No crypto is safe

Ray Peck (rpeck@PureAtria.COM)
Tue, 29 Oct 1996 00:01:05 -0800 (PST)

Date: Tue, 22 Oct 1996 03:41:13 -0400
From: Monty Solomon <monty@roscom.COM>
Subject: A new attack on DES

Excerpt from RISKS DIGEST 18.54

Date: Fri, 18 Oct 1996 16:58:50 +0200
From: Shamir Adi <>
Subject: A new attack on DES

You have recently referred in RISKS [18.50, 18.52] to the ingenious new
attack against public key cryptosystems developed at Bellcore. All the
published information on the subject (including Bellcore's press release)
stress that the attack is not applicable to secret key cryptosystems. Well,
Eli Biham and I have just released a research announcement in which we show
that an extension of the attack can, under the same realistic fault model,
break almost any secret-key algorithm, including DES, multiple DES, IDEA,
etc. The attack on DES was actually implemented on a PC, and it found the
key by analysing fewer than 200 ciphertexts generated from unknown

Adi Shamir

= = = = = =

Research announcement: A new cryptanalytic attack on DES

Eli Biham Adi Shamir
Computer Science Dept. Applied Math Dept.
The Technion The Weizmann Institute
Israel Israel

18 October 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 specifically 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.


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 possession of the
tamperproof device, 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.


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.