The Mathematics of Cryptography: From Ancient Rome to a Quantum Future (FutureLearn)

Offered by University of York,
The Mathematics of Cryptography: From Ancient Rome to a Quantum Future (FutureLearn)

Explore the history of code breaking and cryptography to prepare for the future of communications and quantum computing.

Class Deals by MOOC List - Click here and see FutureLearn's Active Discounts, Deals, and Promo Codes.

Crack the code of cryptography with the University of York
The ability to use codes to send secret messages has been of critical importance to civilisations for thousands of years. Nowadays, the need for messages to remain hidden from anyone intercepting them underpins services we use every day: internet banking, online shopping, instant messaging, and more.
On this course from the University of York, you’ll travel back in time to discover the earliest codes and ciphers. With an emphasis on mathematical developments that have helped make and break some of the strongest codes in history, you’ll learn what makes cryptography vital to humans and society.

Trace the history of cryptography, from Roman times to the Second World War
You’ll start by tracing two millennia of codes and code cracking, from the first ciphers used by Roman emperors to Nazi communications decoded during the Second World War. In Week 2 of the course, you’ll explore in detail the maths which was used to break the legendary Enigma machine.
As you move through the chronology of cryptography, you’ll investigate key mathematical concepts, including modular arithmetic, permutations, and prime numbers.

Explore current and future developments in secure communication and quantum computing
In the last week of the course, you’ll flash forward to the present day of cryptography. You’ll learn about cutting-edge cryptographic techniques, and the mathematics of modern-day secure communications.
Finally, you’ll look to the future of encryption and cryptography. You’ll discuss how quantum computers could transform the way we communicate and share information.
By the end of the course, you’ll have a solid foundation in the mathematical theory underlying a variety of cryptographic techniques.

Syllabus

Week 1: From the Romans to the 1800s
Week 2: The Engima machine
Week 3: 21st century cryptography

What will you achieve?
By the end of the course, you‘ll be able to...

  • Summarise the history of cryptography, and the role played by mathematics in cracking some famous ciphers.
  • Assess how the concepts of frequency analysis and modular arithmetic can be applied to code-breaking.
  • Calculate with permutations and analyse their cycle structure.
  • Explain the importance of prime numbers and factorisation to the security of modern day communications

Who is the course for?
This course is designed for anyone interested in learning more about the history and future of code breaking, with an emphasis on mathematical concepts that have shaped cryptography.
It will particularly interest A-Level or undergraduate students who want to go beyond their syllabus and explore a cutting-edge field of mathematics and technology.

Go to Class
MOOC List is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

Related Courses

Matrix Methods (Coursera) Coursera
University of Minnesota

Matrix Methods (Coursera)

Mathematical Matrix Methods lie at the root of most methods of machine learning and data analysis of tabular data. Learn the basics of Matrix Methods, including matrix-matrix multiplication, solving linear equations, orthogonality, and best least squares approximation. Discover the Singular Value Decomposition that plays a fundamental role in dimensionality reduction, Principal Component Analysis, and noise reduction.

Aug 17th 2026
5-12 Weeks
Flexagons Galore: Advanced Flexagon Fun (FutureLearn) FutureLearn
Weizmann Institute of Science

Flexagons Galore: Advanced Flexagon Fun (FutureLearn)

Learn a systematic approach to making, flexing, and exploring a vast number of flexagons using paper as well as flexagon software. Challenge your maths skills through the magical art of paper folding. Flexagons are twisted strips of folded paper which reveal their properties when flexed. On this course, you’ll learn how to build flexagons ‘bottom-up’ and explore how this approach can significantly increase the number of flexagons that you’re able to build.

Self Paced
5-12 Weeks
Cybersecurity Fundamentals (edX) EdX
Rochester Institute of Technology,RITx

Cybersecurity Fundamentals (edX)

Learn cybersecurity fundamentals, including how to detect threats, protect systems and networks, and anticipate potential cyber attacks. In this introduction to the field of computing security, you will be given an extensive overview of the various branches of computing security. You will learn cybersecurity concepts, issues, and tools that are critical in solving problems in the computing security domain.

Aug 17th 2026
5-12 Weeks
Image and video processing: From Mars to Hollywood with a stop at the hospital (Coursera) Coursera
Duke University

Image and video processing: From Mars to Hollywood with a stop at the hospital (Coursera)

In this course, you will learn the science behind how digital images and video are made, altered, stored, and used. We will look at the vast world of digital imaging, from how computers and digital cameras form images to how digital special effects are used in Hollywood movies to how the Mars Rover was able to send photographs across millions of miles of space.

Aug 10th 2026
5-12 Weeks
Constructivism and Mathematics, Science, and Technology Education (Coursera) Coursera
University of Illinois at Urbana-Champaign

Constructivism and Mathematics, Science, and Technology Education (Coursera)

This course is designed to help participants examine the implications of constructivism for learning and teaching in science, mathematics, and technology focused areas. Course readings, discussions, and assignments will examine constructivist views of learning, research on students' ideas and idea-based interactions, research on instructional approaches taking student ideas into account, and challenges in implementing constructivist perspectives in instruction.

Aug 17th 2026
5-12 Weeks
A Beginner’s Guide to Becoming a Blockchain Developer with Overledger (FutureLearn) FutureLearn
King's College London,Quant

A Beginner’s Guide to Becoming a Blockchain Developer with Overledger (FutureLearn)

Discover the basics of blockchain and distributed ledger technologies to unlock exciting new career paths. Understand the main components of distributed ledgers and blockchains. With the rise of the digital economy, it’s no surprise that cryptocurrencies and blockchains are growing in popularity. This three-week course from King’s College London and Quant Network will empower you with an understanding of how blockchains and distributed ledgers work as well as their advantages over centralised ledgers.

Self Paced
3 Weeks
Numeracy Skills for Employability and the Workplace (FutureLearn) FutureLearn
Loughborough University

Numeracy Skills for Employability and the Workplace (FutureLearn)

Improve your mathematical confidence and gain the skills to pass employers’ numeracy tests with this free online course. In our highly technical world numeracy skills, particularly the ability to interpret data, are becoming increasingly important and are highly sought after by employers. A lack of mathematical confidence and poor numeracy skills are barriers to employment as numeracy tests are increasingly part of the recruitment process, often early on.

No sessions available
3 Weeks
Combinatorics: Strategies and Methods for Counting (FutureLearn) FutureLearn
University of Padova

Combinatorics: Strategies and Methods for Counting (FutureLearn)

Explore the wonderful world of combinatorics with this course exploring simple and efficient ways to count. See combinatorics made simple and how to avoid errors in counting principles. Combinatorics is an area of mathematics primarily concerned with counting. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry. On this free online combinatorics course, you’ll discover a simple and efficient method to translate a combinatorial problem into counting the elements of a reference mathematical structure.

Self Paced
4 Weeks
Precalculus: the Mathematics of Numbers, Functions and Equations (FutureLearn) FutureLearn
University of Padova

Precalculus: the Mathematics of Numbers, Functions and Equations (FutureLearn)

Get an introduction to the essential mathematical knowledge and skills required to take a first course in calculus. This course is the first of two precalculus courses from the University of Padova, providing you with an introduction to the fundamental mathematical skills required to complete a first course in calculus.

Self Paced
5-12 Weeks
An Introduction to Cryptography (FutureLearn) FutureLearn
Coventry University,Institute of Coding

An Introduction to Cryptography (FutureLearn)

Explore how code breakers and spies influenced cryptography and investigate the role it plays in modern secure communication. Investigate the security of encrypted data. Is it possible to prove the security of encrypted data? Will every algorithm fail given sufficient time or computing power? On this course you will get an introduction to cryptography and cryptanalysis. From ancient examples of secret messages and the spies that cracked them to modern cryptographic applications, you will have the opportunity to explore the foundations of data security.

Self Paced
2 Weeks