Skip to main content
MathidiaMathematics Academy
Number theory and cryptography
Lesson 50 of 75
Review

Public-key cryptography

Objective. Explain RSA structure and assumptions.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Public-key cryptography is treated as university mathematics: definitions and hypotheses come before procedures. Congruences, arithmetic functions and public-key ideas. Begin by identifying the mathematical objects, notation, domain and assumptions. Develop the central result from first principles or an explicitly stated theorem, and connect symbolic work to geometric, numerical, probabilistic or computational meaning where appropriate. Compare at least two representations, explain why each implication is valid, and preserve exact structure until approximation is justified. Conclude by testing edge cases, dimensions, limiting behaviour and counterexamples so the argument is rigorous, interpretable and reusable in unfamiliar problems.

Worked example

Match proof method.

assume the negation | bas…
Illustrated card showing assume the negation | base and step | prove not Q implies not P
  1. 1Restate the problem in precise notation, list the hypotheses, and identify the definition or mathematical structure controlling the solution.
  2. 2Select a theorem, representation or algorithm and verify that every condition required for its use is satisfied.
  3. 3Carry out the derivation in explicit justified stages, tracking domains, signs, dimensions, convergence and exceptional cases.
  4. 4Verify independently by substitution, a second representation, a limiting case, computation or counterexample analysis. The checked conclusion is assume the negation | base and step | prove not Q implies not P.

Answer: assume the negation | base and step | prove not Q implies not P

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. A frequent error in public-key cryptography is to manipulate notation before establishing definitions and hypotheses. This can produce a plausible calculation whose implication, domain, convergence or uniqueness claim is false. Name the governing result, test its conditions, preserve equivalence at each step, and challenge the conclusion with a boundary case or counterexample.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard