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Mathematical Foundations for Cryptography
  • Level Foundation
  • Duration 15 hours
  • Course by University of Colorado System
  • Offered by

About

Welcome to Course 2 of Introduction to Applied Cryptography. In this course, you will be introduced to basic mathematical principles and functions that form the foundation for cryptographic and cryptanalysis methods. These principles and functions will be helpful in understanding symmetric and asymmetric cryptographic methods examined in Course 3 and Course 4. These topics should prove especially useful to you if you are new to cybersecurity. It is recommended that you have a basic knowledge of computer science and basic math skills such as algebra and probability.

Modules

Course Introduction

    • 1 Videos
    • 2 Readings
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1 Videos

  • Course Introduction

2 Readings

  • Course Introduction
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Lesson 16. Divisibility, Primes, GCD

    • 1 Videos
    • 3 Readings
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1 Videos

  • Divisibility, Primes, GCD

3 Readings

  • Lecture Slides - Divisibility, Primes, GCD
  • Video - Adam Spencer: Why I fell in love with monster prime numbers
  • L16: Additional Reference Material

Lesson 17. Modular Arithmetic

    • 1 Videos
    • 2 Readings
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1 Videos

  • Modular Arithmetic

2 Readings

  • Lecture Slides - Modular Arithmetic
  • L17: Additional Reference Material

Lesson 18. Multiplicative Inverses

    • 1 Videos
    • 2 Readings
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1 Videos

  • Multiplicative Inverses

2 Readings

  • Lecture Slides - Multiplicative Inverses
  • L18: Additional Reference Material

Lesson 19. Extended Euclidean Algorithm

    • 1 Videos
    • 2 Readings
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1 Videos

  • Extended Euclidean Algorithm

2 Readings

  • Lecture Slides - Extended Euclidean Algorithm
  • L19: Additional Reference Material

Module 1 Discussion

    • 1 Discussion
    • 1 Assignment
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1 Assignment

  • Practice Assessment - Integer Foundation

1 Discussions

  • What do you think?

Module Assessment

    • 1 Assignment
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1 Assignment

  • Graded Assessment - Integer Foundation

Lesson 20. Square-and-Multiply

    • 1 Videos
    • 3 Readings
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1 Videos

  • Square-and-Multiply

3 Readings

  • Lecture Slides - Square-and-Multiply
  • Video - Modular exponentiation made easy
  • L20: Additional Reference Material

Lesson 21. Euler's Totient Theorem

    • 1 Videos
    • 2 Readings
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1 Videos

  • Euler's Totient Theorem

2 Readings

  • Lecture Slide - Euler's Totient Theorem
  • L21: Additional Reference Material

Lesson 22. Euler's Totient Function

    • 1 Videos
    • 2 Readings
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1 Videos

  • Eulers Totient Function

2 Readings

  • Lecture Slide - Eulers Totient Function
  • L22: Additional Reference Material

Lesson 23. Discrete Logarithms

    • 1 Videos
    • 2 Readings
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1 Videos

  • Discrete Logarithms

2 Readings

  • Lecture Slide - Discrete Logarithms
  • L23: Additional Reference Material

Module 2 Discussion

    • 1 Discussion
    • 1 Assignment
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1 Assignment

  • Practice Assessment - Modular Exponentiation

1 Discussions

  • What do you think?

Module Assessment

    • 1 Assignment
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1 Assignment

  • Graded Assessment - Modular Exponentiation

Lesson 24. CRT Concepts, Integer-to-CRT Conversions

    • 1 Videos
    • 2 Readings
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1 Videos

  • CRT Concepts, Integer-to-CRT Conversions

2 Readings

  • Lecture Slide - CRT Concepts, Integer-to-CRT Conversions
  • L24: Additional Reference Material

Lesson 25. Moduli Restrictions, CRT-to-Integer Conversions

    • 1 Videos
    • 1 Readings
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1 Videos

  • Moduli Restrictions, CRT-to-Integer Conversions

1 Readings

  • Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions

Lesson 26. CRT Capabilities and Limitations

    • 1 Videos
    • 2 Readings
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1 Videos

  • CRT Capabilities and Limitations

2 Readings

  • Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions
  • Video - How they found the World's Biggest Prime Number - Numberphile

Module 3 Discussion

    • 1 Discussion
    • 1 Assignment
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1 Assignment

  • Practice Assessment - Chinese Remainder Theorem

1 Discussions

  • What do you think?

Module Assessment

    • 1 Assignment
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1 Assignment

  • Graded Assessment - Chinese Remainder Theorem

Lesson 27. Trial Division

    • 1 Videos
    • 2 Readings
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1 Videos

  • Trial Division

2 Readings

  • Lecture Slide - Trial Division
  • L27: Additional Reference Material

Lesson 28. Fermat's Theorem

    • 1 Videos
    • 2 Readings
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1 Videos

  • Fermat's Primality

2 Readings

  • Lecture Slide - Fermat's Primality
  • L28: Additional Reference Material

Lesson 29. Miller-Rabin

    • 1 Videos
    • 3 Readings
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1 Videos

  • Miller-Rabin

3 Readings

  • Lecture Slide - Miller-Rabin
  • Video - James Lyne: Cryptography and the power of randomness
  • L29: Additional Reference Material

Module 4 Discussion

    • 1 Discussion
    • 1 Assignment
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1 Assignment

  • Practice Assessment - Primality Testing

1 Discussions

  • What do you think?

Module Assessment

    • 1 Assignment
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1 Assignment

  • Graded Assessment - Primality Testing

Course Project

    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Course Project

1 Readings

  • The Science of Encryption

Auto Summary

Discover the Mathematical Foundations for Cryptography, a foundational IT & Computer Science course by Coursera. This course introduces key mathematical principles essential for understanding cryptographic methods. Ideal for cybersecurity beginners with basic algebra and probability skills, it spans 900 minutes and is available under Starter and Professional subscriptions.

William Bahn
Instructors

William Bahn

Richard White
Instructors

Richard White

Sang-Yoon Chang
Instructors

Sang-Yoon Chang