Actually, mathematically he's correct, assuming a maximum password size.

For the sake of illustration, let's say I have a maximum password size of 10 
characters. Let's also say I have 8 possible symbol characters (I'm picking 8 
just because I don't know how many legal symbols there are and it rounds the 
numbers off). For any password, I have to have at least one character from all 
four of the following sets:

Uppercase letters (26)
Lowercase letters (26)
Numbers (10)
Symbols (8)

The choice of character for at least four of my ten possible positions is 
circumscribed, while the other six characters can be from any of the four sets.

26 x 26 x 10 x 8 x 70 x 70 x 70 x 70 x 70 x 70 = 6,362,457,920,000,000

If I didn't have any complexity requirements at all, I'd be able to choose from 
any of the four sets for all 10 characters:

70 x 70 x 70 x 70 x 70 x 70 x 70 x 70 x 70 x 70 = 2,824,752,490,000,000,000

That's pretty clearly a reduction in possible passwords of several orders of 
magnitude.

HOWEVER -- and this is a big however -- the original poster is suffering from a 
logic error (this is what happens when pure mathematics are untempered by a bit 
of common sense). The problem is *not* "how big of a password pool do I have" 
but rather "how big of a password search pool do I need to make the attacker 
have"?

In this case, both the "3 of 4" and "4 of 4" requirements produce exactly the 
same size of pool, precisely because the attacker *doesn't* know which 
positions will be chosen from which character set -- they have to assume that 
any position could be any possible character. Furthermore, by knowing that the 
system requires all four character sets, the attacker *cannot* take a shortcut 
by relying on the fact that most people are lazy when it comes to password and 
will do the bare minimum required of them, and remove one of the character sets 
from their search space -- doing so will not gain them a legitimate password. 
(How many users in a "3 of 4" setting actually bother to use all four sets?)

Finally, one of the assumptions I postulated to show the math doesn't meet the 
real world either -- if I want a stronger password, I just choose a longer one. 
The theoretical maximum length for passwords is truly outrageous, so a paranoid 
admin can bump up the minimum password length and offset any potential 
"weakness" imposed by requiring all four character sets to be present.

In short, the OP is looking at the math from the wrong side of things.

--
Devin L. Ganger, Exchange MVP      Email: [EMAIL PROTECTED]
3Sharp LLC                         Phone: 425.882.1032 x1011
14700 NE 95th Suite 210             Cell: 425.239.2575
Redmond, WA  98052                   Fax: 425.558.5710
(e)Mail Insecurity: http://blogs.3sharp.com/blog/deving/


-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Thor (Hammer of 
God)
Sent: Thursday, August 16, 2007 9:33 AM
To: [email protected]
Subject: RE: Password complexity - improvement

Just to follow up, this is incorrect. More possible source characters ==
more possible combinations.  Can you elaborate on what you mean by this?

t

> >
> > Is there a way to enforce all 4 properties.
>
> Enforcing passwords that MUST consist of uppercase letters, lowercase
> letters, numbers AND special characters reduces the total number of
> possible passwords, which in consequence has a negative impact on your
> security.

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