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Overview

Public key (asymmetric) cryptography uses a mathematically linked key pair to enable secure communication, authentication, and digital signatures. The public key encrypts or verifies; the private key decrypts or signs. While slower than symmetric encryption, it solves the key distribution problem and is commonly combined with symmetric encryption for performance.

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Terminology

Term	Definition
Public Key	Shared key used to encrypt data or verify signatures
Private Key	Secret key used to decrypt data or create signatures
Key Pair	Mathematically linked public and private keys
Digital Signature	Data signed with a private key; verified with the corresponding public key
Certificate Authority (CA)	Trusted entity that signs certificates to establish a chain of trust
Chain of Trust	Hierarchy where a CA vouches for a certificate, and the OS/browser trusts the CA
Diffie-Hellman	Protocol for establishing a shared secret over an insecure channel
PGP / GPG	Pretty Good Privacy / GNU Privacy Guard; used for file encryption and signing

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Core Concepts

Asymmetric Encryption

• Uses a key pair — public key is shared freely, private key must remain secret
• Often used to securely exchange symmetric session keys
• Slower than symmetric encryption — typically used for key exchange and authentication only

RSA

Based on the mathematical difficulty of factoring large prime numbers.

Variable	Description
p, q	Large prime numbers
n	Product of p × q
e	Public exponent
d	Private exponent
m	Plaintext message
c	Ciphertext

• Public key: (n, e)
• Private key: (n, d)

Diffie-Hellman Key Exchange

Establishes a shared secret over an insecure channel without prior key sharing.

• Often paired with RSA — DH handles key exchange, RSA handles authentication/signatures
• Both parties independently compute an identical shared secret using public and private values

Other Asymmetric Algorithms

Algorithm	Description
DSA	Digital Signature Algorithm; designed specifically for signatures
ECDSA	Elliptic curve variant of DSA; smaller keys with strong security
ECDSA-SK	Hardware-backed security key variant of ECDSA
Ed25519	Modern efficient signature scheme using Curve25519
Ed25519-SK	Hardware-backed variant of Ed25519

SSH Key Authentication

SSH uses asymmetric keys for passwordless authentication.

Operation	Command
Generate key pair	ssh-keygen -t rsa
Copy public key to remote	ssh-copy-id user@host
Connect using private key	ssh -i privateKeyFile user@host

• Public key stored in ~/.ssh/authorized_keys on the target system
• Private key must have permissions 600 or stricter
• A compromised private key means unauthorized access

Digital Signatures

• Created using the private key; verified using the public key
• Provides authentication and integrity verification
• Proves the message came from the holder of the private key and was not tampered with

Certificates & Chain of Trust

Used by websites to prove identity over TLS/HTTPS — see TLS & SSL

• Certificate signed by an organization → organization trusted by a CA → browser trusts CA
• Root CAs are pre-trusted by the OS and browsers
• Free certificates available via Let’s Encrypt

PGP / GPG

Used for file encryption and digital signatures, commonly in secure email.

Command	Description
gpg --full-gen-key	Generate a new key pair
gpg --import backup.key	Import an existing key
gpg --decrypt confidential_message.gpg	Decrypt a GPG-encrypted file
gpg2john <keyfile>	Extract hash from passphrase-protected key for cracking

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Related Concepts

• Cryptography Basics
• Hashing Basics
• TLS & SSL

Related Techniques

• RSA Cracking

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References / Images

• RSA key generation diagrams
• Diffie-Hellman key exchange visualization
• Digital signature workflow diagrams
• Certificate trust chain illustration