The Feistel function of the Cryptomeria cipher.
|Key sizes||56 bits|
|Block sizes||64 bits|
|Best public cryptanalysis|
|A boomerang attack breaks all 10 rounds in 248 time with known S-box, or 253.5 with an unknown S-box, using 244 adaptively chosen plaintexts/ciphertexts.|
The Cryptomeria cipher, also called C2, is a proprietary block cipher defined and licensed by the 4C Entity. It is the successor to CSS algorithm (used for DVD-Video) and was designed for the CPRM/CPPM digital rights management scheme which are used by DRM-restricted Secure Digital cards and DVD-Audio discs.
The C2 symmetric key algorithm is a 10-round Feistel cipher. Like DES, it has a key size of 56 bits and a block size of 64 bits. The encryption and decryption algorithms are available for peer review, but implementations require the so-called "secret constant", the values of the substitution box (S-box), which are only available under a license from the 4C Entity.
In 2008, an attack was published against a reduced 8-round version of Cryptomeria to discover the S-box in a chosen-key scenario. In a practical experiment, the attack succeeded in recovering parts of the S-box in 15 hours of CPU time, using 2 plaintext-ciphertext pairs.
A paper by Julia Borghoff, Lars Knudsen, Gregor Leander and Krystian Matusiewicz in 2009 breaks the full-round cipher in three different scenarios; it presents a 224 time complexity attack to recover the S-box in a chosen-key scenario, a 248 boomerang attack to recover the key with a known S-box using 244 adaptively chosen plaintexts/ciphertexts, and a 253.5 attack when both the key and S-box are unknown.
Distributed brute force cracking effort
Following an announcement by Japanese HDTV broadcasters that they would start broadcasting programs with the copy-once broadcast flag starting with 2004-04-05, a distributed Cryptomeria cipher brute force cracking effort was launched on 2003-12-21. To enforce the broadcast flag, digital video recorders employ CPRM-compatible storage devices, which the project aimed to circumvent. However, the project was ended and declared a failure on 2004-03-08 after searching the entire 56-bit keyspace, failing to turn up a valid key for unknown reasons. Because the attack was based on S-box values from DVD-Audio, it was suggested that CPRM may use different S-boxes.
Another brute force attack to recover DVD-Audio CPPM device keys was mounted on 2009-05-06. The attack was intended to find any of 24570 secret device keys by testing MKB file from Queen "The Game" DVD-Audio disc. On 2009-10-20 such key for column 0 and row 24408 was discovered.
The similar brute force attack to recover DVD-VR CPRM device keys was mounted on 2009-10-20. The attack was intended to find any of 3066 secret device keys by testing MKB from Panasonic LM-AF120LE DVD-RAM disc. On 2009-11-27 such key for column 0 and row 2630 was discovered.
By now the CPPM/CPRM protection scheme is deemed unreliable.
- Julia Borghoff, Lars Knudsen, Gregor Leander, Krystian Matusiewicz. "Cryptanalysis of C2". Extended Abstract (Technical University of Denmark).
- Ralf-Philipp Weimann (2008-03-01). "Algebraic Methods in Block Cipher Cryptanalysis". Darmstadt University of Technology. (Abstract is in German, rest is in English)
- "Distributed C2 Brute Force Attack: Status Page". Retrieved 2006-08-14.
"C2 Brute Force Crack - team timecop". Archived version of cracking team's English web site. Archived from the original on 2005-03-06. Retrieved 2006-10-30.
- "Discussion about the attack (Archived)". Archived from the original on 2005-03-16. Retrieved 2006-10-30.
- "C2 Block Cipher Specification" (PDF). 1.0. 4C Entity, LLC. 2003-01-17. Retrieved 2009-02-13.
- "Proceedings of the IASTED International Conference" (PDF). Puerto Vallarta, Mexico. 2006-01-23. Retrieved 2006-08-13.