How Public-Key Cryptography Works

Public-key cryptography, also known as asymmetric cryptography, is the foundation of secure communication on the internet. Unlike symmetric encryption where the same key encrypts and decrypts data, public-key systems use a mathematically related pair of keys: a public key that can be freely shared and a private key that must be kept secret.

The mathematical relationship between the keys is based on problems that are easy to compute in one direction but computationally infeasible to reverse. RSA, one of the most common algorithms, relies on the difficulty of factoring large prime numbers. You can multiply two large primes easily, but given the product, finding the original primes is extraordinarily difficult with current computing power.

This asymmetry enables several crucial capabilities. For encryption, anyone can use your public key to encrypt a message that only you can decrypt with your private key. For digital signatures, you can use your private key to sign a message, and anyone with your public key can verify the signature's authenticity. This solves the key distribution problem that plagued earlier cryptographic systems - you no longer need a secure channel to share encryption keys.

In practice, public-key cryptography is used everywhere: HTTPS connections start with a public-key handshake to establish a shared secret for faster symmetric encryption. SSH uses key pairs for passwordless authentication. Email can be encrypted with PGP. Cryptocurrencies use digital signatures to prove ownership. Understanding these principles helps developers make informed decisions about security, whether choosing appropriate key lengths, managing key storage, or implementing secure communication protocols.