ctf-crypto

name	ctf-crypto
description	Provides cryptography attack techniques for CTF challenges. Use when attacking encryption, hashing, signatures, ZKP, PRNG, or mathematical crypto problems involving RSA, AES, ECC, lattices, LWE, CVP, number theory, Coppersmith, Pollard, Wiener, padding oracle, GCM, key derivation, or stream/block cipher weaknesses.
license	MIT
compatibility	Requires filesystem-based agent (Claude Code or similar) with bash, Python 3, and internet access for tool installation.
allowed-tools	Bash Read Write Edit Glob Grep Task WebFetch WebSearch
metadata	{"user-invocable":"false"}

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):

pip install pycryptodome z3-solver sympy gmpy2 hashpumpy fpylll py_ecc

Linux (apt):

apt install hashcat sagemath

macOS (Homebrew):

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: 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 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
• modern-ciphers-2.md - Modern cipher attacks (continued): 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, 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
• 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: small e (cube root), common modulus, Wiener's, Pollard's p-1, Hastad's broadcast, Fermat/consecutive primes, multi-prime, restricted-digit, Coppersmith structured primes, Manger oracle, polynomial hash
• 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
• 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
• 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
• prng.md - PRNG attacks (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)
• historical.md - Historical ciphers (Lorenz SZ40/42, book cipher implementation)
• 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)
• 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)

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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.
• 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.
• 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.
• Polybius square cipher: 5x5 grid maps letter pairs to plaintext; digits/coordinates encode positions. See classic-ciphers.md.
• 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.

See 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• SRP protocol bypass: Send A = 0 or A = n to force shared secret to 0, bypassing password verification entirely. See modern-ciphers-2.md.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.

See modern-ciphers.md and 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 Miller-Rabin square root technique; succeeds with prob ≥ 1/2 per attempt
• Weak keygen via base representation: Primes p = kp*B + tp with small kp create mixed-radix structure in n; brute-force kp*kq (2^24) to factor
• RSA with gcd(e,phi)>1 (exponent reduction): Reduce e' = e/g, compute d' = e'^(-1) mod phi, partial decrypt to m^g, then take g-th root over integers
• RSA partial key recovery (dp/dq/qinv): CRT exponents from partial PEM leak allow O(e) prime recovery: iterate k, check if (dp*e-1)/k+1 is prime. See rsa-attacks-2.md.