Hash functions

• A a hash function takes an input and produces hash value known as a message digest

General-purpose

MD5 (Message-digest algorithm)

• Size: 128 bits - 16 bytes - 32 hex

cat file.txt | md5sum
# 930db08d7fb48a7e8a524e736f7acae9

SHA-1 (Secure Hash Algorithm 1)

• SHA-1: 160-bit (20-byte)
• Tipically rendered as a 40 hexadecimal digits
• Applications: git

# SHA1 hash
echo -n "Hello" | shasum

• Number of different hashes from SHA1 hash function
• 2^160 = 16^40 = 1.461501637×10^48
• Chance of producing same exact hash for different files in SHA1 (Dice theory)
• Probability of each SHA1 hash: 1/(2^160)
• Probability of same exact hash: (1/(2^160))*(1/_(2^160)) = 1/(2^320)
• Chance of producing any exact hash for different files in SHA1 (Hash collision probability)
• Probability of same any hash: for 2 files: 2.84*10^49
• The probability increases with more files. E.g., 3 files -> 2.05*10^48

SHA-2 (Secure Hash Algorithm 2)

• SHA-224: 224-bit (28-byte)
• SHA-256: 256-bit (32-byte)
• SHA-384: 384-bit (48-byte)
• SHA-512: 512-bit (64-byte)

# SHA256 hash
echo -n "Hello" | shasum -a 256

# SHA512 hash
echo -n "Hello" | shasum -a 512

Password hashing

• Also known as "key derivation functions"

• Designed to be slow to resist brute-force attacks

• bcrypt: Strong, widely supported, adds salt automatically.

• scrypt: Memory-hard, useful against GPU attacks.
• PBKDF2: Iterative key derivation, configurable iterations.
• Argon2: Winner of the Password Hashing Competition (PHC); very secure and memory-hard.

Non-cryptographic

• Also known as "fast hash functions"

• Used for hash tables, checksums, or detecting accidental changes—not for security.

• MurmurHash: Very fast, good distribution

• CityHash / FarmHash / MetroHash: High-performance hashing for large data
• FNV-1a: Simple, fast, good for small data sets

Checksums / error detection

• CRC32: common for files and network packets
• Adler-32: faster than CRC32 for small data