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FYI - Biham/Shamir Differential Fault Analysis of DES, etc.
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- Subject: FYI - Biham/Shamir Differential Fault Analysis of DES, etc.
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- Date: Sun, 20 Oct 1996 20:26:26 +0200
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From: firstname.lastname@example.org (Matt Blaze)
Date: Fri, 18 Oct 1996 19:10:51 GMT
Subject: FYI - Biham/Shamir Differential Fault Analysis of DES, etc.
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From: Shamir Adi <email@example.com>
Date: Fri, 18 Oct 1996 16:30:34 +0200
To: firstname.lastname@example.org, email@example.com,
firstname.lastname@example.org, email@example.com, firstname.lastname@example.org,
email@example.com, firstname.lastname@example.org, email@example.com
Subject: A new attack on DES
Research announcement: A new cryptanalytic attack on DES
Eli Biham Adi Shamir
Computer Science Dept. Applied Math Dept.
The Technion The Weizmann Institute
October 18, 1996
In September 96, Boneh Demillo and Lipton from Bellcore announced an
ingenious new type of cryptanalytic attack which received widespread
attention (see, e.g., John Markoff's 9/26/96 article in the New
York Times). Their full paper had not been published so far, but
Bellcore's press release and the authors' FAQ (available at
state that the attack is applicable only to public key cryptosystems
such as RSA, and not to secret key algorithms such as the Data Encryption
Standard (DES). According to Boneh, "The algorithm that we apply to the
device's faulty computations works against the algebraic structure used
in public key cryptography, and another algorithm will have to be devised
to work against the nonalgebraic operations that are used in secret key
techniques." In particular, the original Bellcore attack is based on
specific algebraic properties of modular arithmetic, and cannot handle
the complex bit manipulations which underly most secret key algorithms.
In this research announcement, we describe a related attack
(which we call Differential Fault Analysis, or DFA), and show that
it is applicable to almost any secret key cryptosystem proposed so far
in the open literature. In particular, we have actually implemented
DFA in the case of DES, and demonstrated that under the same
hardware fault model used by the Bellcore researchers, we can
extract the full DES key from a sealed tamperproof DES encryptor by
analysing fewer than 200 ciphertexts generated from unknown cleartexts.
The power of Differential Fault Analysis is demonstrated by the fact
that even if DES is replaced by triple DES (whose 168 bits of key were
assumed to make it practically invulnerable), essentially the same attack
can break it with essentially the same number of given ciphertexts.
We would like to greatfully acknowledge the pioneering contribution
of Boneh Demillo and Lipton, whose ideas were the starting point of
our new attack.
In the rest of this research announcement, we provide a short technical
summary of our practical implementation of Differential Fault Analysis of
DES. Similar attacks against a large number of other secret key cryptosystems
will be described in the full version of our paper.
TECHNICAL DETAILS OF THE ATTACK
The attack follows the Bellcore fundamental assumption that by exposing
a sealed tamperproof device such as a smart card to certain physical
effects (e.g., ionizing or microwave radiation), one can induce with
reasonable probability a fault at a random bit location in one of the
registers at some random intermediate stage in the cryptographic
computation. Both the bit location and the round number are unknown
to the attacker.
We further assume that the attacker is in physical possesion of the
tamperproofdevice, so that he can repeat the experiment with
the same cleartext and key but without applying the external
physical effects. As a result, he obtains two ciphertexts derived from
the same (unknown) cleartext and key, where one of the ciphertexts is
correct and the other is the result of a computation corrupted by a
single bit error during the computation. For the sake of simplicity,
we assume that one bit of the right half of the data in one of the 16
rounds of DES is flipped from 0 to 1 or vice versa, and that both the
bit position and the round number are uniformly distributed.
In the first step of the attack we identify the round in which the
fault occurred. This identification is very simple and effective: If
the fault occurred in the right half of round 16, then only one bit in
the right half of the ciphertext (before the final permutation) differs
between the two ciphertexts. The left half of the ciphertext can
differ only in output bits of the S box (or two S boxes) to which this
single bit enters, and the difference must be related to non-zero
entries in the difference distribution tables of these S boxes. In
such a case, we can guess the six key bit of each such S box in the
last round, and discard any value which disagree with the expected
differences of these S boxes (e.g., differential cryptanalysis). On
average, about four possible 6-bit values of the key remain for each
active S box.
If the faults occur in round 15, we can gain information on the key
bits entering more than two S boxes in the last round: the difference
of the right half of the ciphertext equals the output difference of
the F function of round 15. We guess the single bit fault in round
15, and verify whether it can cause the expected output difference,
and also verify whether the difference of the right half of the
ciphertext can cause the expected difference in the output of the F
function in the last round (e.g., the difference of the left half of
the ciphertext XOR the fault). If successful, we can discard possible
key values in the last round, according to the expected differences.
We can also analyse the faults in the 14'th round in a similar way.
We use counting methods in order to find the key. In this case, we
count for each S box separately, and increase the counter by one for
any pair which suggest the six-bit key value by at least one of its
possible faults in either the 14'th, 15'th, or 16'th round.
We have implemented this attack on a personal computer. Our analysis
program found the whole last subkey given less than 200 ciphertexts,
with random single-faults in all the rounds.
This attack finds the last subkey. Once this subkey is known, we can
proceed in two ways: We can use the fact that this subkey contains
48 out of the 56 key bits in order to guess the missing 8 bits in
all the possible 2^8=256 ways. Alternatively, we can use our knowledge
of the last subkey to peel up the last round (and remove faults that
we already identified), and analyse the preceding rounds with the same
data using the same attack. This latter approach makes it possible to
attack triple DES (with 168 bit keys), or DES with independent subkeys
(with 768 bit keys).
This attack still works even with more general assumptions on the
fault locations, such as faults inside the function F, or even faults
in the key scheduling algorithm. We also expect that faults in
round 13 (or even prior to round 13) might be useful for the analysis,
thus reducing the number of required ciphertext for the full analysis.
OTHER VULNERABLE CIPHERS
Differential Fault Analysis can break many additional secret key
cryptosystems, including IDEA, RC5 and Feal. Some ciphers, such as
Khufu, Khafre and Blowfish compute their S boxes from the key material.
In such ciphers, it may be even possible to extract the S boxes
themselves, and the keys, using the techniques of Differential Fault
Analysis. Differential Fault Analysis can also be applied against
stream ciphers, but the implementation might differ by some technical
details from the implementation described above.
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