Spark & Anvil Privacy

Real cases

Two of the ideas you practise, meeting in one real situation. Choose, see what actually happens, then reflect.

A case · you decide

The modulus and Euler's φ build a tiny key

The modulus n = p·q & Euler's φ(n) — a 16-year-old building a toy RSA key by hand for maths club

The idea in play: the public modulus is the product of two secret primes, and φ(n) = (p − 1)(q − 1) can only be found if you know them.

Noor picks the primes p = 5 and q = 11. She will publish n and keep p and q secret.

The modulus: n = 5 × 11 = 55.

Euler's φ: (5 − 1) × (11 − 1).

What is φ(n)?

Open the clock →

A case · you decide

The public and private exponents make a pair

The private exponent d & The public exponent e — a 17-year-old finishing the same toy key

The idea in play: the private exponent is the inverse of the public one on the clock of size φ: e × d leaves remainder 1.

With φ = 40, Noor chooses the public exponent e = 3. Now she needs d so that 3 × d leaves a remainder of 1 when divided by 40.

The public exponent e is shared with everyone.

The private exponent d undoes it: e × d ≡ 1 (mod 40).

What is d?

Open the clock →