Codes, cryptography and algorithms · Maths EE idea · Solid

How random are pseudo-random numbers?

A research question to start from

How does the choice of parameters determine the period of a linear congruential generator, and how can its output be tested for randomness?

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

Number theory proves the period conditions; statistics tests the output.

Mathematics you would need

Modular arithmetic
Period conditions (Hull–Dobell)
Chi-squared and serial tests
Lattice structure

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

Prove period results for small cases.
Test generators with good and bad parameters.
Show and explain the lattice structure of pairs.

Scope and difficulty

Solid. Solid.

Pitfalls

Only statistical tests.
Conditions quoted, not explained.

Where to start reading

Search a library catalogue or a university's open lecture notes for: linear congruential generator Hull-Dobell theorem; spectral test lattice. 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.