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

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.