RSA Calculator

Derive an RSA key (n, φ, d) from two primes and a public exponent, and walk through encryption/decryption. For learning only.

Category: Dev Tools

When to use?

Use it in cryptography courses and assignments to see how RSA works. Enter p and q to compute n, φ(n) and the private key d, then encrypt (c = mᵉ mod n) and decrypt (cᵈ mod n) an integer message m.

How to use

  • Enter two primes p, q and a public exponent e (or generate random primes).
  • Review the derived n, φ(n) and private key d.
  • Enter a message integer m to see the ciphertext and decrypted result.

Input Explanation

p and q must be distinct primes; e must satisfy 1 < e < φ(n) and be coprime with φ(n); m must satisfy 0 ≤ m < n.

Calculation Basis

Using BigInt, it computes n = p×q and φ(n) = (p−1)(q−1), finds d = e⁻¹ mod φ(n) with the extended Euclidean algorithm, and encrypts/decrypts via square-and-multiply modular exponentiation.

Usage Examples

  • Learning cryptography - Follow RSA key generation and encryption step by step.
  • Checking assignments - Verify hand-computed RSA results quickly.

Examples

  • p=61, q=53, e=17 → n=3233, φ=3120, d=2753
  • m=65 → c=2790 → decrypts back to 65

Cautions

  • This tool is for learning and verifying RSA math only. Do not use these keys for real encryption or authentication.
  • Real security needs 2048-bit+ keys and padding (e.g. OAEP); small primes are trivially broken.

FAQ

Why the "not prime" error?

p and q must both be prime, or the key cannot be derived.

What value should e be?

In practice 65537 is common; it just needs to be coprime with φ(n).

Can I use it for real encryption?

No. It is educational, with small keys and no padding, so it is not secure.

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