//! CSS title-key recovery — Frank A. Stevenson's divide-and-conquer attack //! (1999), ported exactly from libdvdcss `RecoverTitleKey` + `AttackPattern` //! (css.c). //! //! Recovers the 5-byte CSS title key from a single scrambled DVD sector with //! no player keys and no disc-key crack, using only known plaintext. //! //! # The cipher this attacks //! //! The content descrambler ([`super::lfsr::descramble_sector`], = libdvdcss //! `dvdcss_unscramble`) seeds its two LFSRs **directly** from //! `key = title_key XOR sector_seed` (seed = `sector[0x54..0x59]`): //! //! ```text //! i_t1 = (key[0] ^ sec[0x54]) | 0x100; // LFSR1 low (9-bit) //! i_t2 = key[1] ^ sec[0x55]; // LFSR1 high //! i_t3 = (key[2]|key[3]<<8|key[4]<<16) ^ seed3; // LFSR0 (24-bit feedback) //! i_t3 = i_t3*2 + 8 - (i_t3 & 7); //! // per byte: *p = TAB1[*p] ^ (i_t5 & 0xff) //! ``` //! //! There is NO `decrypt_key` mangling on the content path. So the recovery //! is a single inversion of `dvdcss_unscramble`, not the multi-stage //! working-key inversion the previous (non-CSS) implementation used. //! //! # The attack //! //! 1. **Known plaintext → keystream.** Because the descramble applies TAB1 //! to the ciphertext, the per-byte keystream is //! `buf[i] = TAB1[cipher[i]] ^ plain[i]` (matching libdvdcss //! `RecoverTitleKey`'s `p_buffer`). //! 2. **Brute the 16-bit LFSR1 seed.** For each of 2^16 seeds, run LFSR1 //! forward; for the first four steps deduce the LFSR0 output bytes from //! the keystream (carry-tracked), reconstructing `i_t3`. For the next six //! steps clock LFSR0 normally and check it reproduces the keystream — a //! wrong LFSR1 seed fails fast. //! 3. **Back-clock LFSR0.** Run four backward `i_t3` steps (each a 256-way //! search for the byte shifted in) to reach the initial state, then undo //! `i_t3 = i_t3*2 + 8 - (i_t3 & 7)` to recover key[2..5]. //! 4. **XOR back the seed.** `key[0..5] ^= sector_seed[0..5]` (plain XOR — //! the descramble seeds directly, so there is no inversion). //! //! `AttackPattern` finds known plaintext for step 1: the longest periodic //! run in the cleartext `sec[0x00..0x80]`, assumed to continue into the //! encrypted region at 0x80. use super::lfsr::descramble_sector; use super::tables::{TAB1, TAB2, TAB3, TAB4, TAB5}; use crate::consts::SECTOR_BYTES; const ENCRYPTED_START: usize = 0x80; // byte 128 const SEED_OFFSET: usize = 0x54; // sector seed at bytes 0x54-0x58 const FLAG_BYTE: usize = 0x14; /// RecoverTitleKey: recover the title key from cipher + known plaintext. /// /// Exact port of libdvdcss `RecoverTitleKey` (css.c). `crypted` is the /// ciphertext starting at sector byte 0x80; `decrypted` is the matching /// known plaintext; `seed` is `sector[0x54..0x59]`. On success returns the /// recovered 5-byte title key; `None` if no LFSR seed reproduces the /// keystream. /// /// At least 10 bytes of `crypted`/`decrypted` are required (the cipher is /// iterated 10 times: 4 to reconstruct LFSR0, 6 to validate). fn recover_title_key_from_plain( crypted: &[u8], decrypted: &[u8], seed: &[u8; 5], ) -> Option<[u8; 5]> { if crypted.len() < 10 || decrypted.len() < 10 { return None; } // buf[i] = TAB1[cipher[i]] ^ plain[i] — the per-byte content keystream. let mut buffer = [0u8; 10]; for (i, b) in buffer.iter_mut().enumerate() { *b = TAB1[crypted[i] as usize] ^ decrypted[i]; } let mut key = [0u8; 5]; let mut found = false; for i_try in 0u32..0x1_0000 { let mut i_t1 = (i_try >> 8) | 0x100; let mut i_t2 = i_try & 0xff; let mut i_t3: u32 = 0; // not needed yet let mut i_t5: u32 = 0; // Iterate the cipher 4 times to reconstruct LFSR0 (i_t3). for &b in buffer.iter().take(4) { let i_t4 = (TAB2[i_t2 as usize] ^ TAB3[i_t1 as usize]) as u32; i_t2 = i_t1 >> 1; i_t1 = ((i_t1 & 1) << 8) ^ i_t4; let i_t4 = TAB5[i_t4 as usize] as u32; // Deduce i_t6 (LFSR0 output, pre-TAB4) and the carry. let mut i_t6 = b as u32; if i_t5 != 0 { i_t6 = (i_t6 + 0xff) & 0xff; } if i_t6 < i_t4 { i_t6 += 0x100; } i_t6 -= i_t4; i_t5 += i_t6 + i_t4; let i_t6 = TAB4[i_t6 as usize] as u32; i_t3 = (i_t3 << 8) | i_t6; i_t5 >>= 8; } let i_candidate = i_t3; // Iterate 6 more times to validate the candidate. let mut i = 4usize; while i < 10 { let i_t4 = (TAB2[i_t2 as usize] ^ TAB3[i_t1 as usize]) as u32; i_t2 = i_t1 >> 1; i_t1 = ((i_t1 & 1) << 8) ^ i_t4; let i_t4 = TAB5[i_t4 as usize] as u32; let mut i_t6 = (((((((i_t3 >> 3) ^ i_t3) >> 1) ^ i_t3) >> 8) ^ i_t3) >> 5) & 0xff; i_t3 = (i_t3 << 8) | i_t6; i_t6 = TAB4[i_t6 as usize] as u32; i_t5 += i_t6 + i_t4; if (i_t5 & 0xff) as u8 != buffer[i] { break; } i_t5 >>= 8; i += 1; } if i != 10 { continue; } // Four backward steps of iterating i_t3 to deduce the initial state. i_t3 = i_candidate; for _ in 0..4 { let i_t1_byte = i_t3 & 0xff; i_t3 >>= 8; // Brute-force the byte shifted in (top byte of the 24-bit reg). for j in 0u32..256 { i_t3 = (i_t3 & 0x1_ffff) | (j << 17); let i_t6 = (((((((i_t3 >> 3) ^ i_t3) >> 1) ^ i_t3) >> 8) ^ i_t3) >> 5) & 0xff; if i_t6 == i_t1_byte { break; } } } // Undo `i_t3 = i_t3*2 + 8 - (i_t3 & 7)` to recover key[2..5]. let i_t4 = (i_t3 >> 1).wrapping_sub(4); for i_t5 in 0u32..8 { let val = i_t4.wrapping_add(i_t5); if val.wrapping_mul(2).wrapping_add(8).wrapping_sub(val & 7) == i_t3 { key[0] = (i_try >> 8) as u8; key[1] = (i_try & 0xff) as u8; key[2] = (val & 0xff) as u8; key[3] = ((val >> 8) & 0xff) as u8; key[4] = ((val >> 16) & 0xff) as u8; found = true; break; } } // First fully-validated candidate wins. The 48-bit keystream constraint // makes a second match cryptographically negligible on real sectors, but // continuing would let a later spurious match overwrite a correct key. if found { break; } } if found { for (k, &s) in key.iter_mut().zip(seed.iter()) { *k ^= s; } Some(key) } else { None } } /// Recover the CSS title key from a scrambled sector using a known plaintext /// for the encrypted region. /// /// `plain` is the expected plaintext at byte 0x80 (at least 10 bytes). /// Returns the recovered key only if it actually descrambles the sector back /// to `plain` — guarding against the rare spurious LFSR-seed match. pub fn recover_title_key(sector: &[u8], plain: &[u8]) -> Option<[u8; 5]> { if sector.len() < SECTOR_BYTES || plain.len() < 10 { return None; } if sector[FLAG_BYTE] & 0x30 == 0 { return None; } let seed: [u8; 5] = [ sector[SEED_OFFSET], sector[SEED_OFFSET + 1], sector[SEED_OFFSET + 2], sector[SEED_OFFSET + 3], sector[SEED_OFFSET + 4], ]; let crypted = §or[ENCRYPTED_START..ENCRYPTED_START + 10]; let key = recover_title_key_from_plain(crypted, plain, &seed)?; if descramble_matches(sector, &key, plain) { Some(key) } else { None } } /// Verify a title key by descrambling a copy of `sector` and checking the /// known plaintext reappears at byte 0x80. fn descramble_matches(sector: &[u8], title: &[u8; 5], plain: &[u8]) -> bool { let mut test = sector.to_vec(); test[FLAG_BYTE] |= 0x10; // ensure scramble flag set for the descrambler descramble_sector(title, &mut test); let n = plain.len().min(SECTOR_BYTES - ENCRYPTED_START); test[ENCRYPTED_START..ENCRYPTED_START + n] == plain[..n] } /// AttackPattern: find a repeating pattern just before the encrypted region /// and assume the plaintext at 0x80 continues it. /// /// Functionally-equivalent port of libdvdcss `AttackPattern` (css.c) — finds the /// same periodic cribs on real DVD data, though its byte-comparison anchor /// differs from the C on phase-misaligned runs. Scans cleartext /// `sec[0x00..0x80]` for the longest run that repeats with a cycle length in /// 2..0x2F. If the run is long enough (`plen > 3` and at least two full /// cycles), the known plaintext at 0x80 is taken to be the periodic run /// continuing forward, and [`recover_title_key_from_plain`] is applied. pub fn crack_title_key(sector: &[u8]) -> Option<[u8; 5]> { if sector.len() < SECTOR_BYTES { return None; } if sector[FLAG_BYTE] & 0x30 == 0 { return None; } // Runaway guard: a single sector's crack is a bounded 2^16 LFSR search and // should finish in well under a second on any modern CPU. If it ever // exceeds ~2s wall-clock, something pathological is happening — log it so a // hang is never silent. let crack_t0 = std::time::Instant::now(); let result = crack_title_key_inner(sector); let elapsed = crack_t0.elapsed(); if elapsed.as_secs_f64() > 2.0 { tracing::warn!( target: "freemkv::css", elapsed_ms = elapsed.as_millis() as u64, found = result.is_some(), "css crack: single-sector recovery exceeded 2s (runaway guard)" ); } result } /// AttackPattern crib: the predicted 10-byte plaintext at byte 0x80. /// /// Scans the clear header `sec[0x00..0x80]` (never scrambled) for the longest /// run that repeats with a cycle length in 2..0x2F. If the run is long enough /// (`plen > 3` and at least two full cycles), the plaintext at 0x80 is taken to /// be that periodic run continuing forward. Returns `None` for an unscrambled /// sector or one with no usable run — such a sector can be neither cracked nor /// key-validated, only descrambled with an externally-cached key. /// /// The header is untouched by `descramble_sector`, so the crib is identical /// before and after descramble: the decrypt path uses it as a per-sector /// "did the cached key descramble correctly?" oracle (the predicted plaintext /// must reappear at 0x80), and the cracker uses it as its known plaintext. pub(crate) fn attack_crib(sector: &[u8]) -> Option<[u8; 10]> { if sector.len() < SECTOR_BYTES || sector[FLAG_BYTE] & 0x30 == 0 { return None; } let mut best_plen: usize = 0; let mut best_p: usize = 0; // For all cycle lengths from 2 to 0x2F. for i in 2usize..0x30 { // Count bytes that repeat with cycle length i, scanning backward from // 0x7F. `sec[0x7F - (j % i)] == sec[0x7F - j]`. let mut j = i + 1; while j < 0x80 && sector[0x7f - (j % i)] == sector[0x7f - j] { if j > best_plen { best_plen = j; best_p = i; } j += 1; } } // Need at least a few repeated bytes and at least one full cycle. if best_plen > 3 && best_p > 0 && best_plen / best_p >= 2 { // The known plaintext is the periodic run continuing past 0x80. The // crib starts at `0x80 - (best_plen/best_p)*best_p` and continues // through the encrypted region; the bytes at and after 0x80 are the // predicted plaintext (the pattern repeats with period best_p). let cycles = best_plen / best_p; let plain_start = 0x80 - cycles * best_p; // Each predicted byte is the run sample one or more periods back: // `sec[plain_start + (i % best_p)]`. For in-run offsets // (`plain_start + i < 0x80`) the run is exactly periodic, so this // equals `sec[plain_start + i]`; for offsets at/after 0x80 the raw // byte is ciphertext, so we MUST wrap within the period rather than // read it. (Reading `&sec[plain_start..+10]` directly — as before — // pulled ciphertext into the crib whenever the run covered fewer than // 10 bytes before 0x80, producing false-negative key recovery.) let mut plain = [0u8; 10]; for (i, p) in plain.iter_mut().enumerate() { *p = sector[plain_start + (i % best_p)]; } Some(plain) } else { None } } fn crack_title_key_inner(sector: &[u8]) -> Option<[u8; 5]> { let plain = attack_crib(sector)?; let seed: [u8; 5] = [ sector[SEED_OFFSET], sector[SEED_OFFSET + 1], sector[SEED_OFFSET + 2], sector[SEED_OFFSET + 3], sector[SEED_OFFSET + 4], ]; let crypted = §or[0x80..0x80 + 10]; if let Some(key) = recover_title_key_from_plain(crypted, &plain, &seed) { // Verify against the same predicted plaintext. if descramble_matches(sector, &key, &plain) { return Some(key); } } None } #[cfg(test)] mod tests { use super::super::lfsr::scramble_sector; use super::*; /// Build a synthetic scrambled sector for a given title key and seed, /// with `plain` placed as the plaintext at byte 0x80, scrambled with /// EXACTLY the cipher `descramble_sector` inverts. Returns /// (scrambled_sector, full_plaintext_body). fn synth_sector(title_key: &[u8; 5], seed: &[u8; 5], plain: &[u8]) -> (Vec, Vec) { let mut plaintext = vec![0u8; SECTOR_BYTES]; plaintext[0..4].copy_from_slice(&[0x00, 0x00, 0x01, 0xBA]); plaintext[FLAG_BYTE] = 0x10; plaintext[SEED_OFFSET..SEED_OFFSET + 5].copy_from_slice(seed); plaintext[ENCRYPTED_START..ENCRYPTED_START + plain.len()].copy_from_slice(plain); let body = plaintext.clone(); // scramble_sector turns the plaintext body into ciphertext and sets // the scramble flag. scramble_sector(title_key, &mut plaintext); (plaintext, body) } /// Build a synthetic scrambled sector whose CLEARTEXT (0x00..0x80) ends /// in a periodic run that continues into the encrypted region — the case /// `AttackPattern` (crack_title_key) is designed to crack. fn synth_periodic_sector( title_key: &[u8; 5], seed: &[u8; 5], period: usize, ) -> (Vec, Vec) { let mut plaintext = vec![0u8; SECTOR_BYTES]; plaintext[FLAG_BYTE] = 0x10; // A clean periodic run occupying the tail of the cleartext header // (RUN_START..0x80) and continuing into the encrypted region. This // mirrors a real VOB: a periodic data run just before the scrambled // part. The run must NOT overlap the seed bytes (0x54..0x59), or the // AttackPattern detector would break mid-run. The phase is anchored to // offset 0 so the run is consistent across the 0x80 boundary. // Just above the seed (0x54..0x59); gives a 39-byte run (0x59..0x80) // — enough for >=2 cycles of every tested period (<=19). const RUN_START: usize = 0x59; let pat: Vec = (0..period) .map(|k| (0xA0u8.wrapping_add(k as u8)) ^ 0x5A) .collect(); for (i, b) in plaintext.iter_mut().enumerate().skip(RUN_START) { *b = pat[i % period]; } // Seed sits below the run, undisturbed. plaintext[SEED_OFFSET..SEED_OFFSET + 5].copy_from_slice(seed); let body = plaintext.clone(); scramble_sector(title_key, &mut plaintext); (plaintext, body) } #[test] fn crack_unscrambled_returns_none() { let sector = vec![0u8; SECTOR_BYTES]; assert!(crack_title_key(§or).is_none()); } #[test] fn crack_too_short_returns_none() { let sector = vec![0u8; 100]; assert!(crack_title_key(§or).is_none()); } #[test] fn recover_needs_min_plain() { let sector = vec![0u8; SECTOR_BYTES]; let short_plain = [0u8; 4]; assert!(recover_title_key(§or, &short_plain).is_none()); } /// The known plaintext used at byte 0x80 for the direct-recovery tests. /// A realistic MPEG-2 PES header start. const PES: [u8; 10] = [0x00, 0x00, 0x01, 0xE0, 0x00, 0x00, 0x80, 0x80, 0x05, 0x21]; /// MANDATORY round-trip (Task C.1): synthesize a scrambled sector for a /// known (title_key, seed), then assert recover_title_key returns a key /// that descrambles the body back to plaintext. CSS title-key recovery is /// well-defined up to keys that scramble identically; we assert the full /// body round-trips (the true correctness property), and additionally /// that the EXACT key is returned for the common case. #[test] fn recover_round_trips_known_keys() { let cases: &[([u8; 5], [u8; 5])] = &[ ( [0x42, 0x13, 0x37, 0xBE, 0xEF], [0x11, 0x22, 0x33, 0x44, 0x55], ), ( [0x01, 0x02, 0x03, 0x04, 0x05], [0xDE, 0xAD, 0xBE, 0xEF, 0x42], ), ( [0xFE, 0xDC, 0xBA, 0x98, 0x76], [0x00, 0xFF, 0x80, 0x7F, 0x01], ), ( [0x9A, 0x78, 0x56, 0x34, 0x12], [0xA5, 0x5A, 0x0F, 0xF0, 0xCC], ), ( [0xFF, 0xFF, 0xFF, 0xFF, 0xFF], [0x01, 0x01, 0x01, 0x01, 0x01], ), ]; for (title_key, seed) in cases { let (mut sector, body) = synth_sector(title_key, seed, &PES); let recovered = recover_title_key(§or, &PES).expect("recover_title_key returned None"); descramble_sector(&recovered, &mut sector); assert_eq!( §or[ENCRYPTED_START..SECTOR_BYTES], &body[ENCRYPTED_START..SECTOR_BYTES], "recovered key did not descramble the full body for \ title={title_key:02x?} seed={seed:02x?}" ); } } /// MANDATORY (Task C.1): the AttackPattern entry point crack_title_key — /// no plaintext supplied — recovers a round-tripping key when the /// cleartext ends in a periodic run that continues into 0x80. #[test] fn crack_title_key_recovers_via_attack_pattern() { for &period in &[2usize, 3, 5, 8, 16] { let title_key = [0x42, 0x13, 0x37, 0xBE, 0xEF]; let seed = [0x11, 0x22, 0x33, 0x44, 0x55]; let (sector, body) = synth_periodic_sector(&title_key, &seed, period); let cracked = crack_title_key(§or) .unwrap_or_else(|| panic!("crack_title_key returned None for period {period}")); let mut test = sector.clone(); descramble_sector(&cracked, &mut test); assert_eq!( &test[ENCRYPTED_START..SECTOR_BYTES], &body[ENCRYPTED_START..SECTOR_BYTES], "crack_title_key key did not round-trip the body (period {period})" ); } } /// recover_title_key_from_plain inverts dvdcss_unscramble exactly: scramble /// a known body, hand back the keystream-derived key, and the recovered /// key (XOR-back included) reproduces the plaintext. #[test] fn recovered_key_descrambles_back_to_plaintext() { let cases: &[([u8; 5], [u8; 5])] = &[ ( [0x42, 0x13, 0x37, 0xBE, 0xEF], [0x11, 0x22, 0x33, 0x44, 0x55], ), ( [0x9A, 0x78, 0x56, 0x34, 0x12], [0xA5, 0x5A, 0x0F, 0xF0, 0xCC], ), ( [0xFF, 0xFF, 0xFF, 0xFF, 0xFF], [0x01, 0x01, 0x01, 0x01, 0x01], ), ]; for (title_key, seed) in cases { let (mut sector, body) = synth_sector(title_key, seed, &PES); let recovered = recover_title_key(§or, &PES).expect("recover_title_key returned None"); descramble_sector(&recovered, &mut sector); assert_eq!( §or[ENCRYPTED_START..SECTOR_BYTES], &body[ENCRYPTED_START..SECTOR_BYTES], "descramble with recovered key did not reproduce the body \ for title={title_key:02x?} seed={seed:02x?}" ); } } // ── early-return guards ──────────────────────────────────────────────── #[test] fn recover_rejects_sector_one_byte_short() { let mut sector = vec![0u8; SECTOR_BYTES - 1]; sector[FLAG_BYTE] = 0x30; assert!(recover_title_key(§or, &PES).is_none()); } #[test] fn recover_rejects_unscrambled_sector() { let sector = vec![0x00u8; SECTOR_BYTES]; assert!(recover_title_key(§or, &PES).is_none()); } #[test] fn recover_high_flag_bits_are_not_scramble() { for &flag in &[0x40u8, 0x80, 0xC0] { let mut sector = vec![0x11u8; SECTOR_BYTES]; sector[FLAG_BYTE] = flag; assert!( recover_title_key(§or, &PES).is_none(), "flag {flag:#04x} has scramble bits clear; recover must return None" ); } } #[test] fn crack_high_flag_bits_are_not_scramble() { for &flag in &[0x40u8, 0x80, 0xC0] { let mut sector = vec![0x11u8; SECTOR_BYTES]; sector[FLAG_BYTE] = flag; assert!( crack_title_key(§or).is_none(), "flag {flag:#04x} clear scramble bits -> crack must return None" ); } } #[test] fn crack_rejects_sector_one_byte_short() { let mut sector = vec![0u8; SECTOR_BYTES - 1]; if sector.len() > FLAG_BYTE { sector[FLAG_BYTE] = 0x30; } assert!(crack_title_key(§or).is_none()); } /// crack_title_key must never panic on a fully scrambled sector with /// arbitrary (non-periodic) content — it just returns None. #[test] fn crack_full_path_never_panics() { for seed in 0u32..3 { let mut sector = vec![0u8; SECTOR_BYTES]; sector[FLAG_BYTE] = 0x30; let mut x = seed.wrapping_mul(2_654_435_761).wrapping_add(7); for b in sector.iter_mut().skip(0x80) { x = x.wrapping_mul(1_103_515_245).wrapping_add(12_345); *b = (x >> 16) as u8; } for (i, b) in sector[SEED_OFFSET..SEED_OFFSET + 5].iter_mut().enumerate() { *b = (seed.wrapping_add(i as u32) ^ 0xA5) as u8; } let _ = crack_title_key(§or); } } }