Maths and computer science · Solid · Dissertation or artefact

How RSA keeps payments secure: a maths EPQ idea

Why it works as an EPQ

The mathematics (modular arithmetic and primes) is learnable, small examples can be done by hand, and the security question needs a judgement.

Scope and difficulty

Solid. Solid. Work small examples fully; discuss real key sizes and quantum threats qualitatively.

The maths

Builds on these A Level topics: Proof · Algebra and functions.

You would learn:

• Modular arithmetic and inverses
• Fermat's little theorem and Euler's theorem
• Fast modular exponentiation

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Build RSA from the number theory, proving why decryption works.
2. Encrypt and decrypt small examples by hand and in code.
3. Time factorising numbers of growing size to show why security rests on it.
4. Evaluate the threats, including quantum computing, from reliable sources.

Pitfalls

• Explaining the steps without proving why they work.
• Overstating quantum threats.

Where to start reading

• The Code Book (Simon Singh)
• Cryptography: A Very Short Introduction (Fred Piper and Sean Murphy)

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

Making something? Read the artefact guide first: an artefact still needs a research-based written report.

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All maths and computer science ideas · all 93 ideas

Your EPQ must be your own work. These pages coach: ideas, structure, checklists and planning. Submitting text, proofs, code or analysis written by someone else or by an AI tool as your own is malpractice. How to use help and AI honestly.