - scheme of the system, according to Example 2 - preferred embodiment,

- Fig. 3 - scheme of the system, according to Example 3 - optimal embodiment,

- Fig. 4 - standard polynomial for p = 1009 (attached in PDF format),

- Fig. 5 - visual comparison of computational complexity of the system according to Example 3 and Example R,

- Fig. 6 - a graphical representation of the relationship between bit security and p prime number size.

Detailed Description of the Invention E x a mp l e 1

The Identity and License Verification System for Working with Highly Sensitive Data, according to Fig. 1, has a unique identifier 2 stored in the client's hardware L Via the transfer environment 3 using a higher layer protocol 4, the unique identifier 2 is coupled to a server 5, where, in the evaluation module 6, it is connected to the substitution and calculation module 7. A w polynomial system 8 stored in the persistent memory 9 of the server 5 is also connected to the substitution and calculation module 7, the output of which is a calculated key JO. At the same time, the client's hardware 1 stores a local key IT which is, via the transfer environment 3 using the higher layer protocol 4. connected to the key comparison module 12 to which the calculated key 1Ό is also connected. Positive output 13 as well as negative output J_4 from the key comparison module 12 are both connected via the transfer environment 3 using the higher layer protocol 4 to a response processing module J_5 which is also stored in the client's hardware

1.

The system works by sending the unique identifier 2 from the client's hardware 1, via the transfer environment 3 using the higher layer protocol 4 to the server 5, specifically to the evaluation module 6 which substitutes the transformed unique identifier 2 into the substitution and calculation module 7 as variables into the w polynomial system 8. Based on the results from the substitution and calculation module 7 (after the substitution into the w polynomial system 8), the calculated key JO is created and then, in the key comparison module 12. compared with the local key JT which is obtained from the client's hardware 1 through the transfer environment 3 using the higher layer protocol 4. In case that the calculated key 10 equals to the local key JT, positive output J_3 is activated, otherwise the verification is rejected by negative output 14. The verification result obtained through positive output J_3 or negative output 14 is passed, through the transfer environment 3 using the higher layer protocol 4, to the response processing module 15 stored in the client's hardware 1.

Without substantially increasing the space complexity requirements of the computing resources, the solution described in Example 1 provides a high response speed even for high p values (number of uses and/or licenses) in comparison to existing security systems. The use of finite fields, which will be described in more detail in the final part of Example 3, prevents fraudulent insertion of another user/license, which is a significant security feature of the proposed system.

E x a m p l e 2

The Identity and License Verification System for Working with Highly Sensitive Data, according to Fig. 2, has the unique identifier 2, local key JT and the response processing module 15 stored in the client's hardware E The server 5 again comprises the evaluation module 6 in which there is the substitution and calculation module 7 with output, i.e. the calculated key 10, connected to the key comparison module 12. The w polynomial system 8 stored in the persistent memory 9 of the server 5 is also connected to the substitution and calculation module 7. Then, the subsequent structure of its output links from the key comparison module 12 to the response processing module J_5 is the same as in Example 1.

In addition, in the system, in the evaluation module 6, there is a search module 16 in front of the substitution and calculation module 7. The x-mat matrix module T7, stored in the persistent memory 9 of the server V is connected to the search module 6 together with the unique identifier 2. At the same time, the search module 16, together with the w polynomial system 8, is connected to the substitution and calculation module 7.

The system works by sending the unique identifier 2 from the client's hardware 1_, via the transfer environment 3 using the higher layer protocol 4 to the search module 16 (of the evaluation module 6 of the server 5), which searches for the appropriate column in the x-mat matrix module 17. The found column is then substituted by the substitution and calculation module 7 as variables into the w polynomial system 8. Based on the results from the substitution and calculation module 7 (after the substitution into the w polynomial system 8), the calculated key 10 is created and then in the key comparison module 12, compared with the local key JT which is obtained from the client's hardware 1 through the transfer environment 3 using the higher layer protocol 4. In case that the calculated key 1Ό equals to the local key IT, positive output J_3 is activated, otherwise the verification is rejected by negative output J_4. The verification result obtained through positive output J_3 or negative output 14 is passed, through the transfer environment 3 using the higher layer protocol 4, to the response processing module 15 stored in the client's hardware E

Due to the inclusion of the x-mat matrix module T7, the transformed unique identifier 2 is not directly substituted into the evaluation module 6, but on the basis of the unique identifier 2, the appropriate column is searched in the x-mat matrix module T7 and subsequently substituted into the w polynomial system 8. This solution further increases the level of security without increasing the computational complexity.

E x a m p l e 3

The Identity and License Verification System for Working with Highly Sensitive Data, according to Fig. 3 includes all parts set forth in Example 2 in the same configuration and with the same links. In addition, this system has a p permutation J_8 stored in the persistent memory 9 of the server 5. Both the p permutation J_8 and the x-mat matrix module 17 are connected to the calculated key 1Ό.

The system works by sending the unique identifier 2 from the client's hardware 1, via the transfer environment 3 using the higher layer protocol 4 to the search module J_6 (of the evaluation module 6_of the server 5), which searches for the appropriate column in the x-mat matrix module 17. The found column is then substituted by the substitution and calculation module 7 as variables into the w polynomial system 8. Based on the p permutation 1_8 and results from the substitution and calculation module 7 (after the substitution into the w polynomial system 8), appropriate values are found in the x-mat matrix module 17, thus the values create the calculated key 10. In the key comparison module 12, the calculated key JO is compared with the local key JT which is obtained from the client's hardware 1 through the transfer environment 3 using the higher layer protocol 4. In case that the calculated key 10 equals to the local key JT, positive output J_3 is activated, otherwise the verification is rejected by negative output 14. The verification result obtained through positive output J_3 or negative output 14 is passed through the transfer environment 3 using the higher layer protocol 4 to the response processing module 15 stored in the client's hardware J_.

The above mentioned solution is the optimal implementation of the Identity and License Verification System for Working with Highly Sensitive Data. By utilizing the p permutation 18 simultaneously with the x-mat matrix module 1/7, this module is protected from malicious manipulation because unauthorized single column manipulation invalidates multiple local keys. This results in increased safety over the solution presented in Example 2.

According the invention, the identity and license verification systems for working with highly sensitive data use specifically designed polynomials for computation/validation operations, hereinafter called molded polynomials.

Molded polynomials are created by replacing the conventional q coefficients used in the standard polynomial by a set of a, b coefficients. The molded polynomials have a fundamentally different way/form of notation as well as calculation from the standard polynomials. The molded polynomial has fewer terms than a standard polynomial and its calculation has a constant number of cycles regardless of increasing p values (number of users and/or licenses), which significantly shortens and speeds up verification operations. When calculating molded polynomials, the system works with much more feasible values of coefficients and exponents and, especially with respect to exponents, it greatly reduces the computational complexity. This saves operation time and capacity of computing resources.

The stated effects in terms of speeding up/simplification of the calculation are more visible when there are larger numbers of users/licenses/subsystems involved in the system. The benefit is significant even at the value of p = 37 and with increasing this number, the saving of working time and capacity grows exceptionally fast (see Fig. 5). At high p values, the saving is so extraordinary that the molded polynomials could be called “magic polynomials”.

E x a m p l e R (reference) To illustrate, an example of an existing security system for similar purposes, based on standard polynomials, is given

Pi(x) = qp-ixf ¹ + q _p -2X ^{p 2} + ... + qix ² + qix + qo-

The following are examples of standard polynomials for different p values.

Distribution of a polynomial (standard form) over a field Z ₁₀₁ : p(x) = 25x ¹⁰⁰ + 73x" + 92x ⁹⁸ + 48x ⁹⁷ + 83x ⁹⁶ + 100x ⁹⁵ + 75x ⁹⁴ + 83x ⁹² + 17x ⁹¹ + 93x ⁹⁰ + 30x ⁸⁹ + 74x ⁸⁸ + 40x ⁸⁷ + 25x ⁸⁶ + 38x ⁸⁵ + 78x ⁸⁴ + 73x ⁸³ + 69x ⁸² + 91x ⁸¹ + 4x ⁸⁰ + 84x ⁷⁹ + 4x ⁷⁸ + 61x ⁷⁷ + 98x ⁷⁶ + 19x ⁷⁵ + 100x ⁷⁴ + 91x ⁷³ + 5x ⁷² + 69x ⁷¹ +

36x ⁷⁰ + 91x ⁶⁹ + 76x ⁶⁸ + 81x ⁶⁷ + 53x ⁶⁶ + 81x ⁶⁵ + 91x ⁶⁴ + 82x ⁶³ + 86x ⁶² + 87x ⁶¹ + 59x ⁶⁰ + 3x ⁵⁹ + 38x ⁵⁸ + 94x ⁵⁷ + 84x ⁵⁶ + 57x ⁵⁵ + 20x ⁵⁴ + 97x ⁵³ + 31x ⁵² + 21x ⁵¹ + 30x ⁵⁰ + llx ⁴⁹ + 93x ⁴⁸ + 26x ⁴⁷ + 70x ⁴⁶ + 26x ⁴⁵ + 19x ⁴⁴ + 73x ⁴³ + 99x ⁴² + 52x ⁴¹ +

19x ⁴⁰ + 80x ³⁹ + 55x ³⁸ + 5 lx ³⁷ + 22x ³⁶ + 41x ³⁵ + 75x ³⁴ + 28x ³³ + 19x ³² + 17x ³¹ +

95x ³⁰ + 32x ²⁹ + 91x ²⁸ + 64x ²⁷ + 79x ²⁶ + 13x ²⁵ + 86x ²⁴ + 45x ²³ + 26x ²² + 42x ²¹ +

87x ²⁰ + 23x ¹⁹ + 52x ¹⁸ + 3x ¹⁷ + 6x ¹⁶ + 87x ¹⁵ + 78x ¹⁴ + 89x ¹³ + 44x ¹² + 45x ¹⁴ +

16x ¹⁰ + 38x ⁹ + 2x ⁸ + 25x ⁷ + 15x ⁶ + 7x ⁵ + 94x ⁴ + 15x ² + 55x + 39

Distribution of a polynomial (standard form) over a field Z ₃₁₁ : p(x) = 18x ³⁰² + 8x ³⁰¹ + 122x ³⁰⁰ + 6x ²⁹⁹ + 198x ²⁹⁸ + 20x ²⁹⁷ + 110x ²⁹⁶ + 92x ²⁹⁵ + 64x ²⁹⁴ + 149x ²⁹³ + 269x ²⁹² + 304x ²⁹¹ + 278x ²⁹⁰ + 36x ²⁸⁹ + 117x ²⁸⁸ + 304x ²⁸⁷ + 223x ²⁸⁶ + 193x ²⁸⁵ + 123x ²⁸⁴ + 44x ²⁸³ + 88x ²⁸² + 60x ²⁸¹ + 122x ²⁸⁰ + 302x ²⁷⁹ + 16x ²⁷⁸ + 271x ²⁷⁷ + 237x ²⁷⁶ + 73x ²⁷⁵ + 55x ²⁷⁴ + 192x ²⁷³ + 250x ²⁷² + 186x ²⁷¹ + 171x ²⁷⁰ + 2x ²⁶⁹ + 124x ²⁶⁸ + 28x ²⁶⁷ + 237x ²⁶⁶ + 256x ²⁶⁵ + 42x ²⁶⁴ + 155x ²⁶³ + 194x ²⁶² + 176x ²⁶¹ + 145x ²⁶⁰ + 189x ²⁵⁹ + 51x ²⁵⁸ + 208x ²⁵⁷ + 216x ²⁵⁶ + 124x ²⁵⁵ +

308x ²⁵⁴ + 119x ²⁵³ + 190x ²⁵² + 196x ²⁵¹ + 130x ²⁵⁰ + 292x ²⁴⁹ + 244x ²⁴⁸ + 278x ²⁴⁷ + 132x ²⁴⁶ + 59x ²⁴⁵ + 168x ²⁴⁴ + 175x ²⁴³ + 238x ²⁴² + 178x ²⁴¹ + 235x ²⁴⁰ + 58x ²³⁹ + 226x ²³⁸ + 267x ²³⁷ + 104x ²³⁶ + 29x ²³⁵ + 161x ²³⁴ + 291x ²³³ + 162x ²³² + 231x ²³¹ + 123x ²³⁰ + 15x ²²⁹ + 49x ²²⁸ + 92x ²²⁷ + 307x ²²⁶ + 47x ²²⁵ + 60x ²²⁴ + 257x ²²³ +

97x ²²² + 38x ²²¹ + 139x ²²⁰ + 6x ²¹⁹ + 68x ²¹⁸ + 142x ²¹⁷ + 114x ²¹⁶ + 145x ²¹⁵ + 171x ²¹⁴ + 22x ²¹³ + 93x ²¹² + llx ²¹¹ + 216x ²¹⁰ + 68x ²⁰⁹ + 147x ²⁰⁸ + 269x ²⁰⁷ + 43x ²⁰⁶ + 261x ²⁰⁵ + 82x ²⁰⁴ + 64x ²⁰³ + 203x ²⁰² + 287x ²⁰¹ + 207x ²⁰⁰ + 38x ¹⁹⁹ + 158x ¹⁹⁸ + 56x ¹⁹⁷ + 162x ¹⁹⁶ + 103x ¹⁹⁵ + 217x ¹⁹⁴ + 108x ¹⁹³ + 308x ¹⁹² + 230x ¹⁹¹ +

278x ¹⁹⁰ + 114x ¹⁸⁹ + 131x ¹⁸⁸ + 169x ¹⁸⁷ + 87x ¹⁸⁶ + 50x ¹⁸⁵ + 232x ¹⁸⁴ + 88x ¹⁸³ + 166x ¹⁸² + 182x ¹⁸⁰ + 291x ¹⁷⁸ + 157x ¹⁷⁷ + 234x ¹⁷⁶ + 299x ¹⁷⁵ + 118x ¹⁷⁴ + 58x ¹⁷³ +

283x ¹⁷² + 20x ¹⁷¹ + 208x ¹⁷⁰ + 175x ¹⁶⁹ + 165x ¹⁶⁸ + 157x ¹⁶⁷ + 190x ¹⁶⁶ + 96x ¹⁶⁵ + 43x ¹⁶⁴ + 36x ¹⁶³ + 41x ¹⁶² + 153x ¹⁶¹ + 151x ¹⁶⁰ + 173x ¹⁵⁹ + 190x ¹⁵⁸ + 291x ¹⁵⁷ +

294x ¹⁵⁶ + 58x ¹⁵⁵ + 217x ¹⁵⁴ + 128x ¹⁵³ + 178x ¹⁵² + 174x ¹⁵¹ + 88x ¹⁵⁰ + 96x ¹⁴⁹ + 172x ¹⁴⁸ + 122x ¹⁴⁷ + 189x ¹⁴⁶ + 113x ¹⁴⁵ + 113x ¹⁴⁴ + 48x ¹⁴³ + 282x ¹⁴² + 310x ¹⁴¹ + 241x ¹⁴⁰ + 245x ¹³⁹ + 186x ¹³⁸ + 57x ¹³⁷ + 174x ¹³⁶ + 178x ¹³⁵ + 78x ¹³⁴ + 151x ¹³³ + 125x ¹³² + 26x ¹³¹ + 37x ¹³⁰ + 46x ¹²⁹ + 243x ¹²⁸ + 95x ¹²⁷ + 146x ¹²⁶ + 237x ¹²⁵ + 223x ¹²⁴ + 14x ¹²³ + 153x ¹²² + 282x ¹²¹ + 170x ¹²⁰ + 237x ¹¹⁹ + 128x ¹¹⁸ + 33x ¹¹⁷ +

3 lx ¹¹⁶ + 144x ¹¹⁵ + 37x ¹¹⁴ + 177x ¹¹³ + 195x ¹¹² + 181x ¹¹⁰ + 206x ¹⁰⁹ + 225x ¹⁰⁸ + 81x ¹⁰⁷ + 128x ¹⁰⁶ + 173x ¹⁰⁵ + 310x ¹⁰⁴ + 94x ¹⁰³ + 197x ¹⁰² + 160x ¹⁰¹ + 75x ¹⁰⁰ + 243x" + 18x ⁹⁸ + 108x ⁹⁷ + 27x ⁹⁶ + 126x ⁹⁵ + 191x ⁹⁴ + 89x ⁹³ + 62x ⁹² + 37x ⁹¹ + 133x ⁹⁰ + 9x ⁸⁹ + 95x ⁸⁸ + 157x ⁸⁷ + 100x ⁸⁶ + 273 x ⁸⁵ + 164x ⁸⁴ + 276x ⁸³ + 147x ⁸² + 125x ⁸¹ + 6x ⁸⁰ + 191x ⁷⁹ + 159x ⁷⁸ + 205x ⁷⁷ + lllx ⁷⁶ + 143x ⁷⁵ + 34x ⁷⁴ + 210x ⁷³ + 78x ⁷² + 141x ⁷¹ + x ⁷⁰ + 26x ⁶⁹ + 252x ⁶⁸ + 138x ⁶⁷ + bbc ⁶⁶ + 142x ⁶⁵ + 161x ⁶⁴ +

44x ⁶³ + 240x ⁶² + 187x ⁶¹ + 53x ⁶⁰ + 281x ⁵⁹ + 125x ⁵⁸ + 118x ⁵⁷ + 263x ⁵⁶ + 237x ⁵⁵ + 241x ⁵⁴ + 304x ⁵³ + 109x ⁵² + 17x ⁵¹ + 271x ⁵⁰ + 53x ⁴⁹ + 30x ⁴⁸ + 267x ⁴⁷ + 77x ⁴⁶ + 165x ⁴⁵ + 106x ⁴⁴ + 39x ⁴³ + 248x ⁴² + 273x ⁴¹ + 172x ⁴⁰ + 231x ³⁹ + 217x ³⁸ +

247x ³⁷ + 156x ³⁶ + 302x ³⁵ + 286x ³⁴ + 31x ³³ + 56x ³² + 201x ³¹ + 211x ³⁰ + 230x ²⁹ + 186x ²⁸ + 187x ²⁷ + 204x ²⁶ + 229x ²⁵ + 137x ²⁴ + llx ²³ + 171x ²² + 221x ²¹ +

109x ²⁰ + 28x ¹⁹ + 239x ¹⁸ + 194x ¹⁷ + 243x ¹⁶ + 299x ¹⁵ + 91x ¹⁴ + 99x ¹³ + 257x ¹² + 32x ⁴¹ + 8x ¹⁰ + 109x ⁹ + 250x ⁸ + 217x ⁷ + 142x ⁶ + 183x ⁵ + 90x ⁴ + 269x ³ + 189x ² + 153x + 198

Distribution of a polynomial (standard form) over a field Z ₁₀₀₉ is due to its size listed separately as an attachment in PDF format - see Fig. 4. The figure, illustrating the complexity of the expression, shows the difficulty of calculating the value of a standard polynomial both in terms of computing resources and the impact of complexity on computation speed and system response.

In contrast to standard polynomials with the aforementioned problems and drawbacks, the use of molded polynomials in the system according to the invention allows fast calculations that have a constant number of cycles even for a large number of users, licenses and subsystems. Fig. 5 shows a comparison between the computational complexity of the molded polynomial values (Example 3) and standard polynomials (Example S). The graph illustrates the response time saving as well as the capacity improvement of computing resources, especially at higher p values.

Despite the calculation speed, the security of the system according to the invention remains at a high level. From a security point of view, it is beneficial that the server keys for a user/license/subsystem are represented by columns in the x-mat matrix module 17 stored on the server 5, where the calculated key JO, in case of use of p permutation JjJ, is not a direct result of calculating the individual molded polynomials, but it is then searched for in the x-mat matrix module J/7. Neither polynomial results nor calculated keys JO can be stored on the server 5. Thus, it is difficult to derive the x-mat matrix module J/7 from polynomials and local keys JT, if they were stolen.

The security of the system according to the invention is shown in the Fig. 6., which illustrates the relation between bit security and the prime number p values. Expression of bit security means a conservative estimate of the number of molded polynomials with respect to the selected prime p, where bit security is calculated from the assumption of using a brute force attack and thus trying all different combinations. For a 128-bit key, this is 2 ¹²⁸ combinations; if a prime number p = 31 is chosen, then the number of different molded polynomials is comparable to the number of 121-bit key combinations, i.e. approximately 2 ¹²¹ . In the security of symmetric cryptography, 128-bit keys can be considered safe, to which p = 31 merely approaches. However, the next prime number 37 exceeds this value, it has a bit security of 131 bits. If the prime number 10007 is taken into account, bit security can be compared to 390 bits. This value can currently be considered safe with respect to the existence of quantum computers, where halving bit security is considered. Moreover, it is to be understood that bit security is related only to the individual molded polynomials, not to the entire w polynomial system 8 that the system according to the invention operates with and which is in its preferred variants safer.

Industrial applicability

The Identity and License Verification System for Working with Highly Sensitive Data, according to the invention, is intended for generating and verifying unique license or identification keys used for software licenses validation or unique identification of users, elements of the Internet of Things, use of systems related to decision-making power in military or banking sector. Thus, the system will find application especially for the verification of users of electronic data systems with extremely high security needs and at the same time very fast response times, such as systems for military purposes, security forces, integrated rescue system and other related areas. However, it can also be used in civilian applications, such as building access security, but also for common purposes like entrance tickets, public transportation tickets and other similar applications.

WO 2021/058042 ~ n ~ PCT/CZ2019/050040

List of numbered parts in Figures:

1 - client's hardware

2 - unique identifier

3 - transfer environment

4 - higher layer protocol

5 - server

6 - evaluation module

7 - substitution and calculation module

8 - w polynomial system

9 - persistent memory (of server)

10 - calculated key

11 - local key

12 - key comparison module

13 - positive output (of key comparison module)

14 - negative output (of key comparison module)

15 - response processing module

16 - search module

17 - x-mat matrix module

18 - p permutation