DES-X

In cryptography, DES-X (or DESX) is a variant on the DES (Data Encryption Standard) block cipher intended to increase the complexity of a brute force attack using a technique called key whitening.

The original DES algorithm was specified in 1976 with a 56-bit key size: 2⁵⁶ possibilities for the key. There was criticism that an exhaustive search might be within the capabilities of large governments, particularly the United States' National Security Agency (NSA). One scheme to increase the key size of DES without substantially altering the algorithm was DES-X, proposed by Ron Rivest in May 1984.

The algorithm was included in RSA Security's BSAFE cryptographic library since the late 1980s.

DES-X augments DES by XORing an extra 64 bits of key (K₁) to the plaintext before applying DES, and then XORing another 64 bits of key (K₂) after the encryption:

${\mbox{DES-X}}(M)=K_{2}\oplus {\mbox{DES}}_{K}(M\oplus K_{1})$

The key size is thereby increased to 56 + 2 × 64 = 184 bits.

However, the effective key size (security) is only increased to 56+64-1-lg(M) =119 - lg(M) = ~119 bits, where M is the number of known plaintext/ciphertext pairs the adversary can obtain,and lg() denotes the binary logarithm. (Because of this, some implementations actually make K₂ a strong one way function of K₁ and K.)

DES-X also increases the strength of DES against differential cryptanalysis and linear cryptanalysis, although the improvement is much smaller than in the case of brute force attacks. It is estimated that differential cryptanalysis would require 2⁶¹ chosen plaintexts (vs. 2⁴⁷ for DES), while linear cryptanalysis would require 2⁶⁰ known plaintexts (vs. 2⁴³ for DES.) Note that with 2⁶⁴ plaintexts (known or chosen being the same in this case), DES (or indeed any other block cipher with a 64 bit block size) is totally broken via the elementary codebook attack.

See also

• G-DES
• Triple DES
• Meet-in-the-middle attack

References

• Joe Kilian and Phillip Rogaway, How to protect DES against exhaustive key search (PostScript), Advances in Cryptology - Crypto '96, Springer-Verlag (1996), pp. 252–267.
• P. Rogaway, The security of DESX (PostScript), CryptoBytes 2(2) (Summer 1996).

External links

• RSA FAQ Entry
• Discussion of DES-X and source code samples (Dead link: May 2007)