Zapechnikov Sergey
email: svzapechnikov@mephi.ru

Miloslavskaya Natalia
email: ngmiloslavskaya@mephi.ru

Budzko Vladimir

On Experience of Using Distance Learning Technologies for Teaching Cryptology

Keywords: Cryptology, Teaching cryptologic courses, Mass-oriented Distance Learning Technologies 1

The necessity of using Distance Learning (DL) for teaching cryptology is analyzed. The modern features of applying different DL approaches to solve this task are extracted. The NRNU MEPhI's experience in creating massoriented DL project called Cryptowiki.net is described; its structure and assignments implemented by the students of cryptologic courses are shown. The related works are presented. Cryptowiki.net's difference from the analogs is stressed out. The main findings of the research are formulated in conclusion.

INTRODUCTION

Distance learning (DL) can be defined as a teachers-students interaction at a distance that reflects all the typical learning process's components (objectives, contents, methods, organizational forms, and learning tools) and is realized by the specific means of the Internet technologies or another tools providing interactivity [START_REF] Allen | Michael Allen's Guide to E-Learning: Building Interactive, Fun, and Effective Learning Programs for Any Company[END_REF][START_REF]Laboratorija distanchionnogo obuchenija Rossiyskoy Academii Nauk[END_REF]. Even a new cryptology concept was formed: "Modern cryptography is concerned with the construction of information system that is robust against malicious attempts to make these systems deviate from their prescribed functionality" [START_REF] Goldreich | Foundations of cryptography a primer[END_REF].

The comprehensive DL technologies' (DLT) development is one of the global trends widely supported by almost all universities being at the first places in the world rankings like THE (Times of Education), Quacquarelli Symonds (QS) World University Rankings, Shanghai ranking and others. This trend also affects teaching of different subjects in the field of information security and cryptology in particular. However, the widespread DLT usage for teaching cryptology observed today is due to not only the "spontaneous" world trends, but it is also prepared by a number of objective conditions discussed below.

The subject area of cryptology has significantly expanded over the past two decades. Many new applications and corresponding new scientific and methodological apparatus have appeared. At the same time there is a stabilization (or even some decrease) of scientists' and practitioners' interest to the specific sections of classical cryptology or relatively new sections which were developed dynamically up to this moment. Such significant changes are due to, on the one hand, the rapid information technologies (IT) development and the growing needs of society in ensuring IT security, and on the other hand, new scientific discoveries in cryptology and related fields of applied mathematics. The universities teaching cryptologic disciplines were faced the problem of adequately addressing the extraordinary changes, taking place in the field of computer science in general and in cryptology in particular, in their curricula and educational practice.

The steady and rapid growth of scientific publications in the field of cryptology is observed around the world in recent years. The publications' statistics in the electronic preprint archive of the International Association for Cryptologic Research (IACR) for 1996-2014 (Fig. 1) is a vivid evidence of this fact [START_REF][END_REF].

Fig. 1. Publications' statistics in the IACR's electronic preprint archive

In addition the fact that the scientific and technical information search capabilities were fundamentally changed with the advent of the Internet search services like Google, Yahoo!, Yandex, etc., Electronic encyclopedias such as Wikipedia, the archives of electronic publications and preprints (for example, CiteSeer, IEEExplore, eprint.iacr.org et al.) cannot be ignored. As our practice shows these services are actively used by the students and teachers to find a proper term, article, book, algorithm, protocol, method or application description, etc. A teacher's role is fundamentally changing in the context of this "information explosion". In the past he/she was almost the only affordable student's authoritative source of knowledge. Now he/she turns in some sense into a certain filter that should save the students from the huge flow of superfluous, insignificant or frankly false information and give them only high-quality and systematically organized knowledge. In these circumstances the teacher's task is to organize an educational process in such a way that will maximize the effectiveness of learning and acquisition of the necessary competencies (knowledge, skills and abilities) by the students.

The remainder of the paper is organized as follows. Section 2 includes an overview of related works. Different DLT applications are analyzed in Section 3. Section 4 introduces the NRNU MEPhI's experience in applying the mass-oriented DLT in the form of the Cryptowiki.net site. The main findings of the project are formulated in conclusion.

RELATED WORKS

Of course our idea to create a specialized DL site in not novel. The sharply increasing interest to DL has led to the emergence of a number of DL courses on cryptology in English (with rare exceptions) at present. The courses offered by the MOOC systems (from Massive Open Online Courses) should be noted among them first of all.

The "Cryptography I" course is already available and the "Cryptography II" course is going to start from June 2015 in the Coursera system; both courses are authored by the famous Stanford University's Professor Dan Boneh [START_REF]Cryptography I[END_REF].

The Udacity portal offers the "Applied Cryptography" online course conducted by the University of Virginia's Professor Dave Evans [START_REF][END_REF].

Three courses ("Cryptography and Cryptanalysis", "Advanced Topics in Cryptography", and "Selected Topics in Cryptography") are available at the online educational portal of the Massachusetts Institute of Technology (MIT) [7].

In addition to the online courses a number of carefully designed offline courses on cryptography well suited for self-training can be found on the Internet (not only in the form of lectures' video records and forums that allow to meet with a teacher, but also as notes, lectures, tutorials, home works and their solutions, sample exam assignments, etc.). For example, the courses such as "Modern Cryptography" and "Advanced Cryptography" by Professor Mihir Bellare and Professor Phillip Rogaway from the University of California at San Diego [8], "Cryptographic Protocols" by Ueli Maurer from the ETH Zurich University [START_REF]Information Security & Cryptography[END_REF], and "Introduction to Cryptography" by Rafael Pass from the Cornell University [START_REF]Computer Science. Introduction to Cryptography[END_REF] can be mentioned here.

It is often recommended for the students to use a wiki as a reference tool in some online courses. That mainly affects the sections not included in the curriculum body (typically the wiki textbooks are additional, not obligatory parts of a taught course) and submitted to their independent study. For example, D.Boneh recommends using the wiki tutorial on the basics of discrete mathematics and discrete probability posted on the popular Wikibooks site as a complement to the above courses [START_REF]High School Mathematics Extensions[END_REF]. The wiki book on cryptography can be found at the same site [START_REF]Cryptography[END_REF], but it still looks unfinished.

The given brief analysis shows the necessity of developing a consolidating bilingual (English-Russian) Internet resource in the form of web site containing systematized information on cryptology.

DISTANCE LEARNING TECHNOLOGIES' APPLICATION SCENARIOS

Since cryptology itself is a part of computer science for a long time, the IT role in teaching cryptologic disciplines is dual in modern conditions: they are both a study subject and the tools for organizing an educational process. DLT have the leading role among these tools [START_REF]The Theory and Practice of Online Learning[END_REF].

At present DLT are quite clearly divided into two sectors: mass-oriented "stream" (large-scale) learning and individual-oriented "chamber" learning.

The first type of technologies is called MOOC. There are the completely-ready-touse educational products including both learning tools and information resources available online to a potentially unlimited number of trainees via the web interface. In addition to the traditional courses the MOOC's users may have an access to the new educational resources (videos, interactive tasks' sets and assignments in programming, as well as users' forums), enabling to establish an original community of students, professors and teachers being involved in the educational process [START_REF] Waldrop | Massive Open Online Courses, aka MOOCs[END_REF].

The main MOOC idea is realized most completely in the DL Networks (DLN) available via portals, accumulating extensive themed sets of courses in various subject areas. The characteristics of the most-known and popular DLN are shown in Table 1. The high quality of all DLN educational resources and significant increase in the number of available courses should be marked. The number of trainees for the most successful courses is measured by tens and hundreds of thousands worldwide. For example, the "Artificial Intelligence" course from the Coursera network is a leader with more than 180,000 people signed up all over the world at the same time. Such courses being once "put on a stream" are as a rule repeated periodically in the future.

Focusing on such a large audience determines the MOOC's characteristics: lack of the students' online feedback to a teacher during the sessions (as the main educational form is a video lecture); home works' and long-term projects' check implementation: knowledge progress testing is carried out either by choosing a correct answer from the given set and filling out some online form with automatic check of formats and value meanings entered, or by mutual check and review performed by the students themselves.

In almost all DLN listed in Table 1 the courses in cryptology are presented, for example: "Cryptography I" and "Cryptography II" (D.Boneh) in the Coursera network, "Applied Cryptography" (D.Evans), "Computer Security" conducted by the Stanford University together with the University of California, Berkley (USA) in the same network and several courses on network security and cryptography (both more general and more specialized) in the MIT Open Courseware network (USA).

According to the authors' opinion the obvious advantages of the DLN courses are their high quality and minimum price. That allows to recommend them for selftraining to the universities' teaching staff as well as to the students studying on different degrees. The DLN courses being taken together cover all the stages of educationfrom undergraduate to postgraduate, from Bachelors to Masters and PhD.

However the technologies oriented on massive training do not limited to DLN. They are based on the web technologies as it has been already mentioned. Therefore the creation of multifunctional web sites supporting the educational process and implementing various forms of teachers-students interaction can also benefit.

Technologies of the second type (oriented on individual learning) are essentially different types of videoconferencing with one or more leading (professor/instructor) and a small number of participants actively involved in the process of interaction with the leading. They have a special namewebinars, resulting from compound of the words "web" and "seminar", i.e. a seminar conducted using the web technologies (another names are online seminars, web conferences). All the webinar's participants should either install the special software on their computers or use the special web services provided by several service providers on the Internet. The best-known examples are the services such as Cisco WebEx, Citrix Online, Microsoft Office Live Meeting, HP video conferencing & HP Halo telepresence solutions. However, the number of solutions is increasing every day.

As practice shows the webinars are well suited for the lectures and seminars on different subjects, in particular, a wide range of IT-related disciplines. Currently, some Russian training centers and universities (like the NRNU MEPhI since 2012) implement a few training courses in "Information Security" in the form of webinars.

We would like to point out another model of IT application, having great potential for teaching the cryptologic disciplines. It is no secret that the universities have a very strong and old tradition of "theorizing" (sometimes too redundant) many subjects being taught at the higher school. The reason is the pronounced orientation toward the mass training of scientific and pedagogical personnel required in the past. However, a significant increase in demand for developing the students' practical skills and abilities in using the latest hardware and software and acquisition of practical experience in chosen speciality is observed due to the changes in economic and social life taking place over the past two decades all over the world. The laboratory facilities of many universities and their funding level are not always fully prepared to meet these requirements. At the same time open source software usage is significantly expanding all over the world. In most cases the license agreements for such software allow either its completely free usage for any purpose or at least free usage for non-commercial and educational projects. Free software emerging in the Internet and having a lot of potential applications in cryptology training and its mastering (in particular the development of new labs and practical assignments) can significantly enhance the practical focus of the updated cryptologic courses. The specific examples of such open source software are the libraries of cryptographic algorithms Crypto++, PyCrypto, the prototyping tool for cryptographic constructions Charm, the theoretical and numerical library NZmath and many others.

Experience of Mass-Oriented Distance Learning Technologies' Application

The creation of the Cryptowiki.net site supporting educational process for the cryptologic disciplines at the "Information Security of the Banking Systems" Department of the NRNU MEPI is an example of the first type of DLT application.

The site available at http://cryptowiki.net is used as a reference and information resource for professionals in the field of cryptography and for all kinds of students' home and independent works in their study of the "Cryptographic Protocols and Standards" and "Cryptography in Banking" courses. The site contains various materials for the students' work, rules description for the progress testing rating system and records of webinars previously conducted by the courses' author (Professor S. Zapechnikov).

The site operates under OS Windows on the commercially available hosting with a free content management system (engine) MediaWiki, version BitNami.

Cryptowiki.net's interface is similar to the Wikipedia interface, well known to the absolute majority of users (Figure 2).

The central place on the site is allocated to the reference and information system called the "Encyclopedia of Theoretical and Applied Cryptography" (further Encyclopedia). This is a comprehensive information resource created by the joint efforts of the teachers and students, which includes all content types available for posting: text, graphics, video, demo programs, mathematical expressions, program fragments' listings and others.

Fig. 2. Cryptowiki.net home page

The Encyclopedia consists of 56 substantive sections, each of which is dedicated to one of the major areas of modern cryptography and is available both in English and Russian languages. The Encyclopedia currently includes the following sections.

Part I "Foundations of Cryptography (Cryptographic Primitives)" consists of 25 sections covering all the main sections of the mathematical apparatus used in modern cryptography and the main types of cryptographic constructions such as block and stream ciphers, hash functions, open encryption schemes, digital signature scheme, as well as numerous supporting questions.

Part II "Applications of Cryptography (Cryptographic Protocols)" includes 31 chapters and is devoted to the cryptographic protocols' design and analysis. It gives knowledge on Zero-knowledge proofs, identification protocols, key distribution protocols, Secret sharing schemes, Threshold cryptography, Byzantine agreement protocol, Fair exchange, Protocols for secure communication channels, Protocols for secure databases retrieval, Protocols for secure cloud computing and secure cloud storage, Protocols for mobile security, Secure multi-party computations and many other cryptographic applications. Detailed Encyclopedia's content is presented in Table 2.

The site's sections essentially differ from the majority of online information resources by their content's volume and depth. It should be noted that the site is a joint textbook on theoretical and applied cryptography, co-written by students and teachers. However, its content is more focused at people experiencing practical needs in cryptography usage at their workplace, rather than cryptographers-theorists. Most sections do not present the formulations and rigorous proofs of theorems and propositions, but each section contains extensive information on the best-known methods and algorithms for solving the corresponding cryptographic tasks, especially their implementation, allowing to ensure high performance, to avoid vulnerabilities and to achieve ease of use of cryptographic mechanisms by their customers.

In comparison with the traditional textbooks the site's content can be replenished quicker, but of course it is not edited so carefully as for "paper" publishing.

There are some sections, which cannot be found in traditional textbooks. For example, the "Overview of cryptographic primitives: Roadmap for cryptographers" section provides a roadmap of cryptography primitives usage for security tasks' decision. That allows the readers to easily navigate the variety of available cryptographic constructions, to choose the most suitable among them for solving their problems and to correctly use it in building their own cryptographic protocol.

Completing assignments, their mutual reviewing by the students and commenting by the teachers on the site create an open and transparent environment for all parts of the educational process, and promote the publicity of students' work results and their objective assessment by the teachers.

An assignment given to the students using the site in the educational process consists of three parts:

1. content creation for the selected site's section in Russian. To complete this part of the work it is necessary to create a working team of 2 students (it is allowed to do the work of the whole team alone if a student wants that). The accomplished work is evaluated by the teachers using the 50-points' scale, and the resulting points are distributed among the members of the working team according to their real contribution to the work performed (but not more than 25 points for each member of the working team); 2. content creation for the selected site's section in English. The previously formed working teams are kept to perform this work. The site's section content in English should be adequate to the corresponding section in Russian. The slight reductions are allowed in the event of difficulty of the text interpreting in English. The accomplished work is evaluated by the teachers using the same 50-points' scale, and the resulting points are distributed among the members of the working team according to their real contribution to the work performed (but not more than 25 points for each member of the working team). If very many questions to the work performed appear, the team can be called for the oral defense of their work results; 3. software demo creation demonstrating in practice the execution of one of the cryptographic protocols (algorithms) described in this site's section (or one of the sections created in previous years). The protocol initial data input (for example longterm and (or) one-time keys, parameters, identifiers, etc.) from files or keyboard and program output to the screen and file should be provided in the program. All arithmetic and logical operations performed by the protocol's parties should be implemented. It is enough to make the program run on one computer and to execute sequentially data input for each of the protocol's parties. Similarly to the output data. Default data input should be provided in case of users' refusal of entering their data. The choice of programming tools and libraries is not limited. The user interface can be arbitrary, but it should be clear to a program's user (for example, the protocol implementation can be presented as a table, similar to those discussed during the lectures). It is desirable, but not required, that the interface will be graphical rather than textual. The program should be run under OS Windows. The program's source code and executables will be available on the corresponding pages of Cryptowiki.net after work will be finalized.

In addition to the Encyclopedia the traditional functionality for educational and methodical sites is implemented on the site: there are a lot of information materials, bulletin board, additional materials for lectures, etc.

CONCLUSION

Summarizing the discussion on applying DLT to teaching cryptology, we would like to note the following. 1. The existing DLT's analysis and the authors' personal experience of their application in teaching cryptology testify that DLT can significantly upgrade all kinds of traininglectures, seminars, and laboratory works. The main positive effect in this case is an increase of educational process's effectiveness, as well as the convenience of teachers-students interaction when performing the home works, course projects, organizational issues and mastering of elective discipline sections.

2. Two pronounced current trends of DLT development are DLN (as well as the related multifunctional web resources that address more narrow audience) and webinars. DLN is the most striking manifestation of emerging global educational space and global competition of the world's leading universities in the educational field. A webinar is the most effective form of classes' organization for the small groups of students. DLT combining both approaches are equally applicable in cryptology training.

3. Our gained experience in applying DLT in teaching cryptology can be extended to the other specialized disciplines taught to the students and trainees of short-term training and long-term professional retraining courses in the "Information Security" direction as well as to supervising the students' educational and scientific research, practical and final qualifying works.

4. The main difference between our CryptoWiki project and its analogs is that it organically complements the lectures and practical works in the cryptologic disciplines, supporting the interactive forms of students' teaching. They feel themselves involved in the process of creating a large-scale Encyclopedia, launched by their predecessorsthe students of previous graduation years and planned to continue in the coming years. After graduating from the NRNU MEPhI the former students continue to access the Encyclopedia, in developing which they have contributed, to recommend it to their colleagues and thus spread the cryptologic knowledge.

The project's success is confirmed by the facts that more than 17,000 users have visited the site during the first year of its operation and totally more than 28,000 since 2013.

Table 1 .

 1 Most-known DLN on the Internet

	DLN Name	Internet Address	Founders	Number of available courses 2012 2013 2014	Price; Certificate Issuance
			Universities:
	Coursera	coursera.org	Stanford, Princeton, Berkley, Ohio, Pittsburg, Illinois, Toronto, Georgia,	207	553	1127	Free; certificates are issued at the end of some courses
			Virginia
							Resources -
			Universities:				free;
			Harvard, Mas-				certificates
	edX	edx.org	sachusetts,	9	110	429	are now
			Berkley, since				free; will be
			2013 -Texas				paid in
							future
	UM Global Academy	umga. miami.edu	University of Miami	Middle school (MS) -39, High school (HS) -91	MS -39, HS -73	MS -39, HS -74	Access to all resources and courses -$70 registration fee
	Udacity	udacity.com	Private company	18	33	60	Free
							Resources -
	MIT Open Coursware	ocw.mit.edu	Massachusetts Institute of Technology	2100	2150	2150	free; certificates are not
							issued


Miloslavskaya Natalia
email: ngmiloslavskaya@mephi.ru

Tolstoy Alexander

Professional Competencies Level Assessment for Training of Masters in Information Security

Keywords: Masters in Information Security, Professional Competency, Professional Competencies Level Assessment, Professional Competencies Level Assessment Model 1

The peculiarities of assessing the level of professional competency formation in information security (IS) are discussed. The approach described uses the levels of mastering of specific disciplines forming this competency. Professional competencies in the field of information security and their levels are defined. The paper explains how these competencies can be formed. Metrics for the level of mastery of the discipline are introduced. The competencies level assessment model is proposed. The model application to the "Business Continuity and Information Security Maintenance" program for Masters at the NRNU MEPhI is shown. Important notes on using the model are given in conclusion.

INTRODUCTION

A professional in any field of activity must have specific qualifying characteristics. This is also true for the sphere of information security (IS). The modern approach to the determination of qualifying characteristics is based on the definition of professional competencies (further competencies) as a professional's capacity to solve given problems and to perform specific work within his/her sphere of activity [START_REF] Tolstoy | Basis for the formation of professional competencies of graduates from educational institutions along training directions and specialities included in the enlarge direction 090000 -Information Security[END_REF][START_REF]): A Competency and Functional Framework for IT Security Workforce Development[END_REF][START_REF]Model. A Best Practice Model and Framework[END_REF].

Qualifying characteristics for IS specialists can be presented as a set of their competencies in the field of IS (further IS competencies). They are used while implementing organizational personnel policy (including the role identification and assignment, the personnel recruitment and placement) and training (including the definition of requirements that the educational institutions' graduates must meet, and the implementation of an educational process that meets these requirements). Joint efforts of organizations' personnel departments and educational institutions together with the existence of some unified set of competencies will definitely enable coordination of their activities in order to best meet the staffing needs.

A problem of assessing the level of competencies (CL) formed in the implementation of a specific curriculum in the field of IS arises while conducting personnel training in this area. Two approaches are applicable for assessing this level:

1. assessment at the training completion (can be done via one single examination on all aspects related to a specific IS competency); 2. assessment of the levels of mastery of all specific disciplines forming one IS competency.

This paper describes a model that enables us to implement the second approach, which, from our point of view, is more interesting than the first. The remainder of the paper is organized as follows. Professional IS competencies and their levels are defined in Section 2. Section 3 explains how these IS competencies can be formed. Section 4 introduces metrics to measure the mastery level of the disciplines. The CL assessment model is proposed in Section 5. The model application to the "Business Continuity and Information Security Maintenance" program for Masters at the NRNU MEPhI is shown in Section 6. Some important notes on using the model are given in conclusion.

INFORMATION SECURITY COMPETENCIES AND THEIR LEVELS

Competencies support definitions of job classifications/occupational group profiles, roles and responsibilities, position descriptions, duty statements, etc. [START_REF]Model. A Best Practice Model and Framework[END_REF]. A competency is traditionally defined as a combination of observable and measurable knowledge, abilities and skills (Fig. 1) (as well as individual attributes and work experience) that contribute to enhanced employee performance and ultimately result in organizational success [START_REF]Model. A Best Practice Model and Framework[END_REF][START_REF]What is a Competency[END_REF]. Knowledge is the cognizance of facts, truths and principles gained from formal training and/or experience.

A skill is a developed proficiency or dexterity in mental operations or physical processes that is often acquired through specialized training; using these skills results in successful performance.

Ability is the power or aptitude to perform physical or mental activities that are often affiliated with a particular profession.

Fig. 1. Three competency's parameters

Hence, knowledge, abilities and skills levels are three integral parameters (attributes) of a specific competency, which are necessary to perform a job successfully. In our case this competency is related to the field of IS.

For recruitment it is important not only to formulate all the parameters of a certain competency, but also to determine the necessary levels of these parameters. At present it seems reasonable to use the US Government IS Workforce Development Model defining the following levels of competency [START_REF]Model. A Best Practice Model and Framework[END_REF].

Level 0 (Not Applicable). The knowledge, abilities and skills levels within the framework of this IS competency are unrelated to the requirements set either by an organization engaged in recruitment for a certain employment or by an institution at a student's training completion.

Level 1 (Entry-Level). The level corresponds to the presence of only basic knowledge in the area of professional activity to which this competency is related (basic understanding of IS concepts, common knowledge and its application to computer systems architecture) and limited experience (gained in a classroom and/or experimental scenarios or as a trainee on-the-job) that partially meets the requirements of abilities and skills. A professional has the ability to understand and discuss terminology, concepts and principles, and issues related to this competency. Help or mentoring is needed in performing these skills. The focus is on learning and development of on-the-job experience. When hiring a professional with such CL it is required to provide some mechanism to increase this level. These measures may include training at the workplace under the supervision of experienced staff members or requiring additional training (in the form of retraining courses). In an institution of higher education this level can be raised to the minimum needed to meet the requirements, which characterizes the final level of formation of a specific IS competency.

Level 2 (Intermediate). A professional possessing the IS competency of this level demonstrates solid IS knowledge and skills necessary to successfully solve typical professional tasks within the competency and with minimal guidance. He is able to understand and discuss the competency context and implications of changes to processes, policies and procedures in the professional field. Help or mentoring from an expert may be required from time-to-time (to handle novel or more complex, atypical situations), but the skills can be implemented independently. The focus is on applying and enhancing the levels of IS knowledge and skills. In an educational institution this level characterizes a basic understanding of a specific IS competency.

Level 3 (Advanced). A professional possessing the IS competency of this level has expert understanding, wide knowledge and abilities within that competency. Further, he or she can apply this competency in new or complex situations in related IS areas. He demonstrates expert knowledge of laws, regulations, policies and procedures, and standards in the area of his/her professional activity, including the ability to interpret and to translate subject matter to various audiences and for different applications. This allows him/her to take part in the development of various organizational documents and to focus on broad organizational/professional issues, including participation in senior and executive level discussions regarding this competency. The actions associated with these skills can be performed without assistance and are aimed at solving wide professional and organizational tasks with a focus on well-organized and accu-rate work in a team to implement the modern ideas. This professional provides consistent, practical and relevant ideas and perspectives on process or practice improvements, which may easily be implemented. He is a recognized authority within the organization. He is able to coach and mentor others in applying this IS competency by translating complex nuances into easy to understand terms in various business and technology contexts. In an institution this level characterizes an advanced, final level of gaining competency in a specific IS competency.

This paper is focused on solving the problem of assessing the level of IS competency, developed by the students of the higher education institutions.

INFORMATION SECURITY COMPETENCIES FORMATION

To train IS professionals in an educational institution means to develop the students' IS competencies in a particular area of their professional activity. The existence of such IS competencies when training is complete means the graduate has the ability to perform his job successfully and to solve practical tasks assigned to him by his employer.

Traditional competencies' formation is mastery of a specific number of educational disciplines (further disciplines). In general, they include training courses, various practices (practical works) and completion of a final qualifying work (FQW). One particular institution combined these disciplines to define specific features of an educational program leading to a Bachelor's or Master's degree, or a Specialist diploma, in the IS field [START_REF] Tolstoy | Basis for the formation of professional competencies of graduates from educational institutions along training directions and specialities included in the enlarge direction 090000 -Information Security[END_REF].

Implementation of a specific programme (for example, for Masters in IS) usually aims to develop some number of students' competencies CJ (Fig. 2). A predetermined number M of disciplines [𝑫 𝒎 ] (m=1,…,M) is involved in the formation of each IS competency. A few disciplines directly form a specific competency (e.g. competency 𝑪 𝒋 ). The rest of the disciplines are designed to create the required levels of IS knowledge, abilities and skills, necessary for mastering of disciplines, directly forming all necessary IS competencies. As an example, Fig. 2 shows that N disciplines [𝑫 𝒎𝒏 ] (n=1,…,N) providing the knowledge, skills and abilities for the discipline 𝑫 𝒎 .

Thus, the levels of attributes of a specific IS competency are formed directly and indirectly by the levels of IS knowledge, abilities and skills, obtained by mastering of a set of disciplines.

To determine the levels of competency in the various attributes making up IS, we have to measure the levels of mastery of disciplines making up that competency. We must also assess the contribution of each discipline to achieving IS competency.

METRICS FOR THE LEVELS OF MASTERY OF THE DISCIPLINE

Different scales can be used to assess the level of mastery of the discipline (DML). It may be a mark in points from 0 to 100 (Fig. 3a) or 0 to 10 (Fig. 3b), a literal indexing from J to A (Fig. 3c) or a mixed form (Fig. 3d) from 1 ("very bad") to 5 ("excellent").

There are also other assessment scales.

Fig. 3. Levels of mastery of the IS disciplines

To assess DMLs using CL it is necessary to select a single scale. This paper uses a point scalefrom 0 to 100 (Fig. 3a). Converting the measurement of a DML from one scale to another does not pose difficulties in any particular case (Fig. 3 can be used as an example for that purpose).

The assessment of a specific IS DML for 𝑫 𝒎 designated here as 𝑫𝑨 𝒎 should integrate the assessments of the level of gained IS knowledge 𝑲𝑫 𝒎 , the level of formed IS abilities 𝑨𝑫 𝒎 and the level of acquired IS skills 𝑺𝑫 𝒎 , developed by mastery of this discipline. Then 𝑫𝑨 𝒎 = 𝜶 𝒌𝒎 𝑲𝑫 𝒎 + 𝜶 𝒂𝒎 𝑨𝑫 𝒎 + 𝜶 𝒔𝒎 𝑺𝑫 𝒎 , [START_REF] Tolstoy | Basis for the formation of professional competencies of graduates from educational institutions along training directions and specialities included in the enlarge direction 090000 -Information Security[END_REF] where 𝜶 𝒌𝒎 , 𝜶 𝒂𝒎 , 𝜶 𝒔𝒎 are the weights of the contribution of the attributes (knowledge, abilities and skills) into DML. These attributes must satisfy the condition 𝜶 𝒌𝒎 + 𝜶 𝒂𝒎 + 𝜶 𝒔𝒎 = 𝟏.

The levels 𝑲𝑫 𝒎 , 𝑨𝑫 𝒎 , 𝑺𝑫 𝒎 , which the students develop while mastering specific IS disciplines, are defined during the testing of their progress. Students are evaluated in some way, for example by examination. In that case, the control questions for progress testing should be formulated in such a way that these levels can be clearly assessed based on responses to them.

The following features associated with the peculiarities of a specific IS discipline can also be considered. For example, if the discipline is a training course, its curriculum can be implemented using various forms of training: lectures, seminars, and labs. Lectures mainly form the knowledge level, seminarsabilities level and labsskills level.

If the discipline consists only of the lectures (e.g. a more theoretical discipline studying international law or explaining how to write IS policies), then 𝜶 𝒌𝒎 = 𝟏 , 𝜶 𝒂𝒎 = 𝟎, 𝜶 𝒔𝒎 = 𝟎.

In case of seminars (e.g. with an assignment to write a specific private IS policy), then 𝜶 𝒌𝒎 ≪ 𝜶 𝒂𝒎 , 𝜶 𝒌𝒎 ≤ 𝜶 𝒔𝒎 , 𝜶 𝒂𝒎 ≥ 𝜶 𝒔𝒎 .

If nothing but labs (e.g. how to detect network intrusions using IDS predefined for a student or a group of students), then 𝜶 𝒌𝒎 ≪ 𝜶 𝒔𝒎 , 𝜶 𝒌𝒎 ≤ 𝜶 𝒂𝒎 , 𝜶 𝒂𝒎 ≤ 𝜶 𝒔𝒎 .

In case of practices and FQW, then 𝜶 𝒌𝒎 ≤ 𝜶 𝒂𝒎 , 𝜶 𝒌𝒎 ≪ 𝜶 𝒔𝒎 , 𝜶 𝒂𝒎 ≤ 𝜶 𝒔𝒎 . The values of 𝜶 𝒌𝒎 , 𝜶 𝒂𝒎 , 𝜶 𝒔𝒎 for a specific discipline can be determined by an expert, who can be a professor/instructor/tutor conducting studies on the discipline. ; 𝑻 𝟎 = 𝑻 𝒌 + 𝑻 𝒂 + 𝑻 𝒔 .

(2)

INFORMATION SECURITY COMPETENCIES LEVEL ASSESSMENT MODEL

In the introduction we emphasized that we will assess a specific IS competency 𝑪𝑨 𝒋 and its attributes' values (the levels of IS knowledge 𝑲𝑪 𝒋 , abilities 𝑨𝑪 𝒋 and skills 𝑺𝑪 𝒋 ) using the second approach. That approach is based on the characteristics of disciplines forming this competency (DML 𝑫𝑨 𝒎 , the levels 𝑲𝑫 𝒎 , 𝑨𝑫 𝒎 and 𝑺𝑫 𝒎 ). Let us set the following assumptions for the model. 1. Some disciplines 𝑫 𝒎𝒏 are essential for disciplines 𝑫 𝒎 . These disciplines 𝑫 𝒎 directly form some IS competency 𝑪 𝒋 (Fig. 2). Thus, the disciplines 𝑫 𝒎𝒏 indirectly determine the characteristics of the competency 𝑪 𝒋 . Due to length limits of the paper, we do not consider the characteristics of the underlying disciplines 𝑫 𝒎𝒏 .

2. The results of mastering a specific discipline 𝑫 𝒎𝒏 can be used in the formation of each IS competency 𝑪 𝒋 connected with this discipline. Therefore, the differentiation of the contribution of a particular discipline into the formation of different competencies is not taken into account.

3. We weight the contributions of a discipline 𝑫 𝒎 to the formation of a specific IS competency 𝑪 𝒋 . For 𝑫 𝒎 , m=1,…,M; and M is the number of disciplines 𝑫 𝒎 forming the competency 𝑪 𝒋 , these weights are 𝜷𝒌 𝒋𝒎 for the levels of knowledge, 𝜷𝒂 𝒋𝒎 for the abilities, and 𝜷𝒔 𝒋𝒎 for the skills. The weights 𝜷𝒌 𝒋𝒎 , 𝜷𝒂 𝒋𝒎 , 𝜷𝒔 𝒋𝒎 are defined by experts. From our point of view for the weights' values it is easy to use 11-points range (from 0 to 10 like in Table 1 from Section 5). It is not so important what range the experts will choose, because while assessing the attribute values for 𝑪 𝒋 the levels 𝑲𝑫 𝒎 , 𝑨𝑫 𝒎 and 𝑺𝑫 𝒎 with these weights are normalized by their sums as it is shown further (expressions (3), ( 4), ( 5)).

4. The single points scale from 0 to 100 is used to assess the level of competencies, their attributes and characteristics of disciplines. The transition from this scale to fourlevel IS competency assessment (Section 2) is done in accordance with Fig. 4.

Fig. 4. Linking of scales for competency assessment

The IS competencies level assessment model is shown in Fig. 5.

Fig. 5. Diagram of IS competencies level assessment model

Initial data for the model are the following:

1. a set of IS disciplines 𝑫 𝒎 (where m=1,…,M; M is a number of disciplines), directly forming the selected IS competency 𝑪 𝒋 ; 2. DML assessments 𝑫𝑨 𝒎 (m=1,…,M) and the levels 𝑲𝑫 𝒎 , 𝑨𝑫 𝒎 and 𝑺𝑫 𝒎 ); 3. the coefficients for each discipline 𝜶 𝒌𝒎 , 𝜶 𝒂𝒎 , 𝜶 𝒔𝒎 (m=1,…,M); 4. the weights 𝛃𝐤 𝐣𝐦 , 𝛃𝐚 𝐣𝐦 and 𝛃𝐬 𝐣𝐦 (m=1,…,M) for attributes' assessment for 𝑪 𝒋 .

The main expressions for the model are the following. 1. Assessment of attribute value for 𝑪 𝒋 , determining the IS knowledge level:

𝑲𝑪 𝒋 = ∑ (𝛃𝐤 𝐣𝐦 𝑲𝑫 𝒎 ) 𝑴 𝒎=𝟏 / ∑ (𝛃𝐤 𝐣𝐦 ) 𝑴 𝒎=𝟏 . (3)
2. Assessment of attribute value for 𝑪 𝒋 , determining the IS abilities level:

𝑨𝑪 𝒋 = ∑ (𝛃𝐚 𝐣𝐦 𝑨𝑫 𝒎 ) 𝑴 𝒎=𝟏 / ∑ (𝛃𝐚 𝐣𝐦 ) 𝑴 𝒎=𝟏 . (4)
3. Assessment of attribute value for 𝑪 𝒋 , determining the IS skills level:

𝑺𝑪 𝒋 = ∑ (𝛃𝐬 𝐣𝐦 𝑺𝑫 𝒎 ) 𝑴 𝒎=𝟏 / ∑ (𝛃𝐬 𝐣𝐦 ) 𝑴 𝒎=𝟏 . (5)
4. Assessment of IS competency level 𝑪𝑨 𝒋 according to the points scale. The following options are possible here.

Option 1. If the contributions of attributes into 𝑪𝑨 𝒋 are equal, then the assessment of 𝑪𝑨 𝒋 is calculated as:

𝑪𝑨 𝒋 = (𝑲𝑪 𝒋 + 𝑨𝑪 𝒋 + 𝑺𝑪 𝒋 )/𝟑. (6) Option 2. If the contributions of attributes into 𝑪𝑨 𝒋 are not equal, then it is necessary to introduce 𝛌𝐤 𝒋 , 𝛌𝐚 𝒋 , 𝛌𝐬 𝒋 ( 𝛌𝐤 𝒋 + 𝛌𝐚 𝒋 + 𝛌𝐬 𝒋 = 𝟏) (like for 𝜶 𝒌𝒎 , 𝜶 𝒂𝒎 , 𝜶 𝒔𝒎 from Section 4) determined by experts and to assess 𝑪𝑨 𝒋 as:

𝑪𝑨 𝒋 = 𝛌𝐤 𝒋 𝑲𝑪 𝒋 + 𝛌𝐚 𝒋 𝑨𝑪 𝒋 + 𝛌𝐬 𝒋 𝑺𝑪 𝒋 .

(7) Option 3 (called frontier). It is based on the transition from points to levels (Fig. 4). The assessment of 𝑪𝑨 𝒋 is done by the following rules: «0», if at least one attribute is at this level; «1», if at least one attribute is at this level and the rest are at the higher levels (2, 3); «2», if at least one attribute is at this level and the rest are at the higher level (3); «3», if the values of all competency attributes are at the same level (3). Option 4. If DMLs 𝑫𝑨 𝒎 (forming 𝑪 𝒋 ) are known and the contributions of these disciplines into competency formation µ 𝒋𝒎 (m=1,…,M) are defined, then the assessment of 𝑪𝑨 𝒋 is calculated as:

𝑪𝑨 𝒋 = ∑ (µ 𝒋𝒎 𝑫𝑨 𝒎 ) 𝑴 𝒎=𝟏 / ∑ (µ 𝒋𝒎 ) 𝑴 𝒎=𝟏 . (8)
If weights 𝛃𝐤 𝐣𝐦 , 𝛃𝐚 𝐣𝐦 , 𝛃𝐬 𝐣𝐦 are defined, then values µ 𝒋𝒎 can be calculated as:

µ 𝒋𝒎 = 𝛃𝐤 𝐣𝐦 + 𝛃𝐚 𝐣𝐦 + 𝛃𝐬 𝐣𝐦 . (9)

MODEL USAGE EXAMPLE

The IS competencies assessment model described above is based on the system of assessing the levels of mastery of disciplines forming a specific IS competency. This model was used at the "Cybernetics and Information Security" Faculty of the National Research Nuclear University "MEPhI" (Moscow Engineering Physics Institute) (Russia) at the implementation of the "Business Continuity and Information Security Maintenance" (BC&ISM) program for Masters [START_REF] Miloslavskaya | Business Continuity and Information Security Maintenance" Masters' Training Program[END_REF].

The requirements of the Federal State Educational Standard (FSES) of training Masters in IS were taken into account in developing the curriculum for this program. FSES defines the area and professional activities, for which Masters should be trained. It also lists the professional activities and tasks that Masters graduates should be able to solve. The basic IS competencies are defined for each type of professional activities.

An educational institution has the right to work out its own curriculum (to choose specific disciplines) and to add more IS competencies reflecting the specific program. When a graduate masters the Masters' program, he/she will have developed additional competencies defined by the institution [START_REF] Miloslavskaya | Business Continuity and Information Security Maintenance" Masters' Training Program[END_REF]. At the completion of training they must be able to fulfill the following activities:

 to analyze and to investigate models of systems ensuring business continuity (BC) and models of IS maintenance (𝑪 𝟏 );  to practically implement the standards relating to BC&ISM (𝑪 𝟐 );  to conduct IS risk assessment for the purpose of IS maintenance (𝑪 𝟑 );  to carry out the synthesis and analysis of design projects on BC&ISM for their organization where they work (O's) (𝑪 𝟒 );  to ensure the effective usage of O's IT resources to meet BC&ISM requirements (𝑪 𝟓 );  to participate in the design and operation of O's IS incident management system (𝑪 𝟔 );  to participate in the design and operation of O's BC&ISM system (𝑪 𝟕 );  to conduct technical auditing (monitoring) of O's information protection (𝑪 𝟖 );  to develop proposals for improving O's BC&ISM system (𝑪 𝟗 );  to establish and effectively implement a set of measures (rules, procedures, practical methods, guidelines, methods, tools) for BC&ISM (𝑪 𝟏𝟎 ).

All these competencies are developed during the implementation of a specific curriculum, which includes the specific IS disciplines [START_REF] Miloslavskaya | Business Continuity and Information Security Maintenance" Masters' Training Program[END_REF].

The paper considers the formation of only one competency 𝑪 𝟕 as an example, when a graduate should be able to participate in the design and operation of O's BC&ISM system.

Based on an analysis of the curriculum, ten IS disciplines 𝑫 𝒎 , (m=1,…,M), form this IS competency [START_REF] Miloslavskaya | Business Continuity and Information Security Maintenance" Masters' Training Program[END_REF]:  6 training courses, namely:

─ "Protected IT" (abbreviation PIT), ─ "IS Management" (ISM), ─ "IS Risk Management Basics" (ISRMB), ─ "IS Incident Management Basics" (ISIMB), ─ "IT Security Assessment" (ITSA), ─ "Business Continuity Management" (BCM),  Practical Works during Semesters 1, 2 and 3 (P1, P2, P3), and  Completion of a FQW (FQW).

Initial data for the IS competency assessment model are shown in Table 1. It should be noted that:

 𝜶 𝒌𝒎 , 𝜶 𝒂𝒎 , 𝜶 𝒔𝒎 for the contributions of knowledge, abilities and skills levels into the level of mastery of the particular discipline (6 training courses) were determined on the basis of work involved in mastering the discipline (expression ( 2)) (𝑻 𝟎 𝑻 𝒌 , 𝑻 𝒂 , 𝑻 𝒔 ), taken from the curriculum [START_REF] Miloslavskaya | Business Continuity and Information Security Maintenance" Masters' Training Program[END_REF];  𝜶 𝒌𝒎 , 𝜶 𝒂𝒎 , 𝜶 𝒔𝒎 for the contributions of knowledge, abilities and skills levels into the level of mastery of the particular discipline (P1, P2, P3 and FQW) were determined by experts. The following peculiarities were taken into account: the contributions of the levels of gained knowledge 𝑲𝑫 𝒎 and formed abilities 𝑨𝑫 𝒎 decrease during the training, and the contribution of acquired skills 𝑺𝑫 𝒎 increases;  the levels 𝑲𝑫 𝒎 , 𝑨𝑫 𝒎 and 𝑺𝑫 𝒎 were defined along a 100 point scale during progress testing (exams) for a particular student;  the assessments of DML 𝑫𝑨 m were determined according to the expression (1);  the weights' values for 𝑪 𝟕 attributes (𝛃𝐤 𝟕𝐦 , 𝛃𝐚 𝟕𝐦 and 𝛃𝐬 𝟕𝐦 ) were determined by experts. The attribute values assessments for 𝑪 𝟕 can be determined using data from Table 1: 1) for the knowledge level (expression (3)) 𝑲𝑪 𝟕 = 68; 2) for the abilities level (expression (4)) 𝑨𝑪 𝟕 = 76;

3) for the skills level (expression (5)) 𝑺𝑪 𝟕 = 84. Within the framework of the model let us define competency 𝑪 𝟕 level assessment 𝑪𝑨 𝟕 for four options.

Option 1. When the contributions of competency attributes to the level of competency is equal, then the competency level assessment will be determined by the expression (6) as 𝑪𝑨 𝟕 = 76. The competency level assessment will refer to the second (intermediate) level in accordance with the scale from Fig. 4.

Option 2. When the contribution of competency attributes to the level of competency is unequal, then it is necessary to introduce 𝛌𝐤 𝟕 , 𝛌𝐚 𝟕 , 𝛌𝐬 𝟕 .

If the knowledge level is more important (e.g., 𝛌𝐤 𝟕 = 0,8; 𝛌𝐚 𝟕 = 0,1; 𝛌𝐬 𝟕 = 0,1), then according to the expression (7) 𝑪𝑨 𝟕 = 71, which corresponds to the second (intermediate) level from Fig. 4.

If the abilities and skills levels are more important (e.g., 𝛌𝐤 𝟕 = 0,1; 𝛌𝐚 𝟕 = 0,45; 𝛌𝐬 𝟕 = 0,45), then according to the expression (7) 𝑪𝑨 𝟕 = 79, which also corresponds to the second (intermediate) level from Fig. 4.

Option 3. For frontier approach 𝑪𝑨 𝟕 = 68, which corresponds to the first (entrylevel) level from Fig. 4.

Option 4. Using the expression (9) and data from Table 1 for µ 𝒋𝒎 (m=1,…,M), it is possible to use expression (8) to determine the competency level assessment as 𝑪𝑨 𝟕 = 77, corresponding to the second (intermediate) level from Fig. 4.

CONCLUSION

The model presented in this paper allows the assessment of the level of any professional competency in the IS field. It also allows the assessment of the values of the competency's attributes according to the assessment characteristics of the disciplines that form this competency. The above example uses the model to assess one of the competencies in the IS Masters programme, confirming the usefulness and efficiency of the proposed model. We note that using this model requires changes in the way one assesses mastery of a specific discipline. It is necessary to assess not only the entire discipline in general, but also to separately assess the levels of knowledge, abilities and skills developed by the students as they master the discipline. In addition, the values of some of the model's parameters should be determined by experts.

Approaches that have been used in this model can be applied to construct another model, which solves the inverse task. If the required IS competency level, its attributes and their assessment are known, then the actual problems are the selection and determination of the list of disciplines forming the specific competency, determination of their characteristics (the list and the level of knowledge, skills and abilities to be developed at the training completion), and formulating the initial data for a particular IS professional training curriculum and training courses. But the development of an inverse model is more complicated problem because it should use different synthesis methods. This requires solving a few optimization problems with predefined criteria.

Fig. 2 .

 2 Fig. 2. Diagram of IS competencies' formation

  For example, these values for a discipline being a training course can be determined based on analysis of the work involved in a discipline (we call it a discipline laboriousness) expressed in credits or time of classes' duration in academic hours 𝑻 𝟎 in view of duration of lectures 𝑻 𝒌 , seminars 𝑻 𝒂 and labs 𝑻 𝒔 :

Table 1 .

 1 Initial data for competency assessment modeling 𝑫 𝒎 𝑻 𝟎 𝑻 𝒌 𝑻 𝒂 𝑻 𝒔 𝜶 𝒌𝒎 𝜶 𝒂𝒎 𝜶 𝒔𝒎 𝑲𝑫 𝒎 𝑨𝑫 𝒎 𝑺𝑫 𝒎 𝑫𝑨 𝒎 𝛃𝐤 𝐣𝐦 𝛃𝐚 𝐣𝐦 𝛃𝐬 𝐣𝐦


Zapechnikov Sergey
email: svzapechnikov@mephi.ru

Tolstoy Alexander

Nagibin Sergey

History of Cryptography in Syllabus on Information Security Training

Keywords: Information Security Science, Syllabus, Information Security Training, History of Cryptography 1

This paper discusses the peculiarities and problems of teaching the historical aspects of Information Security Science (ISS) to the students of the "Information Security" specialization. Preferential attention is given to the ISS area with the longest history, namely cryptography. We trace exactly what ideas of fundamental importance for modern cryptography were formed in each of the historical periods, how these ideas can help students in mastering the training courses' material, and how to communicate these ideas to students in the best way. The conclusions are based on the results of studies conducted over a few years at the "Cybernetics and Information Security" Faculty of the NRNU MEPhI, where our ideas are implemented in the educational process. We teach the history of cryptography in a few educational courses for Specialists in IS and Masters in Business Continuity and IS Maintenance in the form of introductory and individual lectures and seminars. Specific recommendations on the use of the historical facts considered during the classes are given.

INTRODUCTION

The study of any science's history is a part of the syllabus for students in disciplines with deep historical roots. Cryptography is one of these areas. The earliest evidence of cryptographic techniques being used for text protection refers to the XX century BC, as is well known from the archaeological data. Thus, cryptography has a history of at least forty centuries. But for a long time this area of activity was not a scientific discipline in the modern sense of the word. Rather, it was an art known to a few people who know how to protect the content of written documents from prying. Information protection (IP), and especially cryptography, began to build actively on a scientific basis only in the late XIXearly XX century. It is due to the fundamental changes in modes of representation, transmission and transformation of information in new technical systems such as the telegraph, telephone and various electromechanical devices. However, the IP method continued to be developed on the old basis until the mid XX century. The appearance of the well-known paper by Shannon, "Communication The-ory of Secrecy Systems", in 1949 and the rapid development of computer technology caused an irreversible transformation of cryptography in mathematical and computer science.

The exploration of the rich heritage of pre-scientific cryptography has a huge cognitive and wide educational value for modern IS specialists because of the abundance of ingenious solutions and good practices gained during a long quest of many generations. That makes it possible to avoid unnecessary repetition of mistakes and missteps when creating IP tools and to prevent accidents while designing cryptosystems.

Certainly, the history of science should take into account not only the history of ideas in the relevant field of expertise, but also the history of all human activities related to the implementation of these ideas. However, in a few academic disciplines it is possible to track only the most important milestones in this history, i.e. the history of ideas in the field of cryptography and other ways of document protection. The history of the facts can be traced to a much lesser extent because of the limited time allotted for the study of academic disciplines.

Therefore, it is possible to list the following reasons for including classes on the history of cryptology as a part of students' training in the field of IS:

 Such a class demonstrates that cryptography as any other significant area of human activity has not only its own theory, but its own history as well. That history helps to better understand the theory, and vice versa;  Such a class can help students better understand how modern cryptography (and ISS in general) was formed and developed, and the laws and patterns for the accumulation and generalization of human knowledge;  Faced with the differences and diversity of forms of man's thought and action through many centuries and countries, students can better understand their own identity and the role of modern science in historical processes.

Thus, the paper is organized as follows. After discussing the purpose of introducing the historical aspects of cryptography into the learning process in Section 2, we note the ways in which the history of cryptography is presented in the syllabus of training Specialists and Masters in the NRNU MEPhI. In Sections 3-6 we discuss in more detail how the most important ideas of the main periods in cryptography development (pre-scientific, classical science, transition phase from classical to modern science and modern science) can best be taught by the lecturers and studied by the students of a few courses on IS. Section 7 briefly presents some related works. The directions of future work are identified in conclusion.

FORMS OF HISTORY OF CRYPTOGRAPHY'S CLASSES

In accordance with the state Russian educational standards, courses training Specialists and Masters do not discuss the history of science. The "History and Methodology of Science" discipline is provided only for post-graduate students. In this regard, we have to look for other ways to have the students learn about the history of the field of science in the process of mastering the syllabus. Some ways are:

 introductory lectures on various subjects;  scientific seminars;  individual lectures on the "Humanitarian Issues of Information Security" and "Cryptographic Protocols and Standards" disciplines for the Specialists in IS;  lectures and workshops as a part of the introductory discipline entitled "Fundamentals of Business Continuity and Information Security Maintenance" for the Masters.

Presenting history in the introductory lectures allows the instructor to place the studied disciplines into their general scientific context, to show communications and parallels with the other disciplines, including those devoted to the study of almost exclusively classical science such as basic mathematical and engineering disciplines. For example, it is very useful to draw a time axis with the major periods in the history of cryptography and to show the development of different areas of this science at the second half of the XX century at the introductory lecture on the "Cryptographic Protocols and Standards" discipline (Fig. 1). Our experience shows that the teachers of classes on the history of cryptography should have a good knowledge not only in the world history, but also in the foundations of cryptography. Since the classes are designed for the students specializing in mathematical and computer sciences, it is better that the teachers' basic education is natural or computer sciences rather than humanitarian sciences.

We recommend seminars in an interactive form. For example, all students take turns preparing reports, discussing them with their teachers and presenting them during the classes. The necessary requirements for getting credits for that part of an educational course that includes one section on the history of cryptography are their own report presentation, reviewing 2-3 reports of other students, and participating in their discussions.

In general, while planning the history of cryptography classes, we divide the history into the following periods: I. Pre-scientific period (from ancient times to the end of the XVII century); II. Classical science period, in which the scientific basis of cryptography was formed (XVIII-XIX centuries); III. Transition phase from classical to modern science (the end of the XIX century the beginning of the XX century); and IV. Modern cryptography (the second half of the XX centurythe beginning of the XXI century).

The history of related sciences (e.g. steganography and methods of protection against falsification of paper documents and banknotes) is also discussed in parallel with the history of cryptography, using the same periods.

Some recommendations for the study of the main periods in the history of cryptography, as well as a few ideas that can be implemented during lectures and seminars, are presented in the following sections.

THE PRE-SCIENTIFIC PERIOD AND ITS LESSONS

The main educational reason for studying the pre-scientific period of cryptography's development is to show the following:

 what main methodological ideas were used in the first known techniques of cryptographic IP;  how these ideas were developed and generalized as time passed; and  why they continue to be the foundation of many cryptographic techniques. This period is illuminated in a number of books on the history of cryptography [START_REF] Kahn | The codebreakers: The story of secret writing[END_REF][START_REF] Mollin | Codes: The guide to secrecy from Ancient to Modern Times[END_REF][START_REF] Bauer | Decrypted secrets: Methods and maxims of cryptology[END_REF][START_REF] Rusetskaya | Istoriya kriptografii v Zapadnoy Evrope v rannee novoe vremya. Tsentr gumanitarnyh initsiativ; Universitetskaya kniga[END_REF][START_REF] Bauer | Secret history: the story of cryptology[END_REF]. However, in most modern textbooks on cryptographic IP methods the prescientific period's codes serve only as a background against which to present the advanced modern techniques. However, research into the ancient techniques of protecing written communications still cannot be considered completed. The codes used in ancient Greece, ancient Rome, and medieval Western Europe are well-known and described in detail. They overshadow the achievements of many other nations and civilizations that also contribute to the history of cryptography. Therefore, when creating material for our classes, we use not only well-known sources, but also rely on the results of our own research [START_REF] Zapechnikov | Cryptography as the phenomenon of Russian literature language (XII -XVII centuries)[END_REF][START_REF] Zapechnikov | Protection of documents, cryptography and secret communications in Byzantium (IV-XV centuries)[END_REF][START_REF] Zapechnikov | Cryptography and secret communications in the Ancient world[END_REF].

The ancient and medieval methods of protecting written texts are very suitable to demonstrate to the students the basic principles of concealing the text contents from unauthorized persons, as well as the simplest methods of their breaking. The main difference between them and modern ciphers is simplicity meaning that they are easily observable. The basic ideas can be easily explained by the teacher during one lecture and can be understood even by those students who do not specialize in the field of IS or other areas of mathematical and computer sciences.

However, the teacher should be cautioned against too direct a comparison of prescientific and modern IP methods. Ancient cryptography should be considered pri-marily a linguistic phenomenon and a specific method of transmitting thoughts by a community of people, knowing one or another "secret language". Its main feature compared to modern cryptography is that the text was merely a sequence of characters, regardless of its semantic content (coherent text, a set of numbers, etc.), whereas modern cryptography is based on mathematical formalism and formal logic.

In this regard, we recommend the teacher emphasize the following while discussing cryptography of the prescientific period.

1. Almost all ancient civilizations knew cryptography as a special linguistic phenomenon, fixing on physical media the "secret languages" that existed in different social groups since time immemorial. These languages have an origin in magical ritual, but later they were understood as a tool for social communication. In this regard, cryptography has two main application areas in the ancient history:

 "magic"to conceal a meaning of names, magic rituals, secret ritual knowledge and another taboo information, i.e. for secret communications with the supernatural (that was an integral part of the lives of all ancient civilizations);  "practical"to protect military reports, personal correspondence, and perhaps trade secrets, i.e. for secret communication in human society.

2. The most important encryption principlesreplacement and permutation of characterswere empirically discovered in the Ancient World. In the Ancient World, these principles exhausted the arsenal of cryptographic protection methods for written texts, and they were realized only for special, very simple cases. Evolution of the cryptographic methods was extremely slow because the existing methods were generally sufficient. 3. Along with cryptography, the ancient civilizations used various methods of physical protection of messages by encoding and steganography. That served different practical purposes such as concealing the fact of message's existence or transfer, hiding the names of senders or recipients, accelerating copying text and reducing the amount of material to be carried or memorized, transmitting messages at a rate greater than a man's speed, and raising the value of the text to the reader. These objectives were often seen as a priority compared to concealing the message's meaning from unauthorized persons.

While studying cryptography in the Middle Ages and the early New Ages (XVI -XVII centuries) it is reasonable to stress the following:

 The encryption methods have become more complex in the Middle Ages: polyalphabetic substitution has been invented. The systematic methods of cryptanalysis have appeared in the Arabian world for the first time;  Signatures and stamps ensured a document's authenticity for the first time in Byzantium, along with encryption ensuring the confidentiality of documents;  Ciphers are still considered a linguistic phenomenon: single words, sentences, paragraphs, sections of the document are converted.

One of the techniques that can be used to indicate a close relationship between history and modernity of cryptography and to inspire students who are accustomed to think in terms of modern mathematics and formal logic is to mathematically analyze ancient ciphers (like shift, replacement, affine and permutation ciphers). However, the general cases of substitutions and (or) permutation were not implemented in any classical ciphers and cryptographic devices, and the particular cases used essentially reduce the cipher strength. Nevertheless, a number of examples might illustrate the fact that the most secure classic ciphers such as the Vigenère cipher and "Latin squares" widely regarded as almost unbreakable until the appearance of computers in the XX century.

Our experience shows that the students analyze classical ciphers with great interest. On the one hand, the examples are readily understandable and the validity of the findings can be checked without using software. On the other hand, similar analysis of the modern ciphers' security such as AES, the Russian standard GOST 28147-89 [START_REF]Russian state encryption standard[END_REF], RC6, etc. is simply impossible in classes because of great complexity of ciphers and the time required.

THE PERIOD OF CLASSICAL SCIENCE

The main educational goal in studying the period of classical science is to show how the important mathematical methods were formed during this period. They have become the basis of a variety of protection methods (including asymmetric cryptography) later in the XX century. Many discoverers cannot anticipate the fundamental importance of their works for the future of science.

The classical science period (the XVI centurythe end of the XIX century) is a stage of historical development of science, during which the system of the most important natural science concepts and ideas was formed. This system is the foundation of today's scientific knowledge and method. Mathematical knowledge particularly flourished during this period. This is fully applicable to cryptography. Many famous scientists can be mentioned here: Leon Battista Alberti, Francois Vieta, Giovanni Battista Porta, Blaise de Vigenère, Francis Bacon, as well as many interesting ciphers' designs of the time: Cardan grille, Vigenère's cipher and many others. Research about this period of cryptography's development has not been completed. Therefore, while creating lessons for the classes we used our own scientific results [START_REF] Zapechnikov | About the history of cryptography: the Leonardo Euler's contribution in formation of mathematical basis for modern cryptology[END_REF].

During the classes, we draw students' attention to the following basic ideas related to the period of classical science:

 Encryption techniques become more complicated: combinations of substitutions and permutations in one cipher are used;  Methods of cryptanalysis are improved and a competition between cryptographers and cryptanalysts is enhanced;  Pure and applied mathematics, long considered just an abstraction, are developed; later in the XX century they served as the foundation for most of the natural sciences and engineering; and  Principles of engineering and technical IP begin to be developed as one of the areas of engineering science.

Our experience shows that one of the most effective forms of studying the classical science's period is to obtain an acquaintance with the biographies of the outstanding scientists who greatly contributed to the mathematical foundations of modern cryptography and its creative and scientific methods.

The most striking example that should be included in the syllabus is a study of Leonard Euler's creative heritage. Euler's contribution to world science is truly priceless. He essentially founded several mathematical sciences: analytic number theory, calculus of variations, complex function theory, differential geometry of surfaces, analytical mechanics, rigid body dynamics, as well as many parts of the theory of differential equations, theory of algorithms, theory of elliptic functions, celestial mechanics and other areas of pure and applied mathematics. This scientist had encyclopedic knowledge. His interests extended to many branches of astronomy, acoustics, optics, statistics, botany, medicine, chemistry, linguistics, music, and engineering. Almost all Euler's results belonging to the areas of mathematics that form the foundations of modern cryptology are centered on his discoveries in numbers theory.

At present Euler's works are considered to be the most important and fundamental works for asymmetric cryptography. Of course, Euler himself could not have foreseen the development of the methods and areas of cryptology known today and studied in different courses as the basis of this science. However, the main ways of using Euler's results can be grouped into four categories:

1. Testing the primality of numbers (widely used to generate asymmetric cryptographic parameters); 2. Computationally complex problems in number theory (e.g. the Euler theorem, study of the properties of quadratic residues and the theory of primitive roots; these are closely related to three computationally complex problems in numbers theory, which now form the basis of the most common asymmetric cryptosystems, namely the Rivest-Shamira-Adleman (RSA) problem, the problem of quadratic residues and the discrete logarithm problem); 3. Cryptosystems based on computationally complex problems. The RSA problem is the basis of security of the RSA encryption scheme and the RSA digital signature scheme. Security of cryptosystems such as the Goldwasser-Micali probabilistic open encryption scheme, the pseudo-random BBS (Blum-Blum-Shub) generator and the Paillier open encryption scheme is based on the problem of quadratic residues. The ElGamal encryption scheme and the ElGamal digital signature scheme and its variants DSA (USA digital signature standard) and GOST R 34.10-2012 (Russian digital signature standard) [START_REF]Russian state digital[END_REF] are based on the discrete logarithm problem; and 4. Cryptographic protocols that use primitives based on the above computationally complex problems. Some constructions, the security of which is based on the same computationally complex problems, can be used in addition to the above listed cryptosystems as the building blocks for cryptographic protocols. The most famous example is the Diffie-Hellman public key distribution protocol and numerous pro-tocols derived from it (e.g. MTI, STS, etc.). Their security is ultimately based on the discrete logarithm problem and the Diffie-Hellman problem. Less well-known examples are the zero-knowledge proof protocols that can use all three of the above problems. For example, security of the Shnorr zero-knowledge authentication scheme is based on the intractabilility of the discrete logarithm problem.

The above examples are enough to make a conclusion about the fundamental significance of Euler's results for modern cryptologic science. The most important results, which seemed during his lifetime to be a game of numbers, have provided the mathematical basis for asymmetric cryptography two hundred years after Euler's death.

Another set of no less spectacular examples that can be discussed in the classroom are the biographies of the great German mathematician Carl Gauss and the brilliant French mathematician Evariste Galois, both far ahead of their time in the creation of group theory and the theory of finite fields.

THE TRANSITION PHASE FROM CLASSICAL TO MODERN SCIENCE

From our point of view, the main educational goal of studying the transition phase from classical to modern science is to become familiar with the concepts that became the basis of "new" cryptography at that time. Scientific and technological progress leads to changes in presentation and communication of information, and formation of the most important concepts such as data (as information provided in a computer form), coding (as a system of rules of information transfer in the data), etc. This is due, primarily, to the development of the telegraph, telephone, and electromechanical devices of information transforming. Thus, during the classes on the history of cryptography it is necessary to identify and explain to the students the following basic ideas related to this period:  There was a fundamental change in media, the ways of presenting, processing, and transmitting information such as electrical signals and electromechanical machines, replace paper and pencil in this period;  The perfectly secret cipher was invented in 1917 (by Vernam of the AT&T company), but its perfect secrecy was justified intuitivelythat property was not strictly proven for the cipher;  Construction principles for the ciphers used in practice evolved nearly to modern principles; codes' design became a complex network of substitutions and permutations, but they were realized by means of the mechanical and electromagnetic devices available at that time; and  Both block and stream ciphers were widely applied in practice.

From our point of view, it is appropriate for the classes to include some materials primarily related to the invention of the one-time cipher pad and the rotor cipher machines.

It is well known that Gilbert Sandford Vernam invented the automated one-time pad (perfectly secret cipher) in 1917. Studying the one-time pad is usually included in the curriculum of the standard cryptologic educational courses. Therefore, to avoid repetition it should be used as a basis to draw parallels with more recent inventions in the field of cryptography as well as to show a specific example of how new discoveries appear as a result of generalization of known results and, in turn, how former discoveries become the special cases of new discoveries. The one-time pad is very useful for that purpose as the inventor of the cipher assumed that it is unbreakable without proving that fact.

The mathematical formulation of the problem of IP, and derivation of the ideal conditions under which its solution is possible, was developed by C.Shannon (1949) [START_REF] Shannon | Communication theory of secrecy systems[END_REF]. Shannon's theory implies that the Vernam cipher is a special case that provides information-theoretic but not practical security. Thus, more than 30 years passed between an invention with an intuitively reasonable argument, and the rigorous proof of that argument.

However, this date does not mark the end of the history associated with the invention of the one-time pad. At the beginning of the 1980s G.R.Blakley has shown [START_REF] Blakley | Key management from a security viewpoint[END_REF] that the Vernam cipher is just a special case of the so-called shadow ciphers.

In addition, with the discovery of the threshold cryptography principle by A.Shamir [START_REF] Shamir | How to share a secret[END_REF], it became possible to assert that the Vernam cipher is a special case of the threshold secret sharing schemes, namely a 2.2 Asmuth-Bloom threshold secret sharing scheme. The study of this example helps the students understand better the typical path of development of scientific knowledge from the particular to the general.

The history of the creation and cryptanalysis of perhaps the most famous families of the rotor cipher machines can be used during the classes to illustrate the period. The lecture should note that the rotor cipher machines are already the direct prototypes of the modern block and stream ciphers, implementing the same principles: layered substitution and permutation transforms for the block ciphers and pseudorandom generator for the stream ciphers. The German Enigma machines, the American Hagelin machines (M-209, C-52 etc.) and the Russian Fialka M-125 machines implemented block ciphers. The German Lorenz SZ 40 and SZ 42 machines implemented the stream ciphers.

It is appropriate to discuss a mathematical description of a rather complex transformation implemented by the rotor cipher machines, and a mathematical formulation of the inverse cryptanalytic problem of finding a transformation key. The teacher can ask the students to conduct their own assessment of the algorithm's complexity. Doing so will allow them to get a clear idea of how much more difficult the problem is while comparing it with cryptanalysis of the pre-scientific ciphers, and why the creation of the first computers by the group under Alan Turing supervision was required to solve it.

The software models of some rotor cipher machines presented on the Internet (for example, a good simulator of Hagelin's M-209 machine [15]) can be used here for illustrative purposes.

Finally, to complete the study of the period it is necessary to characterize Shannon's works and above all his famous "Communication Theory of Secrecy Systems" [START_REF] Shannon | Communication theory of secrecy systems[END_REF] as well as the works of his followers. It should be emphasized that the essential impact of this Shannon's work is that he formulated the idea of information-theoretic secrecy.

The IS concept as a philosophical concept was formulated in the same period. N.J. Danilevsky (1822Danilevsky ( -1885) ) was the first Russian scientists to address the problem [START_REF] Danilevsky | Russia and Europe[END_REF]. Our colleagues developed it further in [START_REF] Malyuk | Information Security Theory Development[END_REF].

STUDYING MODERN CRYPTOGRAPHY

While studying the history of modern cryptography it should be stressed that the subject of cryptography expanded and became one of the computer sciences, along with the other sciences like the theory of algorithms, programming, the computational complexity theory, etc. The history of its development becomes a part of the IT history. Various computer equipment, information, and telecommunications systems provide the technical basis for the implementation of all basic IP methods and tools. The largest manufacturers of IT products, leading universities, and research centers became the driving force behind the development of ISS.

In addition to paper, new media in the form of a global, distributed, electronic environment for information processing appeared. New "computer" cryptography with its two main branches (symmetric and asymmetric) becomes the basis of most, if not all IP methods.

Modern cryptography almost entirely focuses on the computer processing of information and the development of appropriate algorithmic and technical methods. Works devoted to new methods of securing information using paper as well as encryption algorithms that can be executed manually are few in number.

It should be taken into account that the study of many important discoveries of the second half of the XX century is usually included in standard courses on cryptography. To avoid repetition, we recommend the teacher focus on the personalities and companies that greatly contributed to the development of IS science and practice. In this case, a good example is the history of the highest award in the field of Computer Science and ITthe Turing Award, often called the "Nobel Prize of computing". Five outstanding scientists in the field of mathematical foundations of cryptography, formal and logical methods of IS and related fields have been rewarded over the past 20 years [START_REF]Turind Award[END_REF]: Manuel Blum, Andrew Yao, Ronald Rivest, Silvio Micali and Shafi Goldwasser, and Leslie Lamport. They are well known to those skilled in IS. These facts indicate that IS is recognized by the community of scientists as an extremely important area of modern computer science.

During the classes we also recommend giving the students an idea of the work of the cryptographic community, which fundamentally changed in the second half of the XX century. Cryptography is no longer a "secret" science. The perception is that the chance of finding a solution that is stable, free from faults and weaknesses is much higher when an open and comprehensive discussion of new cryptosystems occurs by the whole scientific community. In recent decades, this kind of activity mainly goes through a process of international (and national) standardization.

As an example of the results brought by standardization and its problems, the teacher can mention the development and adoption of the first USA encryption standard DES (1979), the first Russian encryption standard GOST 28147-89 (1989) [START_REF]Russian state encryption standard[END_REF], the new USA encryption standard AES (2001), other USA cryptography standards such as FIPS 140, SHA, DSA, the widely-used international cryptography standard ISO/IEC 18033 (2006-2010), new Russian standards GOST 34.10-2012 (elliptic curve digital signature) [START_REF]Russian state digital[END_REF] and GOST R 34.11-2012 (hash function Streebog) [19], etc.

Another aspect of the history of cryptography is the historiography of cryptography and cryptanalysis. During the second half of the XX century, a number of fundamental works on the history of cryptography from ancient times to the present days appeared. Of course, the greatest impact on the public has been Kahn's book "The Codebreakers: The Story of Secret Writing" [START_REF] Kahn | The codebreakers: The story of secret writing[END_REF]. It initiated a number of other works and in general significantly increased interest in the history of cryptography and cryptanalysis. Many researchers around the world began to study their national traditions and achievements of their countries in the field of cryptography in different epochs.

RELATED WORKS

Of course, we are not the only ones to include historical aspects of ISS in the students' syllabus. The history of ISS and in particular the history of cryptography is not often highlighted as a separate academic discipline (course), but some sections of "Cryptography" or "Network Security" disciplines, dedicated to the history of cryptography, are taught in several Russian and foreign universities. In particular, a section on the history of cryptography is included in the online "Cryptography I" course by Dan Boneh at the "Coursera" portal [START_REF] Boneh | Cryptography" online course[END_REF]. Some other universities worldwide have specific courses on the history of cryptography [21-23], including Russian universities [24].

CONCLUSION

Summarizing the results of introducing the history of cryptography into the syllabus for the students' training on IS direction, we conclude with the following. 1. Studying the history of cryptography serves one of the essential aspects of forming the professional expertise for students preparing to become an IS specialist or the Masters in Business Continuity and Information Security Maintenance.

2. Studying the history of cryptography allows the students to deeply understand why ISS has developed the way it has. The theory cannot explain everything; some issues are due to traditions. And this leads to a deeper understanding of the subject.

3. Knowing the history allows to understand the current trends and predict the future.

Most of our findings are original; they are based on our own investigations of the history of cryptography. We are going to continue this research in order to create a tutorial, which will reflect adequately all periods of cryptologic science, with particular attention to the development of this branch of knowledge in Russia. Any historical research is always laborious and requires a long time, but we hope to report the results of our new research in this area at the next WISE10 conference.

Fig. 1 .

 1 Fig. 1. Scheme's example used during the introductory lecture to the "Cryptographic Protocols and Standards" discipline, showing cryptography's history periodization