Alice, Bob and Mallory: Category Security

A case for using only three different digits in keypad codes

Jonas Elfström — Sun, 27 Sep 2009 21:02:00 +0200

Keypads have obvious security problems and keypads accepting a stream of digits with no # or enter in between, while checking for the four digit long code, are even worse.

The important part is to not leak the digits in the code by wear or intentional markings because if they leak it's suddenly very far from 10000 combinations.

If the "lock picker" only knows that the code contains four digits there are 10000 combinations. Keypads accepting a stream of digits can then be opened in a maximum of 10003 keystrokes using the De Bruijn sequence. That is still quite a lot.

Below is a Ruby implementation of the De Bruijn sequence.

# De Bruijn sequence
# Original implementation by Frank Ruskey (1994)
# translated to C by Joe Sawada
# and further translated to Ruby by Jonas Elfström (2009)

@n=4
@k=10
@a=[0]
@sequence=[]

def debruijn(t, p, alike)
  if t>@n
    if @n%p==0
      1.upto(p) {|j| @sequence<<@a[j]}
    end
  else
    @a[t]=@a[t-p]
    if @a[t]>0
      debruijn(t+1,p,alike+1)
    else
      debruijn(t+1,p,alike)
    end
    (@a[t-p]+1).upto(@k-1) {|j|
      @a[t]=j
      debruijn(t+1,t,alike+1)
    }
  end
end

debruijn(1,1,0)
print @sequence.join

It's not uncommon to find keypads with 4 of the 10 keys worn down and if you do you can be pretty sure that the code contains those four different digits. The number of possible combinations are 4! = 4x3x2x1 = 24. I got curious to see if there's a kind of De Bruijn sequence for this that brings down the 4*24=96 keystrokes. By scribbling in a text editor I quickly realized there's not a clean sequence. Not clean in the way that a sequence following the rules can be created. Also it's probably even quite daunting to present it as mathematically dense and beautiful as the De Bruijn but that could be my less than great combinatorics speaking.

I made a quick and dirty brute force hack to try to find a shorter sequence.

seq=[]
1.upto(4) {|a| 1.upto(4) {|b| 1.upto(4) {|c| 1.upto(4) {|d|
  seq << "%d%d%d%d" % [a,b,c,d] if !(a==b || a==c || a==d || b==c || b==d || c==d)
}}}}

s=seq[0]
seq.delete_at(0)
while (seq.length>0)
  next_code=(seq.select {|c| c[0..2]==s[-3..-1]})
  if next_code.empty?
    next_code=(seq.select {|c| c[0..1]==s[-2..-1]})
    if next_code.empty? 
      next_code=(seq.select {|c| c[0]==s[-1]})
      s+=next_code[0][1..3]
      seq.delete_at(seq.index(next_code[0]))
    else
      s+=next_code[0][2..3]
      seq.delete_at(seq.index(next_code[0]))
    end
  else
    next_code=(seq.select {|c| c[0..2]==s[-3..-1]})
    s+=next_code[0][3].chr
    seq.delete_at(seq.index(next_code[0]))
  end
end

The above code takes the first code "1234" of the 24 and then searches the rest of the array for a code beginning with "234". It finds "2341" and adds "1" to the end of s and continues to look for "341" and so on. Relatively soon there is no three digit match and then it tries two digits and eventually even that fails and then it gets the first one digit match. The resulting sequence is:

123412314231243121342132413214321

From 96 to 33 keystrokes. Not as effective as De Bruijn but still significant. Unlike De Bruijn I have absolutely no proof that this is the shortest one possible but it seems likely. Also notice that in the middle of the sequence we find "3121" and "1213". Those break the criteria of four different digits but they seem to be necessary to be able to enter the reversed mode. Try reading the sequence forward and backwards to see what I mean.

If the code only contains two digits it's gets even more trivial to try them all. There are 14 possible codes and by compressing those to one sequence you get down to 20 keystrokes.

Things get a little more interresting if three buttons are worn. It turns out that the repeated digits can be placed in the code in six different ways.

0012,1002,1200,0102,0120,1020

That's 6x2x3=36 combinations and, maybe a little unintuitive, 12 more than if you are using four different digits. I compressed it down to 49 key strokes. Unlike the sequence for four different digits I can't find it with google and I know it's kind of security by obscurity but that could give a tiny amount of extra trouble to an attacker. I will not be the first one publishing it.

Be aware that if an attacker knows you are using a 0012-like code he gets a smaller space to search. 6x8x9x10=4320 instead of 10000. You have to weight the risk of button leaks against a code protocol leak.

Why you should use four different digits for keypad locks

Jonas Elfström — Wed, 23 Sep 2009 19:49:00 +0200

I made a couple of very bad mistakes in this article so I took it down. Hopefully I'm more on track in the sequel.

Breaking good

Jonas Elfström — Sun, 03 May 2009 23:24:00 +0200

Check out Chris Eng's post on how he broke the code on the cover of the 2009 Verizon Data Breach Investigations Report. He makes it seem so simple and without making a big deal of it he also shows the tools and commands he used.

Swedish hackers

Jonas Elfström — Wed, 31 Dec 2008 00:29:00 +0100

The incident I wrote of in Hello this is special agent Brian were covered in a Swedish radio documentary a little more than a month ago. It's all in Swedish. You can find out more here and you can download the documentary from here.

I also would like to add that we did not press charges like the police officers says 37 minutes into the documentary. Not because we thought it wasn't a big deal but we knew that a couple of big players already had so we thought we could spend our time better.

Drive encryption matters

Jonas Elfström — Tue, 12 Feb 2008 00:26:00 +0100

In a recent release TrueCrypt now supports drive/partition encryption.

One reason to encrypt on disk instead of file level is that operating systems and applications sometimes accidently stores passwords on your hard drive. This can happen in a number of ways and one common mistake applications make is to not prevent to be put on disk by the OS. Modern systems have a page/swap file. If a program gets paged out while holding your clear text password in pageable memory your password will be written to disk. The problem is that there are password recovery tools that can scan your page file for passwords.

You can configure Windows (and surely most other operating systems) to clear the page file on shutdown which will give you better protection (and slower shutdowns). Be aware that if you simply turn off the power the page file will be intact.

Scary tools

Jonas Elfström — Wed, 12 Dec 2007 17:15:00 +0100

I recently attended a session held by Marcus Murray. It seems it was kind of a compressed version of the session he held at TechEd earlier this year. Murray is witty, charismatic and has a broad and deep understanding of IT-security issues. He cracks jokes and practices a little social engineering to keep the audience attentive. If you and your IT-staff wants to be briefed (and scared) with the latest in IT-security I could easily recommend Murray.

He demonstrated a couple of tools that both impressed and scared me. First he demonstrated how to set up a mail based attack using the commercial Core IMPACT. It's a very impressive tool and mail based attacks are only one out of many attacks this software has the ability to execute. Before seeing this I could never have guessed there are tools this advanced and this easy to use. The lists of exploits it can test, in an all automated fashion, were long and seemed to be up to date.

Murray also demonstrated ARP poisoning and hijacking of a RDP session by using the free Cain & Abel tool. You could feel the discomfort in the air as it dawned on the audience how easy this is to set up.

Man in the browser

Jonas Elfström — Mon, 26 Nov 2007 21:40:00 +0100

There's some buzz about a new trojan technique called "Man in the browser". The trojan plugs itself into the users browser and then it intercepts the HTML. This have all sorts of implications, for instance the SSL certificate will seem to be valid.

Even if your virus protection does not detect the "Man in the browser" there are still ways to be quite safe. If your bank uses a security token which you not only logs in with but also use to sign your transactions, the attack will most likely fail. One problem is that it is up to you, the user, to actually verify that you are signing the expected amount to the expected accounts. To get protection against someone who has complete control over your computer the security protocol must "communicate" with the security token both ways.

It is not enough to only let the user enter the total value of the transactions because the tokens answer to such a simple value could be reused (during a short period of time) also the attack could be crafted to create the correct amount but to other accounts. By asking the user to also sign every new account the attacker will not be able to hide a transaction to his account.

The challenge is to make the security protocol clear and simple enough so that the user can understand what he would expect the bank to respond and expect from him.

It's the usual three: have a firewall, an updated virus protection and a secure bank with a digital security token were you sign your transactions and maybe you can sleep a little better.

Blowfish in the URL

Jonas Elfström — Thu, 15 Nov 2007 22:38:00 +0100

Sometimes you do not want to show the database id for a row in the URL. The reason could be that you do not want someone to be able to scan through all the data.

One solution is to use GUID's but they have drawbacks and one of them is that they add a considerable length to the URL. The shortest URL-safe representation of a GUID I've seen is 22 characters but usually they are 36 characters.

Depending on how your id's are implemented a much shorter way could be to simply to encrypt them.

Here's a Ruby-example that Blowfish encrypts, Base64 encodes and URL-encodes an integer value. You can get crypt as a gem:

gem install crypt

require 'rubygems'
require 'crypt/blowfish'
require 'Base64'
blowfish = Crypt::Blowfish.new("A key up to 56 bytes long")
plainId=123456
encryptedBlock = blowfish.encrypt_block(plainId.to_s.ljust(8))
idForURL = URI.escape((Base64.encode64(encryptedBlock).strip))

decryptedId = blowfish.decrypt_block(Base64.decode64(URI.unescape(idForURL))).strip.to_i

The .ljust(8) is because Blowfish is a 64-bit block cipher and the Ruby-implementation does not pad the data itself.

The id in the URL in this case would be c2PSXWgky40=. Its 12 characters long (11 if you skip the equal sign) and that's 10 or 24 characters shorter than a GUID. Also there is zero percent chance of a collusion and if you want to you can even decrypt it.

This is not a super safe implementation but if you start your id's at a random and not too low number you are making it a bit harder for someone to crack the 56-bit key. Actually a truly random and at least 64-bit big number would be a better choice as it would have no connection to the true id at all. You would have to check for uniqueness before storing those in the database though.

Hash functions

Jonas Elfström — Mon, 01 Oct 2007 21:07:00 +0200

Recently I happened to see the FNV hash being mentioned. I had never heard of it before so I googled it and found the authors page but also a true gem. If you want a crash course in hash functions then I can recommend Mulvey's site.

Smart card with LCD

Jonas Elfström — Tue, 31 Jul 2007 23:10:00 +0200

This company is presenting a smart card with built in display. I do not know the underlying protocol for making debit/credit card payments by smart card instead of using the magnetic stripe but if the protocol is sophisticated enough this could help blocking some of the known attacks of those. As Chip and SPIN points out the smart cards has some issues. One of them is that if the terminal is compromised you as a customer have no way to know that you are actually confirming the transaction you think you are while entering your pin code. If your smart card shows the amount, you could at least not be deceived into emptying your account.