Codes, cryptography and algorithms · Maths EE idea · Accessible

Breaking substitution ciphers with statistics

A research question to start from

How reliably can a substitution cipher be broken by letter-frequency analysis, and how much ciphertext is needed?

A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.

Why it works as a maths EE

Statistics applied to a decoding method you evaluate quantitatively.

Mathematics you would need

Frequency distributions
Chi-squared distance
Index of coincidence
Sample size and variability

Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.

One possible line of attack

Define a scoring statistic for candidate decryptions.
Measure success against ciphertext length.
Explain the index of coincidence and use it for a Vigenère cipher.

Scope and difficulty

Accessible. Accessible; the Vigenère extension adds depth.

Pitfalls

Puzzle-solving narrative.
No measure of reliability.

Where to start reading

Search a library catalogue or a university's open lecture notes for: index of coincidence derivation; frequency analysis ciphertext length. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).

Make it your EE

Plan this EEOpens the free EE planner with this question as a starting point. Sharpen the questionSix quick checks for a focused research question. Self-check a draftCheck a section against each criterion, free.