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FYI - Anderson & Kuhn's new "Improved DFA" paper
My appologies if this has been posted already.
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From: Ross Anderson <[email protected]>
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Subject: Research Announcement
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Improved Differential Fault Analysis
Ross J Anderson, Markus G Kuhn
In [1], Biham and Shamir announce an attack on DES based on 200 ciphertexts in
which one-bit errors have been induced by environmental stress. Here we show an
attack that requires less than ten ciphertexts. Furthermore, our attack is
practical in that it uses a fault model that has been implemented in attacks on
real smartcards.
In [2], Biham and Shamir show how their method can be extended to reverse
engineer algorithms whose structure is unknown. Our attack can also be extended
to such cases and is more efficient there too. In [3], Boneh, De Millo and
Lipton discuss how such techniques can be used to attack RSA. Again, their
attack is theoretical only, We show how to do it in practice.
Introduction
A recent research announcement by Biham and Shamir shows that if DES is
implemented in a tamper-resistant package, and this package has the property
that by applying ionising radiation (or some other environmental stress) we can
cause random one-bit errors in the round keys, then we can break DES. If we can
get a series of ciphertexts, each generated from the same plaintext but with a
different one-bit random round key error, then we will need about 200 faulty
ciphertexts to recover the key. In a further announcement [2], they show how on
a similar fault model, the structure of unknown Feistel ciphers can be deduced
from an adequate number of faulty ciphertexts. In each case, the critical
observation is that errors that occur in the last few round of the cipher leak
information about the key, or algorithm structure, respectively.
This work is inspired by a paper of Boneh, DeMillo and Lipton [3] who assume
(as Biham and Shamir do) that one-bit errors can be caused by radiation or
other environmental stresses. That paper goes on to show that with this fault
model, RSA can be attacked.
These results have been widely publicised in the press. A frequently voiced
criticism is that the attacks are purely theoretical: no-one has demonstrated
that single bit errors can actually be induced in a DES key schedule or an RSA
computation in any fielded device. In fact, most smartcards hold keys in EEPROM
which also contains much or all of the device's application software. Thus
errors induced by ionising radiation would be much more likely to corrupt
software, thus leading either to a system crash or to uninformative wrong
answers.
We show here that much faster, and completely practical, attacks are possible.
The trick is to induce small changes in the code rather than trying to cause
them in keys or other data.
The Improved Attack Methodology
In a note posted to relevant Internet newsgroups on the 7th November, one of us
pointed out that using clock and power glitches gives a practical way of
implementing the Lenstra variant of the Boneh attack. In this announcement, we
will expand on the threat model, and also show how attacks using clock and
power glitches can give attacks on DES that require many fewer ciphertexts -
less than ten rather than the 200 or so previously required.
In a paper on tamper resistance due to be published next week, we describe a
number of techniques for attacking smartcards and other security processors
[5]. This paper was written some time ago (the first results were presented at
the Isaac Newton Institute, Cambridge, in June) but has been withheld by
agreement with the manufacturer of one of the security processors we have
attacked, so that banking industry clients had some time to take suitable
precautions. Some of the attacks we describe in this paper are new, while
others are already known in various small communities (such as hackers and chip
testers) and are included for the benefit of the wider crypto and security
communities.
One of the latter type is that smartcards and other security processors can
often be attacked using clock and power glitches. The application of a clock
pulse that is much faster than normal, or of a transient in the power supply,
can often cause faulty behaviour in a microprocessor, under which the program
counter is incremented but the current instruction is executed either
incorrectly or not at all. A standard version of this attack is to replace a
single 5MHz clock pulse to a smartcard with four 20MHz pulses.
We do not claim to have invented this attack; it appears to have originated in
the pay-TV hacking community, which has known about it for at least a year. In
that context, it has not been used for attacks on cryptographic algorithms, but
in order to cause output loops to run for longer than the card's programmer
intended, thus dumping key material to the output port.
The glitch attack is described more fully in our tampering article, which will
appear at next week's Usenix Electronic Commerce Workshop [5].
In this note, we point out that attacks based on faulty instructions are not
only proven practical, unlike the as yet undemonstrated fault model of random
single bit errors induced by radiation. They also provide a much more powerful
attack on many cryptographic algorithms. This holds both when we are seeking to
recover a key for a known algorithm such as DES, and when we are trying to
reverse engineer an unknown algorithm that has been provided in a smartcard or
other tamper resistant processor.
Attacking RSA
A simplified version of the Boneh-DeMillo-Lipton attack, due to Lenstra, is
quoted in [3]: if a smart card computes an RSA signature S on a message M
modulo n = pq by computing it modulo p and q separately and then combining them
using the Chinese Remainder Theorem, and if an error an be induced in (say) the
latter computation, then we can factor n at once as p = gcd(n,S^e-M) where e is
the public exponent.
This is absolutely ideal for a glitch attack. As the card spends most of its
time calculating the signature mod p and mod q, and almost any glitch that
affects the output will do, we do not have to be at all selective about where
in the instruction sequence the glitch is applied. Since only a single
signature is needed, the attack can be performed online: a Mafia eftpos
terminal applies the glitch, factors the modulus, calculates what the correct
signature should be, and sends this on to the bank.
Thus the Mafia can harvest RSA secret keys without the customer or his bank
noticing anything untoward about the transaction he did at their shop. Given
that implementers of the new EMV electronic purse system propose to have only
10,000 different RSA secret keys per issuing bank, the Mafia will soon be able
to forge cards for a substantial proportion of the user population.
Attacking DES
When we can cause an instruction of our choice to fail, then attacking DES is
simple. We remove one of the xor operations that are used to combine the round
keys with the inputs to the S-boxes from the last two rounds of the cipher, and
repeat this for each of these key bytes in turn. The erroneous ciphertext
outputs that we receive as a result of this attack will each differ from the
genuine ciphertext in the output of usually two, and sometimes three, S-boxes.
Using the techniques of differential cryptanalysis, we obtain about five bits
of information about the eight keybits that were not xor'ed as a result of the
induced fault. So, for example, eight faulty ciphertexts should give us about
40 bits of the key, leaving a trivial keysearch.
Thus DES can be attacked with about one correct and eight faulty ciphertexts.
But how realistic is it to assume that we will be able to target particular
instructions?
In most smartcards, the manufacturer supplies a number of routines in ROM.
Though sometimes presented as an `operating system', the ROM code is more of a
library or toolkit that enables application developers to manage communications
and other facilities. Its routines usually include the DES algorithm (or a
proprietary algorithm such as Telepass), and by buying the manufacturer's
smartcard development toolkit (for typically a few thousand dollars) an
attacker can get full documentation plus real specimens for testing. In this
case, individual DES instructions can be targeted.
When confronted with an unfamiliar implementation, we may have to experiment
somewhat (we have to do this anyway with each card in order to find the correct
glitch parameters [5]). However the search space is relatively small, and on
looking at a few DES implementations it becomes clear that we can usually
recognise the effects of removing a single instruction from either of the last
two rounds. (In fact, many of these instructions yield almost as much
information when removed from the implementation as the key xor instructions
do.) We will discuss this at greater length in a later paper.
The ROM Overwrite Attack
Where the implementation is familiar, there is yet another way to extract keys
from the card - the ROM overwrite attack.
Single bits in a ROM can be overwritten using a laser cutter, and where the DES
implementation is well known, we can find one bit (or a small number of bits)
with the property that changing it will enable the key to be extracted easily.
The details will depend on the implementation but we might well be able, for
example, to make a jump instruction unconditional and thus reduce the number of
rounds in the cipher to one or two. Where the algorithm is kept in EEPROM, we
can use two microprobing needles to set or reset the target bit [6].
Where we have incomplete information on the implementation, ROM overwriting
attacks can be used in other ways. For example, if the DES S-boxes in ROM, we
can identify them using an optical microscope and use our laser cutter to make
all their bits equal. This turns DES into a linear transfromation over GF(2),
and we can extract the key from a single plaintext/ciphertext pair.
Although ROM overwrite (unlike the other attacks suggested in this paper)
involves access to the chip surface, it can be carried out using tools that are
relatively cheap and widely available. So it may be used by attackers who do
not have access to the expensive semiconductor test equipment that professional
pirates use to extract keys directly from smartcards [5].
Returning to the non-invasive attack model, we can always apply clock and power
glitches until simple statistical tests suddenly show a high dependency between
the input and output of the encryption function, indicating that we have
succeeded in reducing the number of rounds. This may be practical even where
the implementation details are unknown.
Reverse Engineering an Unknown Block Cipher
In [2], Biham and Shamir discuss how to identify the structure of an unknown
block cipher in a tamper resistant package (e.g., Skipjack) using one-bit
random errors. As before, they identify faults that affected only the last
round or rounds; this can be done by looking for ciphertexts at a low Hamming
distance from each other. They then identify which output bits correspond to
the left and right halves, and next look at which bits in the left half are
affected by one bit changes in the last-but-one right half. In the case of a
cipher such as DES with S boxes, the structure will quickly become clear and
with enough ciphertexts the values of the S-boxes can be reconstructed. They
report that with 500 ciphertexts the gross structure can be recovered, and with
about 10,000 the S-box entries themselves can be found.
Our technique of causing faults in instructions rather than in data bits is
more effective here too. We can attack the last instruction, then the second
last instruction, and so on.
We will give detailed estimates for DES in the final paper. Let us now consider
an actual classified algorithm. `Red Pike' was designed by GCHQ for encrypting
UK government traffic classified up to `Restricted', and the Department of
Health wishes to use it to encrypt medical records. The British Medical
Association, advised by one of us (Anderson) instead recommended that an
algorithm be chosen that had been in the open literature for at least two years
and had withstood attempts to find shortcuts (triple-DES, Blowfish, SAFER
K-128, WAKE,...).
In order to try and persuade the BMA that Red Pike was sound, the government
commissioned a study of it by four academics [7]. This study states that Red
Pike `uses the same basic operations as RC5' (p 4) in that the principal
operations are add, exclusive or, and left shift. It `has no look-up tables,
virtually no key schedule and requires only five lines of code' (p 4). Other
hints include that `the influence of each key bit quickly cascades' (p 10) and
`each encryption involves of the order of 100 operations' (p 19).
We can thus estimate the effort of reverse engineering Red Pike from a tamper
resistant hardware implementation by considering the effort needed to mount a
similar attack on RC5.
Removing the last operation - the addition of key material - yields an output
in which the right hand side is different (it is (B xor A) shl A). This
suggests, correctly, that the cipher is a balanced Feistel network without a
final permutation. Removing the next operation - the shift - makes clear that
it was a 32 bit circular shift but without revealing how it was parametrised.
Removing the next operation - the xor - is transparent, and the next - the
addition of key material in the previous round - yields an output with the
values A and B in the above expression. It thus makes the full structure of
the data-dependent rotation clear. The attacker can now guess that the
algorithm is defined by
A = ((A xor B) shl B) op key
B = ((B xor A) shl A) op key
Reverse engineering RC5's rather complex key schedule (and deducing that `op'
is actually +) would require single-stepping back through it separately; but
once we know that `op' is +, we can find the round key bits directly by working
back through the rounds of encryption.
So, apart from its key schedule, RC5 may be about the worst possible algorithm
choice for secret-algorithm hardware applications, where some implementations
may be vulnerable to glitch attacks. If Red Pike is similar but with a simpler
key schedule, then it could be more vulnerable still. However, since the
government plans to make Red Pike available eventually in software, this is not
a direct criticism of the design or choice of that algorithm.
It does all suggest, though, that secret-hardware algorithms should be more
complex; large S-boxes kept in EEPROM (that is separate from the program
memory) may be a sensible way of pushing up the cost of an attack. Other
protective measures that prudent designers would consider include error
detection, multiple encryption with voting, and designing the key schedule so
that the key material from a small number of rounds is not enough for a break.
Conclusion
We have improved on the Differential Fault Analysis of Biham and Shamir. Rather
than needing about 200 faulty ciphertexts to recover a DES key, we need less
than ten. We can factor RSA moduli with a single faulty ciphertext. We can also
reverse engineer completely unknown algorithms; this appears to be faster than
Biham and Shamir's approach in the case of DES, and is particularly easy with
algorithms that have a compact software implementation such as RC5.
Finally, our attacks - unlike those of Biham, Shamir, Boneh, DeMillo and Lipton
- - use a realistic fault model, which has actually been implemented and can be
used against fielded systems.
Acknowledgement
Mike Roe pointed out that the glitch attack on RSA can be done in real time by
a Mafia owned eftpos terminal.
Bibliography
[1] ``A New Cryptanalytic Attack on DES'', E Biham, A Shamir, preprint,
18/10/96
[2] ``Differential Fault Analysis: Identifying the Structure of Unknown Ciphers
Sealed in Tamper-Proof Devices'', E Biham, A Shamir, preprint, 10/11/96
[3] ``On the Importance of Checking Computations'' D Boneh, RA DeMillo, RJ
Lipton, preprint
[4] ``A practical variant of the Bellcore attack'', RJ Anderson, posted to
sci.crypt as message ID <[email protected]>, 7/11/96
[5] ``Tamper Resistance - A Cautionary Note'', RJ Anderson, MG Kuhn, to appear
in Usenix Electronic Commerce workshop, 19/11/96
[6] ``Hardwaresicherheit von Mikrochips in Chipkarten'', Osman Kocar,
Datenschutz und Datensicherheit v 20 no 7 (July 96) pp 421--424
[7] ``Red Pike --- An Assessment'', C Mitchell, S Murphy, F Piper, P Wild,
Codes and Ciphers Ltd 2/10/96
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