---
name: CTF Cryptography
slug: ctf-cryptography-2
category: Automation
description: CTF Cryptography provides cryptography attack techniques for CTF challenges. Use it for attacking encryption, hashing, signatures, ZKP, PRNG, and mathematical crypto problems involving RSA, AES, ECC, lattices, LWE, and more.
github: "https://github.com/ljagiello/ctf-skills/tree/main/ctf-crypto"
language: Python
stars: 3004
forks: 353
install: "npx degit https://github.com/ljagiello/ctf-skills/tree/main/ctf-crypto ~/.claude/skills/ctf-crypto"
installs_to: ~/.claude/skills/ctf-crypto
source_path: ctf-crypto/SKILL.md
collection_size: 11
category_size: 1523
collection_url: "https://dirskills.com/collections/ljagiello/ctf-skills"
added: 2026-08-17T07:09:20.071Z
last_synced: 2026-08-17T07:09:20.071Z
canonical_url: "https://dirskills.com/skills/ctf-cryptography-2"
---

# CTF Cryptography

CTF Cryptography provides cryptography attack techniques for CTF challenges. Use it for attacking encryption, hashing, signatures, ZKP, PRNG, and mathematical crypto problems involving RSA, AES, ECC, lattices, LWE, and more.

**Install:**

```bash
npx degit https://github.com/ljagiello/ctf-skills/tree/main/ctf-crypto ~/.claude/skills/ctf-crypto
```

## README

# CTF Cryptography

Quick reference for crypto CTF challenges. Each technique has a one-liner here; see supporting files for full details with code.

## Prerequisites

**Python packages (all platforms):**
```bash
pip install pycryptodome z3-solver sympy gmpy2 hashpumpy fpylll py_ecc
```

**Linux (apt):**
```bash
apt install hashcat sagemath
```

**macOS (Homebrew):**
```bash
brew install hashcat
```

**Manual install:**
- SageMath — Linux: `apt install sagemath`, macOS: `brew install --cask sage`
- RsaCtfTool — `git clone https://github.com/RsaCtfTool/RsaCtfTool` (automated RSA attacks)

> **Note:** `gmpy2` requires libgmp — Linux: `apt install libgmp-dev`, macOS: `brew install gmp`.

## Additional Resources

- [classic-ciphers.md](classic-ciphers.md) - Classic ciphers: Vigenere (+ Kasiski examination), Atbash, substitution wheels, XOR variants (+ multi-byte frequency analysis), deterministic OTP, cascade XOR, book cipher, OTP key reuse / many-time pad, variable-length homophonic substitution, grid permutation cipher keyspace reduction, image-based Caesar shift ciphers, XOR key recovery via file format headers
- [modern-ciphers.md](modern-ciphers.md) - Modern cipher attacks: AES (CFB-8, ECB leakage), CBC-MAC/OFB-MAC, padding oracle, S-box collisions, GF(2) elimination, LCG partial output recovery, affine cipher over composite modulus, AES-GCM with derived keys, AES-GCM nonce reuse (forbidden attack), Ascon-like reduced-round differential cryptanalysis, custom linear MAC forgery, CBC padding oracle (full block decryption), Bleichenbacher RSA PKCS#1 v1.5 padding oracle (ROBOT), birthday attack / meet-in-the-middle, CRC32 collision signature forgery, AES key recovery via byte-by-byte zeroing oracle, AES-CBC ciphertext forging via error-message decryption oracle
- [modern-ciphers-2.md](modern-ciphers-2.md) - Modern cipher attacks (Part 2): Blum-Goldwasser bit-extension oracle, hash length extension, compression oracle (CRIME-style), hash function time reversal via cycle detection, OFB mode invertible RNG backward decryption, weak key derivation via public key hash XOR, HMAC-CRC linearity attack, DES weak keys in OFB mode, SRP protocol bypass, modified AES S-Box brute-force, square attack on reduced-round AES, AES-ECB byte-at-a-time chosen plaintext, AES-ECB cut-and-paste block manipulation, AES-CBC IV bit-flip auth bypass, Rabin LSB parity oracle, PBKDF2 pre-hash bypass, MD5 multi-collision via fastcol
- [modern-ciphers-3.md](modern-ciphers-3.md) - Modern cipher attacks (Part 3): custom hash state reversal, CRC32 brute-force for small payloads, noisy RSA LSB oracle error correction, sponge hash MITM collision, CBC IV forgery + block truncation, padding oracle to CBC bitflip RCE, SPN S-box intersection attack, AES-CFB IV recovery from timestamp-seeded PRNG, three-round XOR protocol key cancellation, AES-CBC UnicodeDecodeError side-channel oracle, SHA-256 basis attack for XOR-aggregate hash bypass, custom MAC forgery via XOR block cancellation, HMAC key recovery via XOR+addition arithmetic
- [stream-ciphers.md](stream-ciphers.md) - Stream cipher attacks: LFSR (Berlekamp-Massey, correlation attack, known-plaintext, Galois vs Fibonacci, Galois tap recovery via autocorrelation), RC4 second-byte bias, XOR consecutive byte correlation
- [rsa-attacks.md](rsa-attacks.md) - RSA attacks: small e (cube root), common modulus, Wiener's, Pollard's p-1, Hastad's broadcast, Hastad with linear padding (Coppersmith), Franklin-Reiter related message (e=3), Coppersmith linearly-related primes, Fermat/consecutive primes, multi-prime, restricted-digit, Coppersmith structured primes, Manger oracle, polynomial hash
- [rsa-attacks-2.md](rsa-attacks-2.md) - RSA attacks (specialized): RSA p=q validation bypass, cube root CRT gcd(e,phi)>1, factoring from phi(n) multiple, multiplicative homomorphism signature forgery, weak keygen via base representation, RSA with gcd(e,phi)>1 exponent reduction, batch GCD shared prime factoring, partial key recovery from dp/dq/qinv, RSA-CRT fault attack, homomorphic decryption oracle bypass, small prime CRT decomposition, Montgomery reduction timing attack, Bleichenbacher low-exponent signature forgery, RSA signature bypass with e=1 and crafted modulus
- [ecc-attacks.md](ecc-attacks.md) - ECC attacks: small subgroup, invalid curve, Smart's attack (anomalous, with Sage code), fault injection, clock group DLP, Pohlig-Hellman, ECDSA nonce reuse, Ed25519 torsion side channel, DSA nonce reuse, DSA key recovery via MD5 collision on k-generation
- [zkp-and-advanced.md](zkp-and-advanced.md) - ZKP/graph 3-coloring, Z3 solver guide, garbled circuits, Shamir SSS, bigram constraint solving, race conditions, Groth16 broken setup, DV-SNARG forgery, KZG pairing oracle for permutation recovery, Shamir SSS reused polynomial coefficients
- [prng.md](prng.md) - PRNG attacks (foundational): MT19937, MT float recovery via GF(2) magic matrix for token prediction, LCG, GF(2) matrix PRNG, V8 XorShift128+ Math.random state recovery via Z3, middle-square, deterministic RNG hill climbing, random-mode oracle, time-based seeds, C srand/rand synchronization via ctypes, password cracking, logistic map chaotic PRNG
- [prng-attacks.md](prng-attacks.md) - PRNG attacks (CTF-era, 2017+): MT subset-sum seed recovery, MT19937 constraint propagation, Rule 86 cellular automaton reversal via Z3, Java LCG meet-in-the-middle partial modulo, LCG backward stepping via modular inverse, LFSR bit-fold ASCII parity, Z3 solve-time timing oracle, randcrack DSA k prediction, format-string PRNG seed offset, NTP-poisoned PRNG UUID XOR
- [historical.md](historical.md) - Historical ciphers (Lorenz SZ40/42, book cipher implementation)
- [advanced-math.md](advanced-math.md) - Advanced mathematical attacks (isogenies, Pohlig-Hellman, baby-step giant-step (BSGS) for general DLP, LLL, Merkle-Hellman knapsack via LLL, Coppersmith, quaternion RSA, GF(2)[x] CRT, S-box collision code, LWE lattice CVP attack, affine cipher over non-prime modulus, introspective CRC via GF(2) linear algebra)
- [lattice-and-lwe.md](lattice-and-lwe.md) - Lattice attack triage and workflow: LLL/BKZ/Babai, HNP from partial or biased nonces, truncated LCG state recovery, LWE embedding and CVP, Ring-LWE / Module-LWE recognition, orthogonal lattices, subset sum / knapsack, and common failure modes
- [exotic-crypto.md](exotic-crypto.md) - Exotic algebraic structures (braid group DH / Alexander polynomial, monotone function inversion, tropical semiring residuation, Paillier cryptosystem, Hamming code helical interleaving, ElGamal universal re-encryption, FPE Feistel brute-force, icosahedral symmetry group cipher, Goldwasser-Micali replication oracle)
- [exotic-crypto-2.md](exotic-crypto-2.md) - Exotic algebraic structures (Part 2, 2017+): BB-84 QKD MITM, ElGamal trivial DLP (B=p-1), Paillier LSB oracle via homomorphic doubling, differential privacy noise cancellation, homomorphic encryption bit-extraction, ElGamal over matrices via Jordan normal form, OSS signature forgery via Pollard, Cayley-Purser decryption without private key, BIP39 partial mnemonic checksum brute force, Asmuth-Bloom CRT threshold recovery, Rabin with polynomial primes, LCG period detection, Vandermonde polynomial coefficient recovery

---

## When to Pivot

- If the real blocker is understanding a binary, obfuscated client, or weird VM, switch to `/ctf-reverse`.
- If the challenge is mostly packet carving, disk recovery, or stego extraction before any decryption starts, switch to `/ctf-forensics`.
- If the task is just implementing an exploit against a vulnerable network service after the crypto part is solved, switch to `/ctf-pwn` or `/ctf-web`.
- If the crypto challenge involves adversarial ML, model extraction, or neural-network-based ciphers, switch to `/ctf-ai-ml`.
- If the challenge is really an encoding puzzle, esoteric cipher, or polyglot trick rather than true cryptanalysis, switch to `/ctf-misc`.

## Quick Start Commands

```bash
# Identify cipher type
python3 -c "from Crypto.Util.number import *; n=<N>; print(f'bits={n.bit_length()}')"

# RSA quick check
python3 -c "from sympy import factorint; print(factorint(<n>))"  # Small factors?
openssl rsa -pubin -in key.pub -text -noout  # Extract n, e from PEM

# Quick factorization tools
python3 RsaCtfTool.py -n <n> -e <e> --uncipher <c>

# XOR analysis
python3 -c "from pwn import xor; print(xor(bytes.fromhex('<hex>'), b'flag{'))"

# Hash identification
hashid '<hash>'
hashcat --identify '<hash>'

# SageMath (for lattice/ECC)
sage -c "print(factor(<n>))"
```

## Classic Ciphers

- **Caesar:** Frequency analysis or brute force 26 keys
- **Vigenere:** Known plaintext attack with flag format prefix; derive key from `(ct - pt) mod 26`. Kasiski examination for unknown key length (GCD of repeated sequence distances)
- **Atbash:** A<->Z substitution; look for "Abashed" hints in challenge name
- **Substitution wheel:** Brute force all rotations of inner/outer alphabet mapping
- **Multi-byte XOR:** Split ciphertext by key position, frequency-analyze each column independently; score by English letter frequency (space = 0x20)
- **Cascade XOR:** Brute force first byte (256 attempts), rest follows deterministically
- **XOR rotation (power-of-2):** Even/odd bits never mix; only 4 candidate states
- **Weak XOR verification:** Single-byte XOR check has 1/256 pass rate; brute force with enough budget
- **Deterministic OTP:** Known-plaintext XOR to recover keystream; match load-balanced backends
- **OTP key reuse (many-time pad):** `C1 XOR C2 XOR known_P = unknown_P`; crib dragging when no plaintext known
- **Homophonic (variable-length):** Multi-character ciphertext groups map to single plaintext chars. Find n-grams with identical sub-n-gram frequencies, replace with symbols, solve as monoalphabetic. See [classic-ciphers.md](classic-ciphers.md#variable-length-homophonic-substitution-asis-ctf-finals-2013).
- **Grid permutation cipher:** 5x5 grid with independent row/column permutations collapses keyspace to 5! x 5! = 14,400; brute-force in milliseconds. See [classic-ciphers.md](classic-ciphers.md#grid-permutation-cipher-keyspace-reduction-bsidessf-2026).
- **Image-based Caesar shift:** Pixel rows/columns shifted by per-strip offsets; compare original vs shifted image to extract ASCII-encoded flag from shift amounts. See [classic-ciphers.md](classic-ciphers.md#image-based-caesar-shift-ciphers-bsidessf-2026).
- **Polybius square cipher:** 5x5 grid maps letter pairs to plaintext; digits/coordinates encode positions. See [classic-ciphers.md](classic-ciphers.md#polybius-square-cipher-qiwi-infosec-2016).
- **XOR key recovery via file format headers:** File claims to be PDF/PNG/ZIP but `file` reports "data". XOR first bytes against expected magic bytes to derive repeating key; extend using trailer structures (`%%EOF`, IEND marker). See [classic-ciphers.md](classic-ciphers.md#xor-key-recovery-via-file-format-headers-metactf-flash-2026).

See [classic-ciphers.md](classic-ciphers.md) for full code examples.

## Modern Cipher Attacks

- **AES-ECB:** Block shuffling, byte-at-a-time chosen-plaintext suffix recovery (256 queries per byte, tool: FeatherDuster `ecb_cpa_decrypt`); image ECB preserves visual patterns. ECB cut-and-paste: splice ciphertext blocks to forge JSON fields (e.g., `is_admin: true`). See [modern-ciphers-2.md](modern-ciphers-2.md#aes-ecb-byte-at-a-time-chosen-plaintext-abctf-2016).
- **AES-CBC:** Bit flipping to change plaintext; padding oracle for decryption without key. IV bit-flip: flip specific bits in the IV to change first plaintext block (requires no MAC). See [modern-ciphers-2.md](modern-ciphers-2.md#aes-cbc-iv-bit-flip-authentication-bypass-google-ctf-2016).
- **CBC IV forgery + block truncation:** XOR IV bytes to change decrypted block 0; strip trailing ciphertext blocks (no length integrity in CBC). Forges authenticated tokens when MAC is embedded in the ciphertext. See [modern-ciphers-2.md](modern-ciphers-3.md#cbc-iv-forgery--block-truncation-for-authentication-bypass-0ctf-2017).
- **Padding oracle to CBC bitflip RCE:** Chain padding oracle (recover plaintext) with CBC bitflipping (inject shell metacharacters) for command injection via encrypted parameters. See [modern-ciphers-2.md](modern-ciphers-3.md#padding-oracle-to-cbc-bitflip-command-injection-bsidessf-2017).
- **AES-CFB-8:** Static IV with 8-bit feedback allows state reconstruction after 16 known bytes
- **CBC-MAC/OFB-MAC:** XOR keystream for signature forgery: `new_sig = old_sig XOR block_diff`
- **S-box collisions:** Non-permutation S-box (`len(set(sbox)) < 256`) enables 4,097-query key recovery
- **GF(2) elimination:** Linear hash functions (XOR + rotations) solved via Gaussian elimination over GF(2)
- **Padding oracle:** Byte-by-byte decryption by modifying previous block and testing padding validity
- **LFSR stream ciphers:** Berlekamp-Massey recovers feedback polynomial from 2L keystream bits; correlation attack breaks combined generators with biased combining functions
- **Galois LFSR tap recovery:** XOR known file header (PNG/PDF/ZIP) with ciphertext to get keystream; split into N-bit windows, compute `(state >> 1) XOR next_state` for LSB=1 transitions to directly recover tap mask. Autocorrelation sliding finds correct length. See [stream-ciphers.md](stream-ciphers.md#galois-lfsr-tap-recovery-via-autocorrelation-bsidessf-2026).
- **OFB with invertible RNG:** Known plaintext in any block leaks RNG state; if state transition is bijective, run RNG backwards to decrypt all blocks. See [modern-ciphers-2.md](modern-ciphers-2.md#ofb-mode-with-invertible-rng-backward-decryption-bsidessf-2026).
- **Weak key derivation (public key hash XOR):** AES key derived from `SHA256(public_key) XOR seed` is fully recoverable without private key; "hybrid" RSA+AES provides no security. See [modern-ciphers-2.md](modern-ciphers-2.md#weak-key-derivation-via-public-key-hash-xor-bsidessf-2026).
- **HMAC-CRC linearity:** CRC is linear over GF(2), so HMAC-CRC key is recoverable from a single message-MAC pair via polynomial arithmetic. See [modern-ciphers-2.md](modern-ciphers-2.md#hmac-crc-linearity-attack-boston-key-party-2016).
- **DES weak keys in OFB:** 4 DES weak keys make encryption self-inverse; OFB keystream cycles with period 2, reducing to 16-byte repeating XOR. See [modern-ciphers-2.md](modern-ciphers-2.md#des-weak-keys-in-ofb-mode-boston-key-party-2016).
- **Square attack (reduced-round AES):** 4-round AES broken by integral cryptanalysis: 256-plaintext lambda set, guess last round key bytes via XOR-sum = 0 distinguisher. See [modern-ciphers-2.md](modern-ciphers-2.md#square-attack-on-reduced-round-aes-0ctf-2016).
- **AES-GCM nonce reuse (forbidden attack):** Same nonce = CTR keystream reuse + GHASH authentication key recovery via polynomial factoring over GF(2^128). Tool: `nonce-disrespect`. See [modern-ciphers.md](modern-ciphers.md#aes-gcm-nonce-reuse--forbidden-attack).
- **SRP protocol bypass:** Send `A = 0` or `A = n` to force shared secret to 0, bypassing password verification entirely. See [modern-ciphers-2.md](modern-ciphers-2.md#srp-secure-remote-password-protocol-bypass-via-modular-arithmetic-asis-ctf-finals-2016).
- **Modified AES S-Box brute force:** Custom S-Box with only 16 unique outputs reduces key entropy; brute-force feasible key bytes per round. See [modern-ciphers-2.md](modern-ciphers-2.md#modified-aes-s-box-brute-force-recovery-h4ckit-ctf-2016).
- **Rabin LSB parity oracle:** Rabin ciphertext `c = m^2 mod n` with LSB oracle enables binary search plaintext recovery in `log2(n)` queries via multiplicative homomorphism (`c * 4 mod n` doubles plaintext). See [modern-ciphers-2.md](modern-ciphers-2.md#rabin-cryptosystem-lsb-parity-oracle-plaidctf-2016).
- **Noisy RSA LSB oracle error correction:** When LSB oracle has sporadic errors, run standard attack then inspect output charset. Flip oracle results at error positions to correct remaining decryption. See [modern-ciphers-2.md](modern-ciphers-3.md#noisy-rsa-lsb-oracle-with-post-hoc-error-correction-sharifctf-7-2016).
- **PBKDF2 pre-hash bypass:** HMAC pre-hashes keys > 64 bytes (SHA-1/SHA-256 block size). Login with `SHA1(password)` instead of `password` when original exceeds 64 bytes. See [modern-ciphers-2.md](modern-ciphers-2.md#pbkdf2-pre-hash-bypass-for-long-passwords-backdoorctf-2016).
- **MD5 multi-collision (fastcol):** Chain `fastcol` runs to produce 2^k files with identical MD5. Merkle-Damgard composition: collisions propagate through appended suffixes. See [modern-ciphers-2.md](modern-ciphers-2.md#md5-multi-collision-via-fastcol-backdoorctf-2016).
- **Custom hash state reversal:** When iterative hash leaks intermediate states, isolate per-block hash values by inverting the state update equation, then brute-force each 4-byte block independently. See [modern-ciphers-2.md](modern-ciphers-3.md#custom-hash-state-reversal-via-known-intermediates-backdoorctf-2016).
- **CRC32 brute-force (small payloads):** ZIP CRC32 headers are unencrypted; brute-force content of small files (≤ 6 bytes) by checking all printable strings against stored CRC32. See [modern-ciphers-2.md](modern-ciphers-3.md#crc32-brute-force-for-small-payloads-backdoorctf-2016).
- **Custom MAC forgery via XOR block cancellation:** When MAC key stream repeats periodically, craft three queries where filler blocks cancel via XOR, forging any target command's MAC. See [modern-ciphers-2.md](modern-ciphers-3.md#custom-mac-forgery-via-xor-block-cancellation-with-key-rotation-plaidctf-2018).
- **HMAC key recovery (XOR + addition arithmetic):** Flawed HMAC using `sha256((key XOR msg) + msg)` leaks key bits: `msg=0` gives `sha256(key)`, `msg=2^i` matches iff key bit `i` is set. See [modern-ciphers-2.md](modern-ciphers-3.md#bit-by-bit-hmac-key-recovery-via-xor-plus-addition-arithmetic-midnight-sun-ctf-2018).
- **AES-CBC ciphertext forging (error-message oracle):** Server leaks decrypted bytes in error messages; send zero blocks to learn intermediate state, XOR with desired plaintext to forge ciphertext block-by-block. See [modern-ciphers.md](modern-ciphers.md#aes-cbc-ciphertext-forging-via-error-message-decryption-oracle-nuit-du-hack-ctf-2018).

See [modern-ciphers.md](modern-ciphers.md) and [modern-ciphers-2.md](modern-ciphers-2.md) for full code examples.

## RSA Attacks

- **Small e with small message:** Take eth root
- **Common modulus:** Extended GCD attack
- **Wiener's attack:** Small d
- **Fermat factorization:** p and q close together
- **Pollard's p-1:** Smooth p-1
- **Hastad's broadcast:** Same message, multiple e=3 encryptions
- **Consecutive primes:** q = next_prime(p); find first prime below sqrt(N)
- **Multi-prime:** Factor N with sympy; compute phi from all factors
- **Restricted-digit primes:** Digit-by-digit factoring from LSB with modular pruning
- **Coppersmith structured primes:** Partially known prime; `f.small_roots()` in SageMath
- **Manger oracle (simplified):** Phase 1 doubling + phase 2 binary search; ~128 queries for 64-bit key
- **Manger on RSA-OAEP (timing):** Python `or` short-circuit skips expensive PBKDF2 when Y != 0, creating fast/slow timing oracle. Full 3-step attack (~1024 iterations for 1024-bit RSA). Calibrate timing bounds with known-fast/known-slow samples.
- **Polynomial hash (trivial root):** `g(0) = 0` for polynomial hash; craft suffix for `msg = 0 (mod P)`, signature = 0
- **Polynomial CRT in GF(2)[x]:** Collect ~20 remainders `r = flag mod f`, filter coprime, CRT combine
- **Affine over composite modulus:** CRT in each prime factor field; Gauss-Jordan per prime
- **RSA p=q validation bypass:** Set `p=q` so server computes wrong `phi=(p-1)^2` instead of `p*(p-1)`; test decryption fails, leaking ciphertext
- **RSA cube root CRT (gcd(e,phi)>1):** When all primes ≡ 1 mod e, compute eth roots per-prime via `nthroot_mod`, enumerate CRT combinations (3^k feasible for small k)
- **Factoring from phi(n) multiple:** Any multiple of `phi(n)` (e.g., `e*d-1`) enables factoring via Mil