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Cryptography

Cryptography is the practice of protecting information using mathematical techniques. It is used to provide confidentiality, integrity, authentication, and non-repudiation in modern systems.

Cryptography appears everywhere in cybersecurity: HTTPS, SSH, VPNs, password storage, digital signatures, certificates, file integrity checks, and secure messaging.

Core Concepts

Term Meaning
Plaintext Original readable data before encryption
Ciphertext Scrambled unreadable data after encryption
Cipher Algorithm used to transform plaintext and ciphertext
Key Secret value used by the cryptographic algorithm
Encryption Converting plaintext into ciphertext
Decryption Converting ciphertext back into plaintext

Simple flow:

Plaintext + Cipher + Key -> Ciphertext
Ciphertext + Cipher + Key -> Plaintext

Security Goals

Cryptography supports several security goals.

Goal Description
Confidentiality Prevent unauthorized reading of data
Integrity Detect whether data was changed
Authentication Verify identity or origin
Non-repudiation Prevent a sender from denying an action
Key exchange Securely agree on shared secrets

Symmetric Encryption

Symmetric encryption uses the same key for encryption and decryption.

Shared key encrypts data
Shared key decrypts data

Examples:

Algorithm Status
DES Broken / obsolete
3DES Deprecated / legacy
AES Modern standard

Advantages

  • Fast
  • Efficient for large data
  • Common for disk, file, and network encryption

Disadvantages

  • Key distribution is difficult
  • Anyone with the key can decrypt the data
  • Key compromise exposes protected data

Common Use

Symmetric encryption is often used for bulk data encryption after a secure key exchange.

Example:

TLS uses asymmetric methods to agree on keys,
then symmetric encryption protects the session data.

Asymmetric Encryption

Asymmetric encryption uses a key pair:

Key Purpose
Public key Shared publicly
Private key Kept secret

Data encrypted with one key can only be decrypted with the matching key.

Advantages

  • Easier key distribution
  • Enables digital signatures
  • Useful for authentication and key exchange

Disadvantages

  • Slower than symmetric encryption
  • Requires larger key sizes
  • Depends heavily on private key protection

Common Algorithms

Algorithm Use
RSA Encryption and digital signatures
Diffie-Hellman Key exchange
ECC Efficient public-key cryptography
Ed25519 Modern digital signatures

Symmetric vs. Asymmetric Encryption

Feature Symmetric Asymmetric
Keys One shared key Public/private key pair
Speed Faster Slower
Best for Bulk data encryption Key exchange, identity, signatures
Key distribution Harder Easier
Example AES RSA, Diffie-Hellman, ECC

Modern systems often combine both:

Asymmetric cryptography -> securely agree on a shared key
Symmetric cryptography  -> encrypt the actual data

XOR

XOR is a basic binary operation used in many cryptographic concepts.

Truth table:

A B A XOR B
0 0 0
0 1 1
1 0 1
1 1 0

Important properties:

A XOR A = 0
A XOR 0 = A
A XOR B = B XOR A

Simple XOR encryption:

Ciphertext = Plaintext XOR Key
Plaintext  = Ciphertext XOR Key

Note

XOR by itself is not secure unless used correctly. Reusing XOR keys can completely break confidentiality.

Modulo

Modulo returns the remainder after division.

Examples:

25 mod 5 = 0
23 mod 6 = 5
23 mod 7 = 2

Modulo arithmetic is important in public-key cryptography, especially RSA and Diffie-Hellman.

RSA

RSA is a public-key algorithm based on the difficulty of factoring large numbers.

At a high level:

  1. Choose two large prime numbers.
  2. Multiply them together.
  3. Use the result to create public and private keys.
  4. Encryption and decryption rely on modular arithmetic.

Key idea:

Easy: multiply two large primes
Hard: factor their product back into the original primes

RSA values commonly seen in CTFs and cryptography challenges:

Variable Meaning
p, q Prime numbers
n Modulus, usually p * q
e Public exponent
d Private exponent
m Plaintext message
c Ciphertext

RSA formulas:

c = m^e mod n
m = c^d mod n

Security depends on using strong key sizes and safe padding schemes.

Diffie-Hellman Key Exchange

Diffie-Hellman allows two parties to agree on a shared secret over an insecure channel.

The shared secret is not directly transmitted.

Basic process:

  1. Both parties agree on public values.
  2. Each party chooses a private value.
  3. Each party calculates a public value.
  4. They exchange public values.
  5. Each party independently calculates the same shared secret.

Simplified flow:

Alice private value + Bob public value -> shared secret
Bob private value + Alice public value -> same shared secret

Security relevance:

  • Used for secure key exchange
  • Often appears in TLS and VPNs
  • Must be authenticated to prevent man-in-the-middle attacks

SSH Key Authentication

SSH can use public-key authentication instead of passwords.

Generate a key pair:

ssh-keygen

Use a private key to connect:

ssh -i id_rsa user@host

Copy a public key to a server:

ssh-copy-id user@host

Important files:

File Purpose
id_rsa Private key
id_rsa.pub Public key
~/.ssh/authorized_keys Public keys allowed to log in

Private key permissions should be restricted:

chmod 600 id_rsa

Warning

Treat private keys like passwords. Do not publish them in notes, repositories, screenshots, or writeups.

Digital Signatures

Digital signatures verify authenticity and integrity.

They help prove:

  • Who signed the data
  • That the data was not changed after signing

Basic process:

Sender signs data with private key
Receiver verifies signature with public key

Digital signatures are used in:

  • Software updates
  • Code signing
  • TLS certificates
  • Secure email
  • Document signing

Certificates and Certificate Authorities

Certificates bind a public key to an identity.

In HTTPS, certificates help prove that the server you are connecting to is the correct server.

Certificate chain:

Website Certificate
    ↓
Intermediate CA
    ↓
Root CA trusted by browser/OS

Important terms:

Term Meaning
CA Certificate Authority
Root CA Highly trusted certificate authority
Intermediate CA CA between root and site certificate
TLS certificate Certificate used by HTTPS
Chain of trust Validation path from site certificate to trusted root

Security relevance:

  • Expired certificates cause trust errors.
  • Self-signed certificates are not automatically trusted.
  • Weak certificate validation can enable man-in-the-middle attacks.

TLS and HTTPS

HTTPS is HTTP protected by TLS.

TLS provides:

  • Encryption
  • Server authentication
  • Integrity protection
  • Secure key exchange

Simplified TLS flow:

Client connects to server
Server presents certificate
Client validates certificate
Client and server agree on session keys
Encrypted communication begins

PGP and GPG

PGP and GPG are used for encrypting and signing messages or files.

Term Meaning
PGP Pretty Good Privacy
GPG GNU Privacy Guard, open-source OpenPGP implementation

Common uses:

  • Email encryption
  • File encryption
  • Digital signatures
  • Verifying software releases

Example commands:

# Import a key
gpg --import public.key

# Encrypt a file
gpg --encrypt --recipient user@example.com file.txt

# Decrypt a file
gpg --decrypt file.txt.gpg

Hash Functions

A hash function creates a fixed-size digest from input data.

Example:

Input:  hello
Output: hash digest

Hash functions are one-way. They are designed to be easy to compute and hard to reverse.

Properties of good hash functions:

Property Meaning
Deterministic Same input gives same hash
Fast to compute Efficient to generate
Hard to reverse Cannot easily recover input
Collision resistant Hard to find two inputs with same hash
Avalanche effect Small input change causes large hash change

Hashing vs. Encryption

Hashing and encryption are different.

Feature Hashing Encryption
Direction One-way Reversible
Key required Usually no Yes
Output Fixed-size digest Ciphertext
Main use Integrity, password storage Confidentiality

You do not “decrypt” a hash. You crack or guess the original input by hashing guesses and comparing results.

Common Hash Algorithms

Algorithm Status
MD5 Insecure
SHA-1 Insecure
SHA-256 Common modern hash
SHA-512 Common modern hash
bcrypt Password hashing
scrypt Password hashing
Argon2 Modern password hashing

Warning

MD5 and SHA-1 should not be used for security-sensitive integrity or password storage.

Hashing for Integrity

Hashes can verify that a file has not changed.

Example:

sha256sum file.iso

Compare the result with the hash published by the software provider.

If the hashes match, the file is likely unchanged.

HMAC

HMAC stands for Hash-based Message Authentication Code.

It combines:

Hash function + Secret key

HMAC verifies:

  • Integrity
  • Authenticity

Unlike a normal hash, HMAC proves that the sender knew the shared secret key.

Common uses:

  • API authentication
  • Message integrity
  • Secure tokens
  • Internal service communication

Password Storage

Passwords should not be stored in plaintext or reversibly encrypted form.

Bad practices:

Practice Problem
Plaintext passwords Database leak exposes all passwords
Reversible encryption Key compromise exposes all passwords
Fast unsalted hashes Vulnerable to cracking and rainbow tables

Better practice:

Password + unique salt -> slow password hashing algorithm -> stored hash

Recommended password hashing algorithms:

  • Argon2
  • bcrypt
  • scrypt
  • PBKDF2

Salting

A salt is a unique random value added to a password before hashing.

Purpose:

  • Prevents identical passwords from producing identical hashes
  • Defeats precomputed rainbow tables
  • Forces attackers to crack each password separately

Example:

Password: CorrectHorseBatteryStaple
Salt:     random-user-specific-value
Hash:     hash(password + salt)

Salts do not need to be secret. They are commonly stored next to the password hash.

Recognizing Password Hashes

Password hashes often include format indicators.

Linux password hashes are commonly stored in:

/etc/shadow

Example format:

$prefix$options$salt$hash

Common Linux hash prefixes:

Prefix Algorithm
$y$ yescrypt
$7$ scrypt
$2b$, $2y$ bcrypt
$6$ sha512crypt
$1$ md5crypt

Windows password hashes are commonly associated with:

Hash Notes
NTLM Modern Windows password hash format
LM Legacy and insecure

Password Cracking Concept

Password cracking does not reverse a hash.

Instead:

  1. Guess a password.
  2. Hash the guess using the same algorithm and salt.
  3. Compare the result to the target hash.
  4. If they match, the password was found.
guess -> hash function -> compare with target hash

Common tools:

Tool Use
Hashcat GPU-accelerated cracking
John the Ripper Flexible CPU/GPU cracking

Warning

Only crack hashes in authorized labs, assessments, or recovery scenarios.

Quick Reference

Concept Purpose
Symmetric encryption Fast bulk encryption
Asymmetric encryption Key exchange, signatures, identity
AES Modern symmetric encryption
RSA Public-key cryptography
Diffie-Hellman Shared secret agreement
SSH keys Public-key authentication
Digital signatures Authenticity and integrity
Certificates Bind identity to public key
TLS Secure network communication
PGP/GPG File/email encryption and signing
Hashing Integrity and password verification
HMAC Keyed integrity/authenticity
Salt Protect password hashes from precomputed attacks

Notes to Remember

  • Encryption protects confidentiality.
  • Hashing protects integrity and supports password verification.
  • Symmetric encryption is fast but requires shared key protection.
  • Asymmetric encryption solves key exchange and identity problems.
  • Digital signatures are created with private keys and verified with public keys.
  • Certificates help browsers trust HTTPS websites.
  • Passwords should be stored with slow salted password hashing algorithms.
  • Hashes are cracked by guessing, not decrypted.
  • Private keys must never be shared or committed to Git.