Decimalisation Table Attacks for PIN Cracking
Mike Bond and Piotr Zielinski
University of Cambridge, Computer Laboratory, Gates Building,
JJ Thompson Avenue, Cambridge CB3 0FD, United Kingdom
fMike.Bond, Piotr.Zielinskig@cl.cam.ac.uk
Abstract. We present an attack on hardware security modules used
by retail banks for the secure storage and verication of customer PINs
in ATM (cash machine) infrastructures. By using adaptive decimalisa-
tion tables and guesses, the maximum amount of information is learnt
about the true PIN upon each guess. It takes an average of 15 guesses
to determine a four digit PIN using this technique, instead of the 5000
guesses intended. In a single 30 minute lunch-break, an attacker can thus
discover approximately 7000 PINs rather than 24 with the brute force
method. With a $300 withdrawal limit per card, the potential bounty is
raised from $7200 to $2.1 million and a single motivated attacker could
withdraw $30-50 thousand of this each day. This attack thus presents a
serious threat to bank security.
1 Introduction
Automatic Teller Machines (ATMs) are used by millions of customers every day
to make cash withdrawals from their accounts. However, the wide deployment
and sometimes secluded locations of ATMs make them ideal tools for criminals
to turn traceable electronic money into clean cash.
The customer PIN is the primary security measure against fraud; forgery of
the magnetic stripe on cards is trivial in comparison to PIN acquisition. A street
criminal can easily steal a cash card, but unless he observes the customer enter
the PIN at an ATM, he can only have three guesses to match against a possible
10,000 PINs and would rarely strike it lucky. Even when successful, his theft still
cannot exceed the daily withdrawal limit of around $300 . However, bank pro-
grammers have access to the computer systems tasked with the secure storage of
PINs, which normally consist of a mainframe connected to a \Hardware Security
Module" (HSM) which is tamper-resistant and has a restricted API such that it
will only respond to with a YES/NO answer to a customer's guess.
A crude method of attack is for a corrupt bank programmer to write a pro-
gram that tries all PINs for a particular account, and with average luck this
would require about 5000 transactions to discover each PIN. A typical HSM can
check maybe 60 trial PINs per second in addition to its normal load, thus a
corrupt employee executing the program during a 30 minute lunch break could
only make o with about 25 PINs.
However, HSMs implementing several common PIN generation methods have
a
aw. The rst ATMs were IBM 3624s, introduced widely in the US in around
1980, and most PIN generation methods are based upon their approach. They
calculate the customer's original PIN by encrypting the account number printed
on the front of the customer's card with a secret DES key called a \PIN gener-
ation key". The resulting ciphertext is converted into hexadecimal, and the rst
four digits taken. Each digit has a range of `0'-`F'. In order to convert this
value into a PIN which can be typed on a decimal keypad, a \decimalisation
table" is used, which is a many-to-one mapping between hexadecimal digits and
numeric digits. The left decimalisation table in Figure 1 is typical.
0123456789ABCDEF 0123456789ABCDEF
0123456789012345 0000000100000000
Fig. 1. Normal and attack decimalisation tables
This table is not considered a sensitive input by many HSMs, so an arbitrary
table can be provided along with the account number and a trial PIN. But by
manipulating the contents of the table it becomes possible to learn much more
about the value of the PIN than simply excluding a single combination. For
example, if the right hand table is used, a match with a trial pin of 0000 will
conrm that the PIN does not contain the number 7, thus eliminating over 10%
of the possible combinations. We rst present a simple scheme that can derive
most PINs in around 24 guesses, and then an adaptive scheme which maximises
the amount of information learned from each guess, and takes an average of 15
guesses. Finally, a third scheme is presented which demonstrates that the attack
is still viable even when the attacker cannot control the guess against which the
PIN is matched.
Section 2 of the paper sets the attack in the context of a retail banking envi-
ronment, and explains why it may not be spotted by typical security measures.
Section 3 describes PIN generation and verication methods, and section 4 de-
scribes the algorithms we have designed in detail. We present our results from
genuine trials in section 5, discuss preventative measures in section 6, and draw
our conclusions in section 7.
2 Banking Security
Banks have traditionally led the way in ghting fraud from both insiders and
outsiders. They have developed protection methods against insider fraud includ-
ing double-entry book-keeping, functional separation, and compulsory holiday
periods for sta, and they recognise the need for regular security audits. These
methods successfully reduce fraud to an acceptable level for banks, and in con-
junction with an appropriate legal framework for liability, they can also protect
customers against the consequences of fraud.
However, the increasing complexity of bank computer systems has not been
accompanied by sucient development in understanding of fraud prevention
methods. The introduction of HSMs to protect customer PINs was a step in
the right direction, but even in 2002 these devices have not been universally
adopted, and those that are used have been shown time and time again not to
be impervious to attack [1, 2, 5]. Typical banking practice seeks only to reduce
fraud to an acceptable level, but this translates poorly into security require-
ments; it is impossible to accurately assess the security exposure of a given
aw,
which could be an isolated incident or the tip of a huge iceberg. This sort of
risk management con
icts directly with modern security design practice where
robustness is crucial. There are useful analogues in the design of cryptographic
algorithms. Designers who make \just-strong-enough" algorithms and trade ro-
bustness for speed or export approval play a dangerous game. The cracking of
the GSM mobile phone cipher A5 is but one example [3].
And as \just-strong-enough" cryptographic algorithms continue to be used,
the risk of fraud from brute force PIN guessing is still considered acceptable,
as it should take at least 10 minutes to guess a single PIN at the maximum
transaction rate of typical modules deployed in the 80s. Customers are expected
to notice the phantom withdrawals and report them before the attacker could
capture enough PINs to generate a signicant liability for the banks. Even with
the latest HSMs that support a transaction rate ten times higher, the sums of
money an attacker could steal are small from the perspective of a bank.
But now that the PIN decimalisation table has been identied as an security
relevant data item, and the attacks described in this paper show how to exploit
uncontrolled access to it, brute force guessing is over two orders of magnitude
faster. Enough PINs to unlock access to over $2 million can be stolen in one
lunch break!
A more sinister threat is the perpetration of a smaller theft, where the nec-
essary transactions are well camou
aged within the banks audit trails. PIN ver-
ications are not necessarily centrally audited at all, and if we assume that they
are, the 15 or so transactions required will be hard for an auditor to spot amongst
a stream of millions. Intrusion detection systems do not fare much better { sup-
pose a bank has an extremely strict audit system that tracks the number of
failed guesses for each account, raising an alarm if there are three failures in a
row. The attacker can discover a PIN without raising the alarm by inserting the
attack transactions just before genuine transactions from the customer which
will reset the count. No matter what the policies of the intrusion detection sys-
tem it is impossible to keep them secret, thus a competent programmer could
evade them. The very reason that HSMs were introduced into banks was that
mainframe operating systems only satisfactorily protected data integrity, and
could not be trusted to keep data condential from programmers.
So as the economics of security
aws like these develops into a mature eld,
it seems that banks need to update their risk management strategies to take
account of the volatile nature of the security industry. They also have a respon-
sibility to their customers to reassess liability for fraud in individual cases, as
developments in computer security continually reshape the landscape over which
legal disputes between bank and customer are fought.
3 PIN Generation & Verication Techniques
There are a number of techniques for PIN generation and verication, each pro-
prietary to a particular consortium of banks who commissioned a PIN processing
system from a dierent manufacturer. The IBM CCA supports a representative
sample, shown in Figure 2. We IBM 3624-Oset method in more detail as it is
typical of decimalisation table use.
Method Uses Dectables
IBM 3624 yes
IBM 3624-Oset yes
Netherlands PIN-1 yes
IBM German Bank Pool Institution yes
VISA PIN-Validation Value
Interbank PIN
Fig. 2. Common PIN calculation methods
3.1 The IBM 3624-Oset PIN Derivation Method
The IBM 3624-Oset method was developed to support the rst generation
of ATMs and has thus been widely adopted and mimicked. The method was
designed so that oine ATMs would be able to verify customer PINs without
needing the processing power and storage to manipulate an entire database of
customer account records. Instead, a scheme was developed where the customer's
PIN could be calculated from their account number by encryption with a secret
key. The account number was made available on the magnetic stripe of the card,
so the ATM only needed to securely store a single cryptographic key. An example
PIN calculation is shown in Figure 4.
The account number is represented using ASCII digits, and then interpreted
as a hexadecimal input to the DES block cipher. After encryption with the
secret \PIN generation" key, the output is converted to hexadecimal, and all
but the rst four digits are discarded. However, these four digits might contain
the hexadecimal digits `A'-`F', which are not available on a standard numeric
keypad and would be confusing to customers, so they are mapped back to decimal
digits using a \decimalisation table" (Figure 3).
0123456789ABCDEF
0123456789012345
Fig. 3. A typical decimalisation table
Account Number 4556 2385 7753 2239
Encrypted Accno 3F7C 2201 00CA 8AB3
Shortened Enc Accno 3F7C
0123456789ABCDEF
0123456789012345
Decimalised PIN 3572
Public Offset 4344
Final PIN 7816
Fig. 4. IBM 3624-Oset PIN Generation Method
The example PIN of 3F7C thus becomes 3572. Finally, to permit the card-
holders to change their PINs, an oset is added which is stored in the mainframe
database along with the account number. When an ATM veries an entered PIN,
it simply subtracts the oset from the card before checking the value against the
decimalised result of the encryption.
3.2 Hardware Security Module APIs
Bank control centres and ATMs use Hardware Security Modules (HSMs), which
are charged with protecting PIN derivation keys from corrupt employees and
physical attackers. An HSM is a tamper-resistant coprocessor that runs soft-
ware providing cryptographic and security related services. Its API is designed
to protect the condentiality and integrity of data while still permitting access
according to a congurable usage policy. Typical nancial APIs contain trans-
actions to generate and verify PINs, translate guessed PINs between dierent
encryption keys as they travel between banks, and support a whole host of key
management functions.
The usage policy is typically set to allow anyone with access to the host
computer to perform everyday commands such as PIN verication, but to ensure
that sensitive functions such as loading new keys can only be performed with
authorisation from multiple employees who are trusted not to collude.
IBM's \Common Cryptographic Architecture" [6] is a nancial API imple-
mented by a range of IBM HSMs, including the 4758, and the CMOS Crypto-
graphic Coprocessor (for PCs and mainframes respectively). An example of the
code for a CCA PIN verication is shown in Figure 5.
The crucial inputs are the PAN_data, the decimalisation table and the
encrypted_PIN_block. The rst two are supplied in the clear and are straight-
forward for the attacker to manipulate, but obtaining an encrypted_PIN_block
that represents a chosen trial PIN is rather harder.
Encrypted_PIN_Verify(
A_RETRES , A_ED , // return codes 0,0=yes 4,19=no
trial_pin_kek_in , pinver_key , // encryption keys for enc inputs
(UCHAR*)"3624 " "NONE " // PIN block format
" F" // PIN block pad digit
(UCHAR*)" " ,
trial_pin , // encrypted_PIN_block
I_LONG(2) ,
(UCHAR*)"IBM-PINO" "PADDIGIT" , // PIN verification method
I_LONG(4) , // # of PIN digits = 4
"0123456789012345" // decimalisation table
"123456789012 " // PAN_data (account number)
"0000 " // offset data
);
Fig. 5. Sample code for PIN verication in CCA
3.3 Obtaining chosen encrypted trial PINs
Some bank systems permit clear entry of trial PINs from the host software.
For instance, this functionality may be required to input random PINs when
generating PIN blocks for schemes that do not use decimalisation tables. The
appropriate CCA command is Clear_PIN_Encrypt, which will prepare an en-
crypted PIN block from the chosen PIN. It should be noted that enabling this
command carries other risks as well as permitting our attacks. If there is not
randomised padding of PINs before they are encrypted, an attacker could make
a table of known trial encrypted PINs, compare each arriving encrypted PIN
against this list, and thus easily determine its value. If it is still necessary to
enable clear PIN entry in the absence of randomised padding, some systems can
enforce that the clear PINs are only encrypted under a key for transit to another
bank { in which case the attacker cannot use these guesses as inputs to the local
verication command.
So, under the assumption that clear PIN entry is not available to the attacker,
his second option is to enter the required PIN guesses at a genuine ATM, and
intercept the encrypted PIN block corresponding to each guess as it arrives at
the bank. Our adaptive decimalisation table attack only requires ve dierent
trial PINs { 0000 , 0001 ,0010 , 0100 , 1000. However the attacker might only
be able to acquire encrypted PINs under a block format such as ISO-0, where
the account number is embedded within the block. This would require him to
manually input the ve trial PINs at an ATM for each account that could be
attacked { a huge undertaking which totally defeats the strategy.
A third and more most robust course of action for the attacker is to make
use of the PIN oset capability to convert a single known PIN into the required
guesses. This known PIN might be discovered by brute force guessing, or simply
opening an account at that bank.
Despite all these options for obtaining encrypted trial PINs it might be argued
that the decimalisation table attack is not exploitable unless it can be performed
without a single known trial PIN. To address these concerns, we created a third
algorithm (described in the next section), which is of equivalent speed to the
others, and does not require any known or chosen trial PINs.
4 Decimalisation Table Attacks
In this section, we describe three attacks. First, we present a 2-stage simple static
scheme which needs only about 24 guesses on average. The shortcoming of this
method is that it needs almost twice as many guesses in the worst case. We show
how to overcome this diculty by employing an adaptive approach and reduce
the number of necessary guesses to 22. Finally, we present an algorithm which
uses PIN osets to deduce a PIN from a single correct encrypted guess, as is
typically supplied by the customer from an ATM.
4.1 Initial Scheme
The initial scheme consists of two stages. The rst stage determines which digits
are present in the PIN. The second stage consists in trying all the possible pins
composed of those digits.
Let Dorig be the original decimalisation table. For a given digit i, consider a
binary decimalisation table Di with the following property. The table Di has 1
at position x if and only if Dorig has the digit i at that position. In other words,
Di[x] =
(
1 if Dorig[x] = i;
0 otherwise:
For example, for a standard table Dorig = 0123 4567 8901 2345, the value of D3
is 0001 0000 0000 0100.
In the rst phase, for each digit i, we check the original PIN against the
decimalisation table Di with a trial PIN of 0000. It is easy to see that the test
fails exactly when the original PIN contains the digit i. Thus, using only at most
10 guesses, we have determined all the digits that constitute the original PIN.
In the second stage we try every possible combination of those digits. Their
actual number depends on how many dierent digits the PIN contains. The table
below gives the details.
Digits Possibilities
A AAAA(1)
AB ABBB(4), AABB(6), AAAB(4)
ABC AABC(12), ABBC(12), ABCC(12)
ABCD ABCD(24)
The table shows that the second stage needs at most 36 guesses (when the
original PIN contains 3 dierent digits), which gives 46 guesses in total. The
expected number of guesses is, however, as small as about 23:5.
D10(p) ?= 00
p = 11
yes
D01(p) ?= 10
no
p = 10
yes
D01(p) ?= 01
no
p = 01
yes
p = 00
no
Fig. 6. The search tree for the initial scheme. Dxy denotes the decimalisation table
that maps 0 ! x and 1 ! y.
4.2 Adaptive Scheme
The process of cracking a PIN can be represented by a binary search tree. Each
node v contains a guess, i.e., a decimalisation table Dv and a pin pv. We start
at the root node and go down the tree along the path that is determined by
the results of our guesses. Let porig be the original PIN. At each node, we check
whether Dv(porig) = pv. Then, we move to the right child if yes and to the left
child otherwise.
Each node v in the tree can be associated with a list Pv of original PINs such
that p 2 Pv if and only if v is reached in the process described in the previous
paragraph if we take p as the original PIN. In particular, the list associated with
the root node contains all possible pins and the list of each leaf should contain
only one element: an original PIN porig.
Consider the initial scheme described in the previous section as an example.
For simplicity assume that the original PIN consists of two binary digits and the
decimalisation table is trivial and maps 0 ! 0 and 1 ! 1. Figure 6 depicts the
search tree for these settings.
The main drawback of the initial scheme is that the number of required
guesses depends strongly on the original PIN porig. For example, the method
needs only 9 guesses for porig = 9999 (because after ascertaining that digit 0{8
do not occur in porig this is the only possibility), but there are cases where 46
guesses are required. As a result, the search tree is quite unbalanced and thus
not optimal.
One method of producing a perfect search tree (i.e., the tree that requires the
smallest possible numbers of guesses in the worst case) is to consider all possible
search trees and choose the best one. This approach is, however, prohibitively
inecient because of its exponential time complexity with respect to the number
of possible PINs and decimalisation tables.
It turns out that not much is lost when we replace the exhaustive search with
a simple heuristics. We will choose the values of Dv and pv for each node v in
the following manner. Let Pv be the list associated with node v. Then, we look
at all possible pairs of Dv and pv and pick the one for which the probability of
Dv(p) = pv for p 2 Pv is as close to 1
2 as possible. This ensures that the left and
right subtrees are approximately of the same size so the whole tree should be
quite balanced.
This scheme can be further improved using the following observation. Recall
that the original PIN porig is a 4-digit hexadecimal number. However, we do not
need to determine it exactly; all we need is to learn the value of p = Dorig(porig).
For example, we do not need to be able to distinguish between 012D and ABC3
because for both of them p = 0123. It can be easily shown that we can build
the search tree that is based on the value of p instead of porig provided that the
tables Dv do not distinguish between 0 and A, 1 and B and so on. In general, we
require each Dv to satisfy the following property: for any pair of hexadecimal
digits x, y: Dorig[x] = Dorig[y] must imply Dv[x] = Dv[y]. This property is not
dicult to satisfy and in reward we can reduce the number of possible PINs from
164 = 65 536 to 104 = 10 000. Figure 7 shows a sample run of the algorithm for
the original PIN porig = 3491.
No Possible pins Decimalisation table Dv Trial pin pv Dv(porig) pv
?=
Dv(porig)
1 10000 1000 0010 0010 0000 0000 0000 yes
2 4096 0100 0000 0001 0000 0000 1000 no
3 1695 0111 1100 0001 1111 1111 1011 no
4 1326 0000 0001 0000 0000 0000 0000 yes
5 736 0000 0000 1000 0000 0000 0000 yes
6 302 0010 0000 0000 1000 0000 0000 yes
7 194 0001 0000 0000 0100 0000 0001 no
8 84 0000 1100 0000 0011 0000 0010 no
9 48 0000 1000 0000 0010 0000 0010 no
10 24 0100 0000 0001 0000 1000 1000 yes
11 6 0001 0000 0000 0100 0100 0001 no
12 4 0001 0000 0000 0100 0010 0001 no
13 2 0000 1000 0000 0010 0100 0010 no
Fig. 7. Sample output from adaptive test program
4.3 PIN Oset Adaptive Scheme
When the attacker does not know any encrypted trial PINs, and cannot encrypt
his own guesses, he can still succeed by manipulating the oset parameter used
to compensate for customer PIN change. Our nal scheme has the same two
stages as the initial scheme, so our rst task is to determine the digits present
in the PIN.
Assume that an encrypted PIN block containing the correct PIN for the ac-
count has been intercepted (the vast majority of arriving encrypted PIN blocks
will satisfy this criterion), and for simplicity that the account holder has not
changed his PIN and the correct oset is 0000. Using the following set of dec-
imalisation tables, the attacker can determine which digits are present in the
correct PIN.
Di[x] =
(
Dorig[x] + 1 if Dorig[x] = i;
Dorig[x] otherwise:
For example, for the table Dorig = 0123 4567 8901 2345, the value of D3
is 0124 4567 8901 2445. He supplies the correct encrypted PIN block and the
correct oset each time.
As with the initial scheme, the second phase determines the positions of the
digits present in the PIN, and is again dependent upon the number of repeated
digits in the original PIN. Consider the common case where all the PIN digits
are dierent, for example 1583. We can try to determine the position of the
single 8 digit by applying an oset to dierent digits and checking for a match.
Guess Guess Customer Customer Guess Decimalised Verify
Oset Decimalisation Table Guess + Guess Oset Original PIN Result
0001 0123 4567 9901 2345 1583 1584 1593 no
0010 0123 4567 9901 2345 1583 1593 1593 yes
0100 0123 4567 9901 2345 1583 1683 1593 no
1000 0123 4567 9901 2345 1583 2583 1593 no
Each dierent guessed oset maps the customer's correct guess to a new
PIN which may or may not match the original PIN after it is decimalised using
the modied table. This procedure is repeated until the position of all digits
is known. Cases with all digits dierent will require at most 6 transactions to
determine all the position data. Three dierent digits will need a maximum of
9 trials, two digits dierent up to 13 trials, and if all the digits are the same no
trials are required as there are no permutations. When the parts of the scheme
are assembled, 16.5 guesses are required on average to determine a given PIN.
5 Results
We rst tested the adaptive algorithm exhaustively on all possible PINs. The
distribution in Figure 8 was obtained. The worst case has been reduced from
45 guesses to 24 guesses, and the average has fallen from 24 to 15 guesses. We
then implemented the attacks on the IBM Common Cryptographic Architecture
(version 2.41, for the IBM 4758), and successfully extracted PINs generated using
the IBM 3624 method.We also checked the attacks against the API specications
for the VISA Security Module (VSM) , and found them to be eective. The
VSM is the forerunner of a whole range of hardware security modules for PIN
processing, and we believe that the attacks will also be eective against many
of its successors.
0
500
1000
1500
2000
2500
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Number of Attempts
Number of PINs
Fig. 8. Distribution of guesses required using adaptive algorithm
6 Prevention
It is easy to perform a check upon the validity of the decimalisation table. Several
PIN verication methods that use decimalisation tables require that the table be
0123456789012345 for the algorithm to function correctly, and in these cases the
API need only enforce this requirement to regain security. However, PIN veri-
cation methods that support proprietary decimalisation tables are harder to x.
A checking procedure that ensures a mapping of the input combinations to the
maximum number of possible output combinations will protect against the rst
two decimalisation table attacks, but not against the attack which exploits the
PIN oset and uses only minor modications to the genuine decimalisation table.
To regain full security, the decimalisation table input must be cryptographically
protected so that only authorised tables can be used.
The only short-term alternative to the measures above is to use more ad-
vanced intrusion detection measures, and it seems that the long term message
is clear: continuing to support decimalisation tables is not a robust approach
to PIN verication. Unskewed randomly generated PINs stored encrypted in an
online database such as are already used in some banks are signicantly more
secure.
7 Conclusions
We are currently starting discussions with HSM manufacturers with regard to
the practical implications of the attacks. It is very costly to modify the soft-
ware which interacts with HSMs, and while update of the HSM software is
cheaper, the system will still need testing, and the update may involve a costly
re-initialisation phase. Straightforward validity checking for decimalisation ta-
bles should be easy to implement, but full protection that retains compatibility
with existing mainframe software will be hard to achieve. It will depend upon
the intrusion detection capabilities oered by each particular manufacturer. We
hope to have a full understanding of the impact of these attacks and of the
optimal preventative measures in the near future.
Although HSMs have existed for two decades, formal study of their security
APIs is still in its infancy. Previous work by one of the authors [5, 4] has un-
covered a whole host of diverse
aws in APIs, some at the protocol level, some
exploiting properties of the underlying crypto algorithms, and some exploiting
poor design of procedural controls. The techniques behind the decimalisation
table attacks do not just add another string to the bow of the attacker { they
further conrm that designing security APIs is one of the toughest challenges
facing the security community. It is hard to see how any one methodology for
gaining assurance of correctness can provide worthwhile guarantees, given the
diversity of attacks at the API level. More research is needed into methods for
API analysis, but for the time being we may have to concede that writing correct
API specications is as hard as writing correct code, and enter the traditional
arms race between attack and defence that so many software products have to
ght.
Acknowledgements
We would like to thank Richard Clayton and Ross Anderson for their helpful
contributions and advice. Mike Bond was able to conduct the research thanks to
the funding received from the UK Engineering and Physical Research Council
(EPSRC) and Marconi plc. Piotr Zielinski was supported by a Cambridge Over-
seas Trust Scholarship combined with an ORS Award, as well as by a Thaddeus
Mann Studentship from Trinity Hall College.
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