Public Key Concepts

What Is Public Key Cryptography

Public key cryptography (also called asymmetric cryptography) is a cryptographic system that uses mathematically linked key pairs: a public key that can be freely shared and a private key that must be kept secret. Unlike symmetric encryption where both parties share a single secret key, public key cryptography solves the key distribution problem — two parties can communicate securely without ever having exchanged a secret in advance.

Public key cryptography is the foundation of digital signatures, TLS/HTTPS, SSH, PGP email encryption, cryptocurrency, and certificate-based authentication. Invented independently by Diffie-Hellman (1976) and Rivest-Shamir-Adleman (RSA, 1977), it remains one of the most important innovations in the history of computer science.

How Public Key Cryptography Works

A key pair is generated using a mathematical trapdoor function — an operation that is easy to compute in one direction but computationally infeasible to reverse:

Core Operations

Operation	Uses	How It Works
Encryption	Public key	Anyone can encrypt a message using the recipient's public key. Only the matching private key can decrypt it.
Decryption	Private key	Only the private key holder can decrypt messages encrypted with their public key.
Signing	Private key	The sender signs a message using their private key, creating a digital signature.
Verification	Public key	Anyone can verify the signature using the signer's public key, confirming authenticity and integrity.

Common Algorithms

Algorithm	Based On	Key Sizes	Status
RSA	Integer factorization	2048-4096 bit	Widely used; 2048-bit minimum recommended
ECDSA	Elliptic curve discrete logarithm	256-384 bit	Preferred for performance; same security with smaller keys
Ed25519	Twisted Edwards curve	256-bit	Modern; fast, constant-time, resistant to side channels
X25519	Montgomery curve	256-bit	Key exchange (Diffie-Hellman); used in TLS 1.3 and WireGuard
Kyber	Lattice-based	Various	Post-quantum candidate; NIST standardized as ML-KEM

Common Use Cases

• Understanding TLS/HTTPS: Learn how web browsers and servers use public key cryptography to establish encrypted connections
• SSH key management: Understand why SSH key pairs work and how Ed25519 differs from RSA for server authentication
• Digital signature concepts: Explore how code signing, document signing, and certificate chains rely on asymmetric operations
• Post-quantum awareness: Understand why current public key algorithms are vulnerable to quantum computers and what replacement algorithms are being standardized
• Certificate authority trust: Learn how the chain of trust from root CAs to leaf certificates uses public key signing

Best Practices

1. Use Ed25519 for new deployments — Unless compatibility requires RSA or ECDSA, Ed25519 provides the best combination of security, performance, and implementation safety.
2. Minimum RSA key size: 2048 bits — NIST and major browsers require at least 2048-bit RSA keys. Plan migration to 3072-bit or 4096-bit for longevity beyond 2030.
3. Protect private keys with hardware — Store private keys in Hardware Security Modules (HSMs), TPMs, or secure enclaves. Never store unprotected private keys on disk.
4. Prepare for post-quantum cryptography — NIST finalized ML-KEM (Kyber) and ML-DSA (Dilithium) as post-quantum standards. Begin evaluating hybrid deployments that combine classical and post-quantum algorithms.
5. Rotate keys on a schedule — Even without compromise, rotate keys periodically. TLS certificates expire (typically 90-398 days), and SSH keys should be rotated at least annually.