Talk:Advantage (cryptography)

Wait... [Either something's wrong or more explanation's needed]
"a permutation selected at random from the (264)! possible permutations on 64-bit blocks." ... "Note from Stirling's approximation that (264)! is around 103.47×10 20, so even specifying which permutation is selected requires writing down a number too large to represent exactly in any real computer. "

There are 64! (~2296 or ~1089) permutations of 64 items (bits or anything else,) NOT (264)!. The fact that the permutation may be specified by a 64-bit key rather than a 56-bit key doesn't change that, though a 56-bit key might further reduce the size of the utilized subset compared to specification by a 64-bit key...reducing the work function by 2(64-56) = 28 = 256. Specifying a particular 64P requires only 64 6-bit values, or 384-bits, not the given figure, so at most, the ratio is 2(384-56) = 2328 = 5.53×1098, which, though large, is far below what one would get using the given figure.

Either the quote from the article is flat-out wrong or there's missing information that would make clear how it isn't.  — Preceding unsigned comment added by Ultracrypt (talk • contribs) 03:59, 28 March 2015 (UTC)
 * The article looks correct to me. DES takes a 64-bit input block and produces a 64-bit output block. Hence, for each key we have a permutation of a set with 264 elements (each possible input). 2A02:120B:2C4F:7900:55C8:3A06:7922:B43 (talk) 06:03, 1 April 2015 (UTC)
 * Then why not 64! × 264 ≈ 2360...i.e. every permutation of each value of a block? This remains far less than 103.47×10 20 .  Ultracrypt (talk) 06:59, 6 April 2015 (UTC)