A cryptographic system using pairs of keys - one public and one private - that enables secure communication and digital signatures without requiring prior shared secrets.

Public Key Cryptography

Public key cryptography (also known as asymmetric cryptography) represents a revolutionary breakthrough in the field of cryptography, fundamentally changing how secure communication can be achieved across untrusted channels.

Core Principles

The system relies on two mathematically linked keys:

A public key that can be freely shared
A private key that must be kept secret

This two-key approach solved the classical key distribution problem that had plagued cryptographic systems for millennia.

Mathematical Foundation

The security of public key systems rests on certain mathematical problems that are:

Easy to compute in one direction
Computationally infeasible to reverse

Common examples include:

Major Applications

Secure Communication

Sender encrypts message using recipient's public key
Only recipient's private key can decrypt the message
Enables confidentiality without pre-shared secrets

Digital Signatures

Private key signs documents
Public key verifies signatures
Provides authentication and non-repudiation

Key Exchange

Enables secure key exchange protocols like:

Diffie-Hellman protocol
RSA key exchange

Historical Impact

Developed in the 1970s by researchers including Whitfield Diffie and Martin Hellman, public key cryptography enabled:

Challenges and Considerations

Computational overhead compared to symmetric encryption
Need for public key infrastructure (PKI)
Vulnerability to quantum computing attacks
Key size requirements for adequate security

Modern Implementation

Common algorithms and standards include:

RSA (Rivest-Shamir-Adleman)
ECC (Elliptic Curve Cryptography)
PGP (Pretty Good Privacy)

Public key cryptography remains fundamental to modern digital security, forming the backbone of protocols like TLS and secure email systems.