Skip to main content

Applied mathematics: CryptologyLaajuus (3 cr)

Code: TZLM7020

Credits

3 op

Teaching language

  • Finnish
  • English

Responsible person

  • Sirpa Alestalo

Objective

Course purpose
Cryptology is an alternative to the applied mathematics course in information and communication technology. In this course, you will focus your knowledge on the mathematics needed in information security and especially encryption methods.

Course competences
EUR-ACE Knowledge and understanding
• knowledge and understanding of mathematics needed in information and communication technology
• knowledge and understanding of engineering fundamentals underlying the specialisation, at a level necessary to achieve the other programme outcomes, including some awareness at their forefront
EUR-ACE Engineering Practice
• understanding of applicable techniques and methods of analysis, design and investigation and of their limitations in their field of study

Learning outcomes
You know and understand the mathematical principles of the most common encryption methods. You can solve simple linear congruences. You know how to choose the encryption method that suits the situation and you have the skills to deepen your knowledge independently.

Content

Properties of functions (surjection, injection, bijection), number theory (divisibility, prime numbers, congruence, modular arithmetic), random number generation, classical encryption methods, symmetric and asymmetric encryption, elliptic curves

Qualifications

You know the basics of set theory and combinatorics, you understand the concept of divisibility and congruence.

Assessment criteria, approved/failed

You know and understand the key mathematical concepts and calculation rules related to cryptology. You can solve simple linear congruences. You understand the mathematical principles of encryption methods and know the purposes of different encryption methods. After the course, you will be able to study more about the subject on your own.

Enrollment

01.04.2025 - 30.04.2025

Timing

12.05.2025 - 15.08.2025

Number of ECTS credits allocated

3 op

Virtual portion

3 op

Mode of delivery

Online learning

Unit

School of Technology

Campus

Lutakko Campus

Teaching languages
  • Finnish
Seats

0 - 35

Degree programmes
  • Bachelor's Degree Programme in Information and Communications Technology
Teachers
  • Sirpa Alestalo
Groups
  • TTV23S2
    Tieto- ja viestintätekniikka (AMK)
  • TTV23S3
    Tieto- ja viestintätekniikka (AMK)
  • TTV23S5
    Tieto- ja viestintätekniikka (AMK)
  • TTV23SM
    Tieto- ja viestintätekniikka (AMK)
  • TTV23S1
    Tieto- ja viestintätekniikka (AMK)

Objectives

Course purpose
Cryptology is an alternative to the applied mathematics course in information and communication technology. In this course, you will focus your knowledge on the mathematics needed in information security and especially encryption methods.

Course competences
EUR-ACE Knowledge and understanding
• knowledge and understanding of mathematics needed in information and communication technology
• knowledge and understanding of engineering fundamentals underlying the specialisation, at a level necessary to achieve the other programme outcomes, including some awareness at their forefront
EUR-ACE Engineering Practice
• understanding of applicable techniques and methods of analysis, design and investigation and of their limitations in their field of study

Learning outcomes
You know and understand the mathematical principles of the most common encryption methods. You can solve simple linear congruences. You know how to choose the encryption method that suits the situation and you have the skills to deepen your knowledge independently.

Content

Properties of functions (surjection, injection, bijection), number theory (divisibility, prime numbers, congruence, modular arithmetic), random number generation, classical encryption methods, symmetric and asymmetric encryption, elliptic curves

Time and location

Opintojakso toteututetaan viikoilla 20 - 33 (12.5.-15.8.2025) verkossa.

Learning materials and recommended literature

Opettajan oppimisympäristössä jakama kirjallinen materiaali ja videomateriaali.

Teaching methods

Virtuaaliopetus, itsenäisesti, omaan tahtiin opiskeltava toteutus.
Ei lukujärjestykseen merkittyjä tunteja, ohjausta saa opintojakson Teams-kanavalla viikoittaisissa ohjaustapaamisissa touko-kesäkuussa sekä elokuussa.
Palautettavat laskuharjoitukset.
Viikkotestit oppimisympäristössä.

Itsenäistä opiskelua varten on olemassa luentovideot

Exam dates and retake possibilities

Julkaistaan opintojakson alussa oppimisympäristössä.

Alternative completion methods

Hyväksilukemisen menettelytavat kuvataan tutkintosäännössä ja opinto-oppaassa. Opintojakson opettaja antaa lisätietoa mahdollisista opintojakson erityiskäytänteistä.

Student workload

Itsenäinen opiskelu ja tenttiin valmistautuminen 49 h
Palautettavat laskuharjoitukset 2 x 9 h = 18 h
Viikkotestit 5 x 1 h = 5 h
Tentti 3 h

Kuormitus on tasainen koko opintojakson ajan, yhteensä 81 h.

Further information for students

Opintojakso arvioidaan tentin, palautettavien laskuharjoitusten ja viikkotestien avulla. Suoritteet pisteytetään. Hyväksyttyyn suoritukseen vaaditaan vähintään puolet koko opintojakson maksimipistemäärästä ja vähintään kolmasosa kokeen maksimipistemäärästä.

Opintojakson koe järjestetään kahteen kertaan, kesäkuussa ja elokuussa. Opiskelija voi valita, kumpaan osallistuu.

Evaluation scale

Pass/Fail

Evaluation criteria, pass/failed

You know and understand the key mathematical concepts and calculation rules related to cryptology. You can solve simple linear congruences. You understand the mathematical principles of encryption methods and know the purposes of different encryption methods. After the course, you will be able to study more about the subject on your own.

Prerequisites

You know the basics of set theory and combinatorics, you understand the concept of divisibility and congruence.

Enrollment

01.08.2024 - 22.08.2024

Timing

21.10.2024 - 18.12.2024

Number of ECTS credits allocated

3 op

Virtual portion

1 op

Mode of delivery

67 % Face-to-face, 33 % Online learning

Unit

School of Technology

Campus

Lutakko Campus

Teaching languages
  • Finnish
Seats

0 - 35

Degree programmes
  • Bachelor's Degree Programme in Information and Communications Technology
Teachers
  • Sirpa Alestalo
Groups
  • TTV23S2
    Tieto- ja viestintätekniikka (AMK)
  • TTV23S3
    Tieto- ja viestintätekniikka (AMK)
  • TTV23S5
    Tieto- ja viestintätekniikka (AMK)
  • TTV23SM
    Tieto- ja viestintätekniikka (AMK)
  • TTV23S1
    Tieto- ja viestintätekniikka (AMK)

Objectives

Course purpose
Cryptology is an alternative to the applied mathematics course in information and communication technology. In this course, you will focus your knowledge on the mathematics needed in information security and especially encryption methods.

Course competences
EUR-ACE Knowledge and understanding
• knowledge and understanding of mathematics needed in information and communication technology
• knowledge and understanding of engineering fundamentals underlying the specialisation, at a level necessary to achieve the other programme outcomes, including some awareness at their forefront
EUR-ACE Engineering Practice
• understanding of applicable techniques and methods of analysis, design and investigation and of their limitations in their field of study

Learning outcomes
You know and understand the mathematical principles of the most common encryption methods. You can solve simple linear congruences. You know how to choose the encryption method that suits the situation and you have the skills to deepen your knowledge independently.

Content

Properties of functions (surjection, injection, bijection), number theory (divisibility, prime numbers, congruence, modular arithmetic), random number generation, classical encryption methods, symmetric and asymmetric encryption, elliptic curves

Time and location

Lessons are between 21.10.2024 and 18.12.2024 in Dynamo, at the Lutakko campus.

Learning materials and recommended literature

Opettajan oppimisympäristössä jakama kirjallinen materiaali ja videomateriaali.

Teaching methods

Contact teaching 2+2 hours per week, including lectures and problem-solving sessions.
Assigned problem sets for submission.
Weekly tests in the learning environment.

Lecture videos available for independent study.

Exam dates and retake possibilities

Julkaistaan opintojakson alussa oppimisympäristössä.

Alternative completion methods

Hyväksilukemisen menettelytavat kuvataan tutkintosäännössä ja opinto-oppaassa. Opintojakson opettaja antaa lisätietoa mahdollisista opintojakson erityiskäytänteistä.

Student workload

Luennot + laskuharjoitukset 24 h
Palautettavat laskuharjoitukset 2 x 9 h = 18 h
Viikkotestit 5 x 1 h = 5 h
Itsenäinen opiskelu ja tenttiin valmistautuminen 25 h
Tentti 3 h

Kuormitus on tasainen koko opintojakson ajan, yhteensä 81 h.

Further information for students

Opintojakso arvioidaan tentin, palautettavien laskuharjoitusten ja viikkotestien avulla. Suoritteet pisteytetään. Hyväksyttyyn suoritukseen vaaditaan vähintään puolet koko opintojakson maksimipistemäärästä ja vähintään kolmasosa kokeen maksimipistemäärästä.

Opintojakson kontakteilla on 80 % läsnäolovelvoite.

Evaluation scale

Pass/Fail

Evaluation criteria, pass/failed

You know and understand the key mathematical concepts and calculation rules related to cryptology. You can solve simple linear congruences. You understand the mathematical principles of encryption methods and know the purposes of different encryption methods. After the course, you will be able to study more about the subject on your own.

Prerequisites

You know the basics of set theory and combinatorics, you understand the concept of divisibility and congruence.

Enrollment

01.08.2024 - 22.08.2024

Timing

21.10.2024 - 18.12.2024

Number of ECTS credits allocated

3 op

Virtual portion

1 op

Mode of delivery

67 % Face-to-face, 33 % Online learning

Unit

School of Technology

Campus

Lutakko Campus

Teaching languages
  • English
Seats

0 - 35

Degree programmes
  • Bachelor's Degree Programme in Information and Communications Technology
Teachers
  • Sirpa Alestalo
Groups
  • TIC23S1
    Bachelor's Degree Programme in Information and Communications Technology

Objectives

Course purpose
Cryptology is an alternative to the applied mathematics course in information and communication technology. In this course, you will focus your knowledge on the mathematics needed in information security and especially encryption methods.

Course competences
EUR-ACE Knowledge and understanding
• knowledge and understanding of mathematics needed in information and communication technology
• knowledge and understanding of engineering fundamentals underlying the specialisation, at a level necessary to achieve the other programme outcomes, including some awareness at their forefront
EUR-ACE Engineering Practice
• understanding of applicable techniques and methods of analysis, design and investigation and of their limitations in their field of study

Learning outcomes
You know and understand the mathematical principles of the most common encryption methods. You can solve simple linear congruences. You know how to choose the encryption method that suits the situation and you have the skills to deepen your knowledge independently.

Content

Properties of functions (surjection, injection, bijection), number theory (divisibility, prime numbers, congruence, modular arithmetic), random number generation, classical encryption methods, symmetric and asymmetric encryption, elliptic curves

Time and location

Lessons are between 21.10.2024 and 18.12.2024 in Dynamo, at the Lutakko campus.

Learning materials and recommended literature

Course material consists of written material and video material available in the e-learning environment (Moodle).

Teaching methods

Contact teaching 3+2 h/week, with lecture and exercises.
Returnable exercises.
Weekly tests in a learning environment.

Exam dates and retake possibilities

The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.

Student workload

Lectures and exercises 30 h
Returnable exercises 18 h
Weekly tests 5 h
Independent study and exam 25 h

The overall workload is 81 h.

Further information for students

The course is evaluated using an exam, returnable exercises and weekly tests
Pass requirements are
-at least 50 % of the maximum course scores
-at least one third of the maximum exam scores

Evaluation scale

Pass/Fail

Evaluation criteria, pass/failed

You know and understand the key mathematical concepts and calculation rules related to cryptology. You can solve simple linear congruences. You understand the mathematical principles of encryption methods and know the purposes of different encryption methods. After the course, you will be able to study more about the subject on your own.

Prerequisites

You know the basics of set theory and combinatorics, you understand the concept of divisibility and congruence.

Enrollment

01.08.2024 - 22.08.2024

Timing

26.08.2024 - 18.12.2024

Number of ECTS credits allocated

3 op

Virtual portion

2.5 op

Mode of delivery

17 % Face-to-face, 83 % Online learning

Unit

School of Technology

Teaching languages
  • Finnish
Seats

0 - 35

Degree programmes
  • Bachelor's Degree Programme in Information and Communications Technology
Teachers
  • Sirpa Alestalo
Groups
  • TTV23S2
    Tieto- ja viestintätekniikka (AMK)
  • TTV23S3
    Tieto- ja viestintätekniikka (AMK)
  • TTV23S5
    Tieto- ja viestintätekniikka (AMK)
  • TTV23SM
    Tieto- ja viestintätekniikka (AMK)
  • TTV23S1
    Tieto- ja viestintätekniikka (AMK)

Objectives

Course purpose
Cryptology is an alternative to the applied mathematics course in information and communication technology. In this course, you will focus your knowledge on the mathematics needed in information security and especially encryption methods.

Course competences
EUR-ACE Knowledge and understanding
• knowledge and understanding of mathematics needed in information and communication technology
• knowledge and understanding of engineering fundamentals underlying the specialisation, at a level necessary to achieve the other programme outcomes, including some awareness at their forefront
EUR-ACE Engineering Practice
• understanding of applicable techniques and methods of analysis, design and investigation and of their limitations in their field of study

Learning outcomes
You know and understand the mathematical principles of the most common encryption methods. You can solve simple linear congruences. You know how to choose the encryption method that suits the situation and you have the skills to deepen your knowledge independently.

Content

Properties of functions (surjection, injection, bijection), number theory (divisibility, prime numbers, congruence, modular arithmetic), random number generation, classical encryption methods, symmetric and asymmetric encryption, elliptic curves

Time and location

Opintojakso toteututetaan viikoilla 35 - 50 (26.8.-18.12.2024) verkossa.

Learning materials and recommended literature

Opettajan oppimisympäristössä jakama kirjallinen materiaali ja videomateriaali.

Teaching methods

Virtuaaliopetus, itsenäisesti, omaan tahtiin opiskeltava toteutus.
Ei lukujärjestykseen merkittyjä tunteja, ohjausta saa opintojakson Teams-kanavalla viikoittaisissa ohjaustapaamisissa.
Palautettavat laskuharjoitukset.
Viikkotestit oppimisympäristössä.

Itsenäistä opiskelua varten on olemassa luentovideot

Exam dates and retake possibilities

Julkaistaan opintojakson alussa oppimisympäristössä.

Alternative completion methods

Hyväksilukemisen menettelytavat kuvataan tutkintosäännössä ja opinto-oppaassa. Opintojakson opettaja antaa lisätietoa mahdollisista opintojakson erityiskäytänteistä.

Student workload

Itsenäinen opiskelu ja tenttiin valmistautuminen 49 h
Palautettavat laskuharjoitukset 2 x 9 h = 18 h
Viikkotestit 5 x 1 h = 5 h
Tentti 3 h

Kuormitus on tasainen koko opintojakson ajan, yhteensä 81 h.

Further information for students

Opintojakso arvioidaan tentin, palautettavien laskuharjoitusten ja viikkotestien avulla. Suoritteet pisteytetään. Hyväksyttyyn suoritukseen vaaditaan vähintään puolet koko opintojakson maksimipistemäärästä ja vähintään kolmasosa kokeen maksimipistemäärästä.

Opintojakson koe järjestetään syksyn aikana kahteen kertaan, lokakuussa ja joulukuussa. Opiskelija voi valita, kumpaan osallistuu.

Opintojakso on tarkoitettu monimuoto-opiskelijoille sekä 3. - 4. vuoden opiskeijoille.

Evaluation scale

Pass/Fail

Evaluation criteria, pass/failed

You know and understand the key mathematical concepts and calculation rules related to cryptology. You can solve simple linear congruences. You understand the mathematical principles of encryption methods and know the purposes of different encryption methods. After the course, you will be able to study more about the subject on your own.

Prerequisites

You know the basics of set theory and combinatorics, you understand the concept of divisibility and congruence.

Enrollment

20.11.2023 - 04.01.2024

Timing

04.03.2024 - 30.04.2024

Number of ECTS credits allocated

3 op

Virtual portion

1 op

Mode of delivery

67 % Face-to-face, 33 % Online learning

Unit

School of Technology

Campus

Lutakko Campus

Teaching languages
  • English
Seats

20 - 35

Degree programmes
  • Bachelor's Degree Programme in Information and Communications Technology
Teachers
  • Sirpa Alestalo
Groups
  • TTV22S5
    Tieto- ja viestintätekniikka (AMK)
  • TTV22S2
    Tieto- ja viestintätekniikka (AMK)
  • TTV22S3
    Tieto- ja viestintätekniikka (AMK)
  • TIC22S1
    Bachelor's Degree Programme in Information and Communications Technology
  • TTV22S1
    Tieto- ja viestintätekniikka (AMK)
  • TTV22S4
    Tieto- ja viestintätekniikka (AMK)

Objectives

Course purpose
Cryptology is an alternative to the applied mathematics course in information and communication technology. In this course, you will focus your knowledge on the mathematics needed in information security and especially encryption methods.

Course competences
EUR-ACE Knowledge and understanding
• knowledge and understanding of mathematics needed in information and communication technology
• knowledge and understanding of engineering fundamentals underlying the specialisation, at a level necessary to achieve the other programme outcomes, including some awareness at their forefront
EUR-ACE Engineering Practice
• understanding of applicable techniques and methods of analysis, design and investigation and of their limitations in their field of study

Learning outcomes
You know and understand the mathematical principles of the most common encryption methods. You can solve simple linear congruences. You know how to choose the encryption method that suits the situation and you have the skills to deepen your knowledge independently.

Content

Properties of functions (surjection, injection, bijection), number theory (divisibility, prime numbers, congruence, modular arithmetic), random number generation, classical encryption methods, symmetric and asymmetric encryption, elliptic curves

Time and location

The course is implemented between 11.3.2024 and 26.4.2024

Learning materials and recommended literature

Course material consists of written material and video material available in the e-learning environment (Moodle).

Teaching methods

Contact teaching 2+2 h/week, with lecture and exercises.
Returnable exercises.
Weekly tests in a learning environment.

Exam dates and retake possibilities

The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.

Student workload

Lectures and exercises 30 h
Returnable exercises 18 h
Weekly tests 5 h
Independent study and exam 28 h

Further information for students

The course is evaluated using an exam, returnable exercises and weekly tests
Pass requirements are
-at least 50 % of the maximum course scores
-at least one third of the maximum exam scores

Evaluation scale

Pass/Fail

Evaluation criteria, pass/failed

You know and understand the key mathematical concepts and calculation rules related to cryptology. You can solve simple linear congruences. You understand the mathematical principles of encryption methods and know the purposes of different encryption methods. After the course, you will be able to study more about the subject on your own.

Prerequisites

You know the basics of set theory and combinatorics, you understand the concept of divisibility and congruence.

Enrollment

20.11.2023 - 04.01.2024

Timing

08.01.2024 - 23.02.2024

Number of ECTS credits allocated

3 op

Virtual portion

1 op

Mode of delivery

67 % Face-to-face, 33 % Online learning

Unit

School of Technology

Campus

Lutakko Campus

Teaching languages
  • Finnish
Seats

20 - 35

Degree programmes
  • Bachelor's Degree Programme in Information and Communications Technology
Teachers
  • Sirpa Alestalo
Groups
  • TTV22S5
    Tieto- ja viestintätekniikka (AMK)
  • TTV22S2
    Tieto- ja viestintätekniikka (AMK)
  • TTV22S3
    Tieto- ja viestintätekniikka (AMK)
  • TTV22S1
    Tieto- ja viestintätekniikka (AMK)
  • TTV22S4
    Tieto- ja viestintätekniikka (AMK)

Objectives

Course purpose
Cryptology is an alternative to the applied mathematics course in information and communication technology. In this course, you will focus your knowledge on the mathematics needed in information security and especially encryption methods.

Course competences
EUR-ACE Knowledge and understanding
• knowledge and understanding of mathematics needed in information and communication technology
• knowledge and understanding of engineering fundamentals underlying the specialisation, at a level necessary to achieve the other programme outcomes, including some awareness at their forefront
EUR-ACE Engineering Practice
• understanding of applicable techniques and methods of analysis, design and investigation and of their limitations in their field of study

Learning outcomes
You know and understand the mathematical principles of the most common encryption methods. You can solve simple linear congruences. You know how to choose the encryption method that suits the situation and you have the skills to deepen your knowledge independently.

Content

Properties of functions (surjection, injection, bijection), number theory (divisibility, prime numbers, congruence, modular arithmetic), random number generation, classical encryption methods, symmetric and asymmetric encryption, elliptic curves

Time and location

Opintojakso toteututetaan viikoilla 2 -8 (8.1.-23.2.2024) Dynamolla, Lutakon kampuksella.

Learning materials and recommended literature

Opettajan oppimisympäristössä jakama kirjallinen materiaali ja videomateriaali.

Teaching methods

Kontaktiopetus 2+2 h/viikko, joissa luentoa ja laskuharjoituksia.
Palautettavat laskuharjoitukset.
Viikkotestit oppimisympäristössä.

Itsenäistä opiskelua varten on olemassa luentovideot

Exam dates and retake possibilities

Julkaistaan opintojakson alussa oppimisympäristössä.

Alternative completion methods

Hyväksilukemisen menettelytavat kuvataan tutkintosäännössä ja opinto-oppaassa. Opintojakson opettaja antaa lisätietoa mahdollisista opintojakson erityiskäytänteistä.

Student workload

Luennot + laskuharjoitukset 24 h
Palautettavat laskuharjoitukset 2 x 9 h = 18 h
Viikkotestit 5 x 1 h = 5 h
Itsenäinen opiskelu ja tenttiin valmistautuminen 25 h
Tentti 3 h

Kuormitus on tasainen koko opintojakson ajan, yhteensä 81 h.

Further information for students

Opintojakso arvioidaan tentin, palautettavien laskuharjoitusten ja viikkotestien avulla. Suoritteet pisteytetään. Hyväksyttyyn suoritukseen vaaditaan vähintään puolet koko opintojakson maksimipistemäärästä ja vähintään kolmasosa kokeen maksimipistemäärästä.

Evaluation scale

Pass/Fail

Evaluation criteria, pass/failed

You know and understand the key mathematical concepts and calculation rules related to cryptology. You can solve simple linear congruences. You understand the mathematical principles of encryption methods and know the purposes of different encryption methods. After the course, you will be able to study more about the subject on your own.

Prerequisites

You know the basics of set theory and combinatorics, you understand the concept of divisibility and congruence.

Enrollment

01.08.2023 - 24.08.2023

Timing

23.10.2023 - 19.12.2023

Number of ECTS credits allocated

3 op

Virtual portion

1 op

Mode of delivery

67 % Face-to-face, 33 % Online learning

Unit

School of Technology

Campus

Lutakko Campus

Teaching languages
  • Finnish
Seats

20 - 35

Degree programmes
  • Bachelor's Degree Programme in Information and Communications Technology
Teachers
  • Sirpa Alestalo
Groups
  • TTV22S5
    Tieto- ja viestintätekniikka (AMK)
  • TTV22S2
    Tieto- ja viestintätekniikka (AMK)
  • TTV22S3
    Tieto- ja viestintätekniikka (AMK)
  • TTV22S1
    Tieto- ja viestintätekniikka (AMK)
  • TTV22S4
    Tieto- ja viestintätekniikka (AMK)

Objectives

Course purpose
Cryptology is an alternative to the applied mathematics course in information and communication technology. In this course, you will focus your knowledge on the mathematics needed in information security and especially encryption methods.

Course competences
EUR-ACE Knowledge and understanding
• knowledge and understanding of mathematics needed in information and communication technology
• knowledge and understanding of engineering fundamentals underlying the specialisation, at a level necessary to achieve the other programme outcomes, including some awareness at their forefront
EUR-ACE Engineering Practice
• understanding of applicable techniques and methods of analysis, design and investigation and of their limitations in their field of study

Learning outcomes
You know and understand the mathematical principles of the most common encryption methods. You can solve simple linear congruences. You know how to choose the encryption method that suits the situation and you have the skills to deepen your knowledge independently.

Content

Properties of functions (surjection, injection, bijection), number theory (divisibility, prime numbers, congruence, modular arithmetic), random number generation, classical encryption methods, symmetric and asymmetric encryption, elliptic curves

Time and location

Opintojakso toteututetaan viikoilla 43 - 50 (23.10.-15.12.2023) Dynamolla, Lutakon kampuksella.

Learning materials and recommended literature

Opettajan oppimisympäristössä jakama kirjallinen materiaali ja videomateriaali.

Teaching methods

Kontaktiopetus 2+2 h/viikko, joissa luentoa ja laskuharjoituksia.
Palautettavat laskuharjoitukset.
Viikkotestit oppimisympäristössä.

Itsenäistä opiskelua varten on olemassa luentovideot

Exam dates and retake possibilities

Julkaistaan opintojakson alussa oppimisympäristössä.

Alternative completion methods

Hyväksilukemisen menettelytavat kuvataan tutkintosäännössä ja opinto-oppaassa. Opintojakson opettaja antaa lisätietoa mahdollisista opintojakson erityiskäytänteistä.

Student workload

Luennot + laskuharjoitukset 24 h
Palautettavat laskuharjoitukset 2 x 9 h = 18 h
Viikkotestit 5 x 1 h = 5 h
Itsenäinen opiskelu ja tenttiin valmistautuminen 25 h
Tentti 3 h

Kuormitus on tasainen koko opintojakson ajan, yhteensä 81 h.

Further information for students

Opintojakso arvioidaan tentin, palautettavien laskuharjoitusten ja viikkotestien avulla. Suoritteet pisteytetään. Hyväksyttyyn suoritukseen vaaditaan vähintään puolet koko opintojakson maksimipistemäärästä ja vähintään kolmasosa kokeen maksimipistemäärästä.

Evaluation scale

Pass/Fail

Evaluation criteria, pass/failed

You know and understand the key mathematical concepts and calculation rules related to cryptology. You can solve simple linear congruences. You understand the mathematical principles of encryption methods and know the purposes of different encryption methods. After the course, you will be able to study more about the subject on your own.

Prerequisites

You know the basics of set theory and combinatorics, you understand the concept of divisibility and congruence.

Enrollment

01.08.2023 - 24.08.2023

Timing

28.08.2023 - 19.12.2023

Number of ECTS credits allocated

3 op

Virtual portion

2.5 op

Mode of delivery

17 % Face-to-face, 83 % Online learning

Unit

School of Technology

Campus

Lutakko Campus

Teaching languages
  • Finnish
Seats

20 - 35

Degree programmes
  • Bachelor's Degree Programme in Information and Communications Technology
Teachers
  • Sirpa Alestalo
Groups
  • TTV22S5
    Tieto- ja viestintätekniikka (AMK)
  • TTV22S2
    Tieto- ja viestintätekniikka (AMK)
  • TTV22S3
    Tieto- ja viestintätekniikka (AMK)
  • TTV22S1
    Tieto- ja viestintätekniikka (AMK)
  • TTV22SM
    Tieto- ja viestintätekniikka (AMK)
  • TTV22S4
    Tieto- ja viestintätekniikka (AMK)

Objectives

Course purpose
Cryptology is an alternative to the applied mathematics course in information and communication technology. In this course, you will focus your knowledge on the mathematics needed in information security and especially encryption methods.

Course competences
EUR-ACE Knowledge and understanding
• knowledge and understanding of mathematics needed in information and communication technology
• knowledge and understanding of engineering fundamentals underlying the specialisation, at a level necessary to achieve the other programme outcomes, including some awareness at their forefront
EUR-ACE Engineering Practice
• understanding of applicable techniques and methods of analysis, design and investigation and of their limitations in their field of study

Learning outcomes
You know and understand the mathematical principles of the most common encryption methods. You can solve simple linear congruences. You know how to choose the encryption method that suits the situation and you have the skills to deepen your knowledge independently.

Content

Properties of functions (surjection, injection, bijection), number theory (divisibility, prime numbers, congruence, modular arithmetic), random number generation, classical encryption methods, symmetric and asymmetric encryption, elliptic curves

Time and location

Opintojakso toteututetaan viikoilla 35 - 50 (28.8.-15.12.2023) verkossa.

Learning materials and recommended literature

Opettajan oppimisympäristössä jakama kirjallinen materiaali ja videomateriaali.

Teaching methods

Virtuaaliopetus, itsenäisesti, omaan tahtiin opiskeltava toteutus.
Ei lukujärjestykseen merkittyjä tunteja, ohjausta saa opintojakson Teams-kanavalla.
Palautettavat laskuharjoitukset.
Viikkotestit oppimisympäristössä.

Itsenäistä opiskelua varten on olemassa luentovideot

Exam dates and retake possibilities

Julkaistaan opintojakson alussa oppimisympäristössä.

Alternative completion methods

Hyväksilukemisen menettelytavat kuvataan tutkintosäännössä ja opinto-oppaassa. Opintojakson opettaja antaa lisätietoa mahdollisista opintojakson erityiskäytänteistä.

Student workload

Itsenäinen opiskelu ja tenttiin valmistautuminen 49 h
Palautettavat laskuharjoitukset 2 x 9 h = 18 h
Viikkotestit 5 x 1 h = 5 h
Tentti 3 h

Kuormitus on tasainen koko opintojakson ajan, yhteensä 81 h.

Further information for students

Opintojakso arvioidaan tentin, palautettavien laskuharjoitusten ja viikkotestien avulla. Suoritteet pisteytetään. Hyväksyttyyn suoritukseen vaaditaan vähintään puolet koko opintojakson maksimipistemäärästä ja vähintään kolmasosa kokeen maksimipistemäärästä.

Opintojakson koe järjestetään syksyn aikana kahteen kertaan, lokakuussa ja joulukuussa. Opiskelija voi valita, kumpaan osallistuu.

Evaluation scale

Pass/Fail

Evaluation criteria, pass/failed

You know and understand the key mathematical concepts and calculation rules related to cryptology. You can solve simple linear congruences. You understand the mathematical principles of encryption methods and know the purposes of different encryption methods. After the course, you will be able to study more about the subject on your own.

Prerequisites

You know the basics of set theory and combinatorics, you understand the concept of divisibility and congruence.

Enrollment

01.11.2022 - 05.01.2023

Timing

06.03.2023 - 28.04.2023

Number of ECTS credits allocated

3 op

Virtual portion

1 op

Mode of delivery

67 % Face-to-face, 33 % Online learning

Unit

School of Technology

Campus

Lutakko Campus

Teaching languages
  • English
Seats

0 - 35

Degree programmes
  • Bachelor's Degree Programme in Information and Communications Technology
Teachers
  • Sirpa Alestalo
Groups
  • TIC21S1
    Bachelor's Degree Programme in Information and Communications Technology

Objectives

Course purpose
Cryptology is an alternative to the applied mathematics course in information and communication technology. In this course, you will focus your knowledge on the mathematics needed in information security and especially encryption methods.

Course competences
EUR-ACE Knowledge and understanding
• knowledge and understanding of mathematics needed in information and communication technology
• knowledge and understanding of engineering fundamentals underlying the specialisation, at a level necessary to achieve the other programme outcomes, including some awareness at their forefront
EUR-ACE Engineering Practice
• understanding of applicable techniques and methods of analysis, design and investigation and of their limitations in their field of study

Learning outcomes
You know and understand the mathematical principles of the most common encryption methods. You can solve simple linear congruences. You know how to choose the encryption method that suits the situation and you have the skills to deepen your knowledge independently.

Content

Properties of functions (surjection, injection, bijection), number theory (divisibility, prime numbers, congruence, modular arithmetic), random number generation, classical encryption methods, symmetric and asymmetric encryption, elliptic curves

Time and location

The course is implemented between 13.3.2023 and 28.4.2023

Learning materials and recommended literature

Course material consists of written material and video material available in the e-learning environment (Moodle).

Teaching methods

Contact teaching 2+2 h/week, with lecture and exercises.
Returnable exercises.
Weekly tests in a learning environment.
Voluntary practical work independently.
Video tutorials for independent study

Exam dates and retake possibilities

The timetable of the course is agreed on at the first meeting of the course and then published in the e-learning environment.

Student workload

Lectures and exercises 30 h
Returnable exercises 18 h
Weekly tests 5 h
Independent study and exam 25 h

Further information for students

The course is evaluated using an exam, returnable exercises, weekly tests and voluntary practice work.
Pass requirements are
-at least 50 % of the maximum course scores
-at least one third of the maximum exam scores

Evaluation scale

Pass/Fail

Evaluation criteria, pass/failed

You know and understand the key mathematical concepts and calculation rules related to cryptology. You can solve simple linear congruences. You understand the mathematical principles of encryption methods and know the purposes of different encryption methods. After the course, you will be able to study more about the subject on your own.

Prerequisites

You know the basics of set theory and combinatorics, you understand the concept of divisibility and congruence.

Enrollment

01.08.2022 - 25.08.2022

Timing

24.10.2022 - 16.12.2022

Number of ECTS credits allocated

3 op

Mode of delivery

Face-to-face

Unit

School of Technology

Campus

Lutakko Campus

Teaching languages
  • Finnish
Seats

0 - 35

Degree programmes
  • Bachelor's Degree Programme in Information and Communications Technology
Teachers
  • Sirpa Alestalo
Groups
  • TTV21S3
    Tieto- ja viestintätekniikka (AMK)
  • TTV21S5
    Tieto- ja viestintätekniikka (AMK)
  • TTV21SM
    Tieto- ja viestintätekniikka (AMK)
  • TTV21S2
    Tieto- ja viestintätekniikka (AMK)
  • TTV21S1
    Tieto- ja viestintätekniikka (AMK)

Objectives

Course purpose
Cryptology is an alternative to the applied mathematics course in information and communication technology. In this course, you will focus your knowledge on the mathematics needed in information security and especially encryption methods.

Course competences
EUR-ACE Knowledge and understanding
• knowledge and understanding of mathematics needed in information and communication technology
• knowledge and understanding of engineering fundamentals underlying the specialisation, at a level necessary to achieve the other programme outcomes, including some awareness at their forefront
EUR-ACE Engineering Practice
• understanding of applicable techniques and methods of analysis, design and investigation and of their limitations in their field of study

Learning outcomes
You know and understand the mathematical principles of the most common encryption methods. You can solve simple linear congruences. You know how to choose the encryption method that suits the situation and you have the skills to deepen your knowledge independently.

Content

Properties of functions (surjection, injection, bijection), number theory (divisibility, prime numbers, congruence, modular arithmetic), random number generation, classical encryption methods, symmetric and asymmetric encryption, elliptic curves

Time and location

Opintojakso toteututetaan viikoilla 43 - 50 (24.10.-16.12.2022) Dynamolla, Lutakon kampuksella.

Learning materials and recommended literature

Opettajan oppimisympäristössä jakama kirjallinen materiaali ja videomateriaali.

Teaching methods

Kontaktiopetus 2+2 h/viikko, joissa luentoa ja laskuharjoituksia.
Palautettavat laskuharjoitukset.
Viikkotestit oppimisympäristössä.
Vapaaehtoinen harjoitustyö itsenäisesti.
Itsenäistä opiskelua varten on olemassa luentovideot

Exam dates and retake possibilities

Julkaistaan opintojakson alussa oppimisympäristössä.

Alternative completion methods

Hyväksilukemisen menettelytavat kuvataan tutkintosäännössä ja opinto-oppaassa. Opintojakson opettaja antaa lisätietoa mahdollisista opintojakson erityiskäytänteistä.

Student workload

Luennot + laskuharjoitukset 24 h
Palautettavat laskuharjoitukset 2 x 9 h = 18 h
Viikkotestit 5 x 1 h = 5 h
Itsenäinen opiskelu ja tenttiin valmistautuminen 25 h
Tentti 3 h
Vapaaehtoinen harjoitustyö 0-12 h
Kuormitus on tasainen koko opintojakson ajan, yhteensä 81 h.

Further information for students

Opintojakso arvioidaan tentin, palautettavien laskuharjoitusten, viikkotestien ja mahdollisen harjoitustyön avulla. Suoritteet pisteytetään. Hyväksyttyyn suoritukseen vaaditaan vähintään puolet koko opintojakson maksimipistemäärästä ja vähintään kolmasosa kokeen maksimipistemäärästä.

Evaluation scale

Pass/Fail

Evaluation criteria, pass/failed

You know and understand the key mathematical concepts and calculation rules related to cryptology. You can solve simple linear congruences. You understand the mathematical principles of encryption methods and know the purposes of different encryption methods. After the course, you will be able to study more about the subject on your own.

Prerequisites

You know the basics of set theory and combinatorics, you understand the concept of divisibility and congruence.

Enrollment

01.08.2022 - 25.08.2022

Timing

29.08.2022 - 16.12.2022

Number of ECTS credits allocated

3 op

Virtual portion

3 op

Mode of delivery

Online learning

Unit

School of Technology

Teaching languages
  • Finnish
Seats

0 - 70

Degree programmes
  • Bachelor's Degree Programme in Information and Communications Technology
Teachers
  • Sirpa Alestalo
Groups
  • TTV21S3
    Tieto- ja viestintätekniikka (AMK)
  • TTV21S5
    Tieto- ja viestintätekniikka (AMK)
  • TTV21SM
    Tieto- ja viestintätekniikka (AMK)
  • TTV21S2
    Tieto- ja viestintätekniikka (AMK)
  • TTV21S1
    Tieto- ja viestintätekniikka (AMK)

Objectives

Course purpose
Cryptology is an alternative to the applied mathematics course in information and communication technology. In this course, you will focus your knowledge on the mathematics needed in information security and especially encryption methods.

Course competences
EUR-ACE Knowledge and understanding
• knowledge and understanding of mathematics needed in information and communication technology
• knowledge and understanding of engineering fundamentals underlying the specialisation, at a level necessary to achieve the other programme outcomes, including some awareness at their forefront
EUR-ACE Engineering Practice
• understanding of applicable techniques and methods of analysis, design and investigation and of their limitations in their field of study

Learning outcomes
You know and understand the mathematical principles of the most common encryption methods. You can solve simple linear congruences. You know how to choose the encryption method that suits the situation and you have the skills to deepen your knowledge independently.

Content

Properties of functions (surjection, injection, bijection), number theory (divisibility, prime numbers, congruence, modular arithmetic), random number generation, classical encryption methods, symmetric and asymmetric encryption, elliptic curves

Time and location

Opintojakso toteututetaan viikoilla 35 - 50 (29.8.-16.12.2022) Dynamolla, Lutakon kampuksella.

Learning materials and recommended literature

Opettajan oppimisympäristössä jakama kirjallinen materiaali ja videomateriaali.

Teaching methods

Virtuaaliopetus, itsenäisesti, omaan tahtiin opiskeltava toteutus.
Ei lukujärjestykseen merkittyjä tunteja, ohjausta saa opintojakson Teams-kanavalla.
Palautettavat laskuharjoitukset.
Viikkotestit oppimisympäristössä.
Vapaaehtoinen harjoitustyö itsenäisesti.
Itsenäistä opiskelua varten on olemassa luentovideot

Exam dates and retake possibilities

Julkaistaan opintojakson alussa oppimisympäristössä.

Alternative completion methods

Hyväksilukemisen menettelytavat kuvataan tutkintosäännössä ja opinto-oppaassa. Opintojakson opettaja antaa lisätietoa mahdollisista opintojakson erityiskäytänteistä.

Student workload

Itsenäinen opiskelu ja tenttiin valmistautuminen 49 h
Palautettavat laskuharjoitukset 2 x 9 h = 18 h
Viikkotestit 5 x 1 h = 5 h
Tentti 3 h
Vapaaehtoinen harjoitustyö 0-12 h
Kuormitus on tasainen koko opintojakson ajan, yhteensä 81 h.

Further information for students

Opintojakso arvioidaan tentin, palautettavien laskuharjoitusten, viikkotestien ja mahdollisen harjoitustyön avulla. Suoritteet pisteytetään. Hyväksyttyyn suoritukseen vaaditaan vähintään puolet koko opintojakson maksimipistemäärästä ja vähintään kolmasosa kokeen maksimipistemäärästä.

Opintojakson koe järjestetään syksyn aikana kahteen kertaan, lokakuussa ja joulukuussa. Opiskelija voi valita, kumpaan osallistuu.

Evaluation scale

Pass/Fail

Evaluation criteria, pass/failed

You know and understand the key mathematical concepts and calculation rules related to cryptology. You can solve simple linear congruences. You understand the mathematical principles of encryption methods and know the purposes of different encryption methods. After the course, you will be able to study more about the subject on your own.

Prerequisites

You know the basics of set theory and combinatorics, you understand the concept of divisibility and congruence.

Enrollment

01.11.2021 - 09.01.2022

Timing

07.03.2022 - 29.04.2022

Number of ECTS credits allocated

3 op

Virtual portion

1 op

Mode of delivery

67 % Face-to-face, 33 % Online learning

Unit

School of Technology

Campus

Lutakko Campus

Teaching languages
  • Finnish
Seats

0 - 35

Degree programmes
  • Bachelor's Degree Programme in Information and Communications Technology
Teachers
  • Sirpa Alestalo
Groups
  • TTV20S5
    Tieto- ja viestintätekniikka
  • TTV20S3
    Tieto- ja viestintätekniikka
  • TTV20S2
    Tieto- ja viestintätekniikka
  • TTV20S1
    Tieto- ja viestintätekniikka

Objectives

Course purpose
Cryptology is an alternative to the applied mathematics course in information and communication technology. In this course, you will focus your knowledge on the mathematics needed in information security and especially encryption methods.

Course competences
EUR-ACE Knowledge and understanding
• knowledge and understanding of mathematics needed in information and communication technology
• knowledge and understanding of engineering fundamentals underlying the specialisation, at a level necessary to achieve the other programme outcomes, including some awareness at their forefront
EUR-ACE Engineering Practice
• understanding of applicable techniques and methods of analysis, design and investigation and of their limitations in their field of study

Learning outcomes
You know and understand the mathematical principles of the most common encryption methods. You can solve simple linear congruences. You know how to choose the encryption method that suits the situation and you have the skills to deepen your knowledge independently.

Content

Properties of functions (surjection, injection, bijection), number theory (divisibility, prime numbers, congruence, modular arithmetic), random number generation, classical encryption methods, symmetric and asymmetric encryption, elliptic curves

Time and location

Opintojakso toteututetaan viikoilla 11 - 17 (14.3.-29.4.2022) Dynamolla, Lutakon kampuksella tai etänä Zoomissa

Learning materials and recommended literature

Opettajan oppimisympäristössä jakama kirjallinen materiaali ja videomateriaali.

Teaching methods

Kontaktiopetus/etäopetus 3+2 h/viikko, joissa luentoa ja laskuharjoituksia.
Palautettavat laskuharjoitukset.
Viikkotestit oppimisympäristössä.
Vapaaehtoinen harjoitustyö itsenäisesti.
Itsenäistä opiskelua varten on olemassa luentovideot

Exam dates and retake possibilities

Julkaistaan opintojakson alussa oppimisympäristössä.

Alternative completion methods

Hyväksilukemisen menettelytavat kuvataan tutkintosäännössä ja opinto-oppaassa. Opintojakson opettaja antaa lisätietoa mahdollisista opintojakson erityiskäytänteistä.

Student workload

Luennot + laskuharjoitukset 30 h
Palautettavat laskuharjoitukset 2 x 9 h = 18 h
Viikkotestit 5 x 1 h = 5 h
Itsenäinen opiskelu ja tenttiin valmistautuminen 25 h
Tentti 3 h
Vapaaehtoinen harjoitustyö 12 h
Kuormitus on tasainen koko opintojakson ajan, yhteensä 81 h.

Further information for students

Opintojakso arvioidaan tentin, palautettavien laskuharjoitusten, viikkotestien ja mahdollisen harjoitustyön avulla. Suoritteet pisteytetään. Hyväksyttyyn suoritukseen vaaditaan vähintään puolet koko opintojakson maksimipistemäärästä ja vähintään kolmasosa kokeen maksimipistemäärästä.

Evaluation scale

Pass/Fail

Evaluation criteria, pass/failed

You know and understand the key mathematical concepts and calculation rules related to cryptology. You can solve simple linear congruences. You understand the mathematical principles of encryption methods and know the purposes of different encryption methods. After the course, you will be able to study more about the subject on your own.

Prerequisites

You know the basics of set theory and combinatorics, you understand the concept of divisibility and congruence.