Interactive explainer of public key cryptography concepts: key generation, encryption, signing, and the math behind RSA.
Public key cryptography works because of modular arithmetic, but the algebra hides behind large numbers. This tool makes it visible: it generates a key pair from two primes, then walks encryption and decryption step by step, and flips the same operations around to demonstrate digital signatures. Small, hand-computable values keep every intermediate number on screen. The surprise most people hit: the two keys are interchangeable partners. Encryption with one key is undone by the other, in either direction, and that reversibility is exactly what turns encryption into signing. Secrecy is one use; proving you wrote a message is another.
Key generation picks two distinct primes p and q. Their product n = p x q becomes the modulus both keys share, and (p-1)(q-1) is Euler's totient phi. The tool picks an exponent e coprime with phi, then derives d as the modular inverse of e modulo phi, meaning e x d leaves remainder 1 modulo phi. The public key is (n, e); the private key is (n, d).
Encryption raises the message m to the exponent e modulo n, giving ciphertext c = m^e mod n; decryption raises c to d, recovering m, because e x d is a multiple of phi plus 1 and the exponents cancel. Signing runs the same computation with the keys swapped: s = m^d mod n, and anyone verifies it by checking that s^e mod n equals m.
No. Any key pair whose generation you can watch step by step uses numbers small enough to reason about, and such a modulus is trivially factored. Use the tool to understand the math, then generate real keys with a trusted library at 2048 bits or larger, ideally via the browser's Web Crypto API, and never copy demo values into production code.
For the textbook math this tool shows, yes: signing and verification are the same modular exponentiation as decryption and encryption, with the keys swapped, and that symmetry is why the trick works. Production systems add different padding for each operation and use them for different goals, secrecy versus authenticity, so the answer is mathematically yes and practically no.
The behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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