another feature RNGs could provide

[David Malone]

On Tue, Dec 27, 2005 at 03:26:59AM -0600, Travis H. wrote:
> On 12/26/05, Ben Laurie <ben at algroup.co.uk> wrote:
> > Surely if you do this, then there's a meet-in-the middle attack: for a
> > plaintext/ciphertext pair, P, C, I choose random keys to encrypt P and
> > decrypt C. If E_A(P)=D_B(C), then your key was A.B, which reduces the
> > strength of your cipher from 2^x to 2^(x/2)?

> Almost true.  The cardinality of the symmetric group S_(2^x) is
> (2^x)!, so it reduces it from (2^x)! to roughly sqrt((2^x)!).  That's
> still a lot.

I'm fairly sure knowing that E(P) = C reduces the key space from
(2^x)!  to (2^x - 1)!, because you've just got to choose images for
the remaining 2^x - 1 possible blocks.

I think a problem with Ben's arument is in assuming that knowing
E_A(P)=D_B(C) tells you that your key was A.B. For example, suppose
my key K is the permutation:

	1 -> 2
	2 -> 3
	3 -> 4
	4 -> 1

and my P = 2. Now we know E_K(P) = C = 3. Ben guesses A:

	1 -> 1
	2 -> 3
	3 -> 2
	4 -> 4

and B:

	1 -> 1
	2 -> 2
	3 -> 3
	4 -> 4

He sees that E_A(P) = E_A(2) = 3 = D_B(3), and so assumes that K =
A.B. But A.B = A != K.

(In this example, imagine x = 2, and we label the blocks 00 = 1,
01 = 2, 10 = 3, 11 = 4.)

	David.

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