Math

Toy RSA Demonstrator

Walk through tiny RSA with user-provided small primes: n, φ(n), e, d, and encrypt/decrypt steps. Educational only—not production keys.

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Educational

Prime p

Distinct prime ≤ 100,000.

Prime q

Distinct prime ≤ 100,000.

Public exponent e

Must satisfy 1 < e < φ(n) and gcd(e, φ(n)) = 1.

Message integer m

Integer with 0 ≤ m < n.

n = pq

φ(n)

Private d

Ciphertext c

Decrypted m

How it works

Toy RSA uses small primes so you can see n = pq, φ(n) = (p−1)(q−1), choose e, compute d = e⁻¹ mod φ(n), then encrypt/decrypt integers. Primes must be ≤ 100,000. Educational only—not production keys.

Pick distinct small primes p and q, a public exponent e coprime to φ(n), and a message integer m with 0 ≤ m < n. Related: Modular Exponentiation, Extended GCD / Modular Inverse, Euler Totient.

\[ c \equiv m^{e} \pmod n,\quad m \equiv c^{d} \pmod n \]
Never use these keys for real security; production RSA uses large random primes and audited libraries.

\[ d \equiv e^{-1} \pmod{\varphi(n)} \]

Reference →

Sources

https://en.wikipedia.org/wiki/RSA_(cryptosystem)

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Toy RSA Demonstrator

Sources

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