RSA Cryptography
Public-key encryption using prime factorisation difficulty.
Key idea
Public-key encryption using prime factorisation difficulty.
In depth
Choose primes p, q, set n = pq, and a public exponent e coprime to φ(n); the private exponent d satisfies ed ≡ 1 (mod φ(n)). Encrypt c = mᵉ mod n, decrypt m = cᵈ mod n. Security rests on the difficulty of factoring n.
Worked example
p = 3, q = 11, n = 33, φ = 20, e = 3, d = 7. Encrypt m = 4: 4³ = 64 ≡ 31; decrypt: 31⁷ ≡ 4 (mod 33).
Formula
Real-world uses
- Protecting online banking, email and HTTPS connections with public-key encryption
Common mistake
Using small or poorly chosen primes.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is RSA Cryptography?
Public-key encryption using prime factorisation difficulty. It is a topic at the expert level in Discrete Math & Number Theory.
What is the formula for RSA Cryptography?
The key formula is c = mᵉ mod n.
Where is RSA Cryptography used in real life?
Real-world examples: Protecting online banking, email and HTTPS connections with public-key encryption.
What should I learn before RSA Cryptography?
Make sure you are comfortable with Goldbach and Twin Prime Conjectures, the previous topic in Discrete Math & Number Theory.
What is a common mistake with RSA Cryptography?
Using small or poorly chosen primes.
How can I practise RSA Cryptography?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after RSA Cryptography?
Move on to Diffie–Hellman Key Exchange next.
Related expert topics in Discrete Math & Number Theory
- Strong Induction – Assume all earlier cases to prove the next.
- Well-Ordering Principle – Every nonempty set of positive integers has a least element.
- Partial Orders – Reflexive, antisymmetric, transitive relations.
- Cardinality of Sets – Comparing sizes of infinite sets.
- Countable and Uncountable Sets – ℕ and ℚ are countable; ℝ is not.
- Cantor’s Diagonal Argument – Proof that real numbers are uncountable.