Re: ``Better DES challenge'' solved by John Gilmore and ``Deep Crack''

Paulo Barreto (pbarreto@nw.com.br)
Sun, 19 Jul 1998 17:03:35 -0300

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At 12:35 1998.07.19 -0400, Doug Elznic wrote:

>What is the complementation property?

Let x denote some data (a plaintext, a ciphertext, or a key, for our
purposes), and let x* denote the result of flipping every bit in x, i.e. if
any given bit of x is 0 (resp. 1), the corresponding bit of x* is 1 (resp. 0).

Let E(x, k) denote the encryption of plaitext x under key k. The DES
complementation property states that E(x*, k*) = (E(x, k))*. In simpler
terms, encrypt the complement of a plaintext with the complement of a key
and you get the complement of the ciphertext. N.B. this is NOT a general
property of block ciphers, but it's true for DES.

Hence, given the presented solution:

        key = 0E329232EA6D0D73
        plaintext = 8787878787878787
        ciphertext = 0000000000000000

a second solution is obtained by taking the complement of all data (and
correcting the key parity when needed), i.e.

        key = F1CD6DCD1592F28C
        plaintext = 7878787878787878
        ciphertext = FFFFFFFFFFFFFFFF

Disclaimer: I didn't check these values in an actual implementation,
especially the key parity.

Regards,

Paulo.

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