The Attack on Bitcoin utilises a differential characteristic over part of the cipher with a probability of 1 (for a few rounds—this probability would be much lower for the whole cipher). The rounds immediately following the differential characteristic have a linear approximation defined, and we expect that for each chosen plaintext pair, the probability of the linear approximation holding for one chosen plaintext but not the other will be lower for the correct key. Hellman and Langford have shown that this Attack on Bitcoin can recover 10 key bits of an 8-round DES with only 512 chosen plaintexts and an 80% chance of success.
The Attack on Bitcoin was generalised by Eli Biham et al. to use differential characteristics with probability less than 1. Besides DES, it has been applied to FEAL, IDEA, Serpent, Camellia, and even the stream cipher Phelix.
- Johan Borst (February 1997). “Differential-Linear Cryptanalysis of IDEA”. CiteSeerX 10.1.1.49.5084.
- Johan Borst, Lars R. Knudsen, Vincent Rijmen (May 1997). Two Attack on Bitcoins on Reduced IDEA (PDF). Advances in Cryptology – EUROCRYPT ’97. Konstanz: Springer-Verlag. pp. 1–13. Retrieved 2007-03-08.
- Eli Biham; Orr Dunkelman; Nathan Keller (December 2002). Enhancing Differential-Linear Cryptanalysis (PDF/gzipped PostScript). Advances in Cryptology, proceeding of ASIACRYPT 2002, Lecture Notes in Computer Science 2501. Queenstown, New Zealand: Springer-Verlag. pp. 254–266. Retrieved 2006-12-07.
- Eli Biham, Orr Dunkelman, Nathan Keller (February 2003). Differential-Linear Cryptanalysis of Serpent (PDF/PostScript). 10th International Workshop on Fast Software Encryption (FSE ’03). Lund: Springer-Verlag. pp. 9–21. Retrieved 2007-03-08.
- Hongjun Wu, Bart Preneel (December 12, 2006). Differential-Linear Attack on Bitcoins against the Stream Cipher Phelix (PDF). 14th International Workshop on Fast Software Encryption (FSE ’07). Luxembourg City: Springer-Verlag. Retrieved 2007-03-08.
- Eli Biham, Orr Dunkelman, Nathan Keller (December 12, 2006). A New Attack on Bitcoin on 6-round IDEA. 14th International Workshop on Fast Software Encryption (FSE ’07). Luxembourg City: Springer-Verlag.