Given:   MAC = H(secret || original_message)
Known:   original_message, len(secret), MAC value
Compute: H(secret || original_message || padding || extension)
         WITHOUT knowing the secret!
 
How: The MAC value IS the internal hash state after processing
     (secret || original_message || padding).
     Initialize hash with this state, continue hashing extension.

def md5_padding(message_len_bytes):
    """Calculate MD5/SHA padding for given message length."""
    bit_len = message_len_bytes * 8
    # Pad with 0x80 + zeros until length ≡ 56 (mod 64)
    padding = b'\x80'
    padding += b'\x00' * ((55 - message_len_bytes) % 64)
    # Append original length as 64-bit little-endian (MD5)
    # or big-endian (SHA)
    padding += bit_len.to_bytes(8, 'little')  # MD5
    # padding += bit_len.to_bytes(8, 'big')    # SHA
    return padding

# HashPump
hashpump -s "known_mac_hex" \
         -d "original_data" \
         -k 16 \            # secret length
         -a "extension_data"
 
# Output: new_mac, new_data (original + padding + extension)
 
# hash_extender
hash_extender --data "original" \
              --secret 16 \
              --append "extension" \
              --signature "known_mac_hex" \
              --format md5

import struct
def md5_extend(original_mac, original_data_len, secret_len, extension):
    """
    Perform MD5 length extension attack.
    original_mac: hex string of H(secret || original_data)
    """
    # Parse MAC into MD5 internal state (4 × 32-bit words, little-endian)
    h = struct.unpack('<4I', bytes.fromhex(original_mac))
    # Calculate total length after padding
    total_original = secret_len + original_data_len
    padding = md5_padding(total_original)
    forged_len = total_original + len(padding) + len(extension)
    # Continue MD5 from saved state with extension
    # (requires MD5 implementation that accepts initial state)
    from hashlib import md5
    # Most stdlib md5 doesn't expose state setting
    # Use: hlextend library or custom MD5
    import hlextend
    sha = hlextend.new('md5')
    new_hash = sha.extend(extension, original_data, secret_len,
                          original_mac)
    new_data = sha.payload  # includes original + padding + extension
    return new_hash, new_data

# Generate collision pair
fastcoll -p prefix_file -o collision1.bin collision2.bin
 
# Result: MD5(collision1.bin) == MD5(collision2.bin)
# Files differ in exactly 128 bytes (two MD5 blocks)

# hashclash (Marc Stevens)
./hashclash prefix1.bin prefix2.bin
 
# Result: MD5(prefix1 || suffix1) == MD5(prefix2 || suffix2)

Application: forge two PDF/PE files with same MD5
  - File 1: benign content
  - File 2: malicious content
  - Same MD5 hash

// PHP: md5($_GET['a']) == md5($_GET['b']) && $_GET['a'] != $_GET['b']
 
// Method 1: Array trick (not real collision)
?a[]=1&b[]=2  // md5(array) returns NULL, NULL == NULL
 
// Method 2: Real collision (fastcoll output, URL-encoded binary)
?a=<collision1_urlencoded>&b=<collision2_urlencoded>
 
// Method 3: 0e magic hashes (loose comparison ==)
// md5("240610708") = "0e462097431906509019562988736854"
// md5("QNKCDZO")   = "0e830400451993494058024219903391"
// PHP: "0e..." == "0e..." is TRUE (both evaluate to 0 as floats)

SHA-1 should NOT be used for:
  ✗ Digital signatures
  ✗ Certificate fingerprints
  ✗ Git commit integrity (migration to SHA-256 in progress)
  ✗ Deduplication based on hash
 
SHA-1 is still OK for:
  ✓ HMAC-SHA1 (collision resistance not required)
  ✓ HKDF-SHA1 (PRF security suffices)
  ✓ Non-adversarial checksums

For n-bit hash: expected collisions after ~2^(n/2) hashes
 
Hash     Bits    Birthday bound
MD5      128     2^64
SHA-1    160     2^80
SHA-256  256     2^128
 
CTF application: if hash is truncated to k bits,
collision in ~2^(k/2) attempts

import hashlib
import os
def birthday_attack(hash_func, output_bits, max_attempts=2**28):
    """Find collision for truncated hash."""
    mask = (1 << output_bits) - 1
    seen = {}
    for _ in range(max_attempts):
        msg = os.urandom(16)
        h = int(hash_func(msg).hexdigest(), 16) & mask
        if h in seen and seen[h] != msg:
            return seen[h], msg  # collision!
        seen[h] = msg
    return None
# Example: find collision for first 32 bits of SHA-256
result = birthday_attack(hashlib.sha256, 32)

# VULNERABLE: early-exit string comparison
def verify_hmac(received, expected):
    return received == expected  # Python == compares left to right
# The comparison may short-circuit on first differing byte,
# leaking timing information

import requests
import time
def hmac_timing_attack(url, data, hmac_len=32):
    """Byte-by-byte HMAC recovery via timing."""
    known = ""
    for pos in range(hmac_len * 2):  # hex chars
        best_char = ""
        best_time = 0
        for c in "0123456789abcdef":
            candidate = known + c + "0" * (hmac_len * 2 - len(known) - 1)
            times = []
            for _ in range(50):  # multiple samples for accuracy
                start = time.perf_counter_ns()
                requests.get(url, params={**data, "mac": candidate})
                elapsed = time.perf_counter_ns() - start
                times.append(elapsed)
            avg_time = sorted(times)[len(times)//2]  # median
            if avg_time > best_time:
                best_time = avg_time
                best_char = c
        known += best_char
        print(f"Position {pos}: {known}")
    return known

import hmac
# SECURE: constant-time comparison
def verify_hmac_secure(received, expected):
    return hmac.compare_digest(received, expected)

Hash computation: H = f(g(x₁), h(x₂))
 
Precompute: table[g(x₁)] = x₁  for all x₁ in space₁
Search:     for each x₂ in space₂:
              if h(x₂) in table:
                found! (x₁, x₂)
 
Time:  O(2^(n/2)) instead of O(2^n)
Space: O(2^(n/2))

# Format 1: Find x such that SHA256(prefix + x) starts with N zero bits
import hashlib
def solve_pow_prefix(prefix, zero_bits):
    target = '0' * (zero_bits // 4)
    i = 0
    while True:
        candidate = prefix + str(i)
        h = hashlib.sha256(candidate.encode()).hexdigest()
        if h.startswith(target):
            return str(i)
        i += 1
# Format 2: Find x such that SHA256(x) ends with specific suffix
def solve_pow_suffix(suffix_hex, hash_func=hashlib.sha256):
    i = 0
    while True:
        h = hash_func(str(i).encode()).hexdigest()
        if h.endswith(suffix_hex):
            return str(i)
        i += 1

# hashcat for SHA256 PoW
hashcat -a 3 -m 1400 --hex-charset \
  "0000000000000000000000000000000000000000000000000000000000000000:prefix" \
  "?a?a?a?a?a?a?a?a"

Precomputed chain: password → hash → reduce → password₂ → hash₂ → ...
Lookup: given hash h, check if h appears in any chain
Time-memory tradeoff: less space than full table, more time than direct lookup

Without salt: H(password) — same password always produces same hash
With salt:    H(salt || password) — different salt per user
 
Rainbow tables are password-specific, not (salt+password)-specific
Each unique salt requires a separate table → infeasible

Hash-related challenge — what's the scenario?
│
├─ Have H(secret || message), need to extend?
│  ├─ Hash is MD5/SHA1/SHA256/SHA512?
│  │  └─ Yes → Length extension attack
│  │     └─ Need: MAC value, original message, secret length
│  │        └─ Tool: HashPump or hash_extender
│  │
│  └─ Hash is SHA3/HMAC/BLAKE2?
│     └─ Length extension doesn't work
│        └─ Look for other vulnerabilities
│
├─ Need two inputs with same hash?
│  ├─ MD5?
│  │  ├─ Same prefix → fastcoll (seconds)
│  │  ├─ Different prefixes → hashclash (hours)
│  │  └─ CTF PHP loose comparison → 0e magic hashes
│  │
│  ├─ SHA-1?
│  │  └─ SHAttered (expensive, use precomputed if possible)
│  │
│  └─ SHA-256+?
│     └─ No practical collision attack
│        └─ Look for logic flaws instead
│
├─ Need to forge HMAC?
│  ├─ Timing side channel available?
│  │  └─ Byte-by-byte timing attack
│  │
│  ├─ Key is short/weak?
│  │  └─ Brute force key with hashcat
│  │
│  └─ No weakness?
│     └─ HMAC is secure — look elsewhere
│
├─ Hash is truncated (short output)?
│  └─ Birthday attack — collision in 2^(bits/2)
│
├─ Proof of work?
│  └─ Brute force with parallel computation
│     ├─ Python multiprocessing for < 28 bits
│     ├─ hashcat/GPU for > 28 bits
│     └─ Optimize: pre-increment string, avoid re-encoding
│
└─ Password hash cracking?
   ├─ No salt → rainbow tables (pre-computed)
   ├─ Known salt → hashcat / John the Ripper
   └─ Memory-hard (Argon2/scrypt) → limited by memory, slow brute force