A serious weakness of DES

Draft - 2nd November 1996

Abstract

Eli Biham and Adi Shamir [RISKS-18.56] recently pointed out that if an attacker can induce unidirectional faults in key memory of cryptographic devices, then keys could be extracted quickly. Although their attack is very elegant, it is not practical against many fielded systems. For example, inducing a single-bit change in a DES key will cause a proper implementation to return a key parity error.

However, when combined with Peter Gutman's recent work on memory remanence, there are two very practical attacks. One of them allows smartcard electronic wallet keys to be extracted with much less expensive equipment than that currently used by pay-TV pirates; the other yields an effective attack against fielded banking security modules. These attacks show that a feature of DES that had long been thought innocuous is actually a serious design error.

Introduction

In a research announcement of 30th October, Biham and Shamir [RISKS-18.54] point out that if a cryptographic hardware module employs EEPROM for key memory only, an opponent who can turn EEPROM values from `1' to `0' with a small controlled probability (e.g., by applying UV light) might cause a test input to be encrypted with a series of keys, each of Hamming distance one from the next in the series, and ending with the all zero key [1].

There are a number of reasons why their attack is not likely to work against real systems. For example, the typical smartcard system has several kilobytes of program code in EEPROM as well as typically two to five DES keys. An undirected stress applied to such a card is more likely to cause a program crash or an uninformative error than to yield a ciphertext encrypted under a key at Hamming distance one from a genuine key. Even if we only had to cause a hundred cards to fail to get a single input for the Biham-Shamir attack, if we needed on average 28 inputs to recover a DES key, then the number of cards required could be O(100^28).

The situation is made still worse by the fact that DES keys have odd parity, and a proper implementation will reject a key if any of its bytes has even parity. So one would be reduced to looking for keys at a Hamming distance of two rather than one. It is this objection that inspired the following work.

A Modified Attack

My idea is to turn the DES key parity problem on its head and enable parity to help rather than hinder the attack. Let us first consider an opponent who can perform directed attacks on the chip. Reading the contents of an EEPROM cell directly is difficult, and people who do it for a living use focused ion beam workstations to modify the chip [2]. However, it is trivial to set an EEPROM cell to the value of your choice if you do not have to read it first; you only need two microprobes. A 10mS 18V pulse from the cell's source to its control gate will do the trick [3].

My modified attack therefore proceeds as follows. Set the first bit of the EEPROM containing the target DES key to 1 (or 0, the choice doesn't matter) and operate the device. If it still works, the keybit was a 1. If you get a `key parity error' message, then the bit was zero. Move on to the next bit; set it to 1 and see if this changes the device's response (from encryption to error or vice versa).

This is a practical attack even on chips whose software we do not know in detail, as many smartcard software writers seem to have adopted a convention that the keys are located at the bottom end of the EEPROM memory. It will also work with protocols that use redundancy which we do not understand: we just change each key bit back to its original value.

The use of predictable memory addresses for keys is not restricted to smartcards; many banking security modules also keep keys at low memory. I will now describe a related attack that extracts master keys from these modules.

An Attack on Fielded Systems

In a brilliant Usenix paper [4], Peter Gutman described the mechanisms that cause both static and dynamic RAM to `remember' values that they have stored for a long period of time. A prudent security engineer will ask what the effect of this is in the real world.

I looked at an instance of a security module used in banking. This security module has 12 pairs of DES master keys stored in low memory. The device is tamper resistant in that power to the key memory is cut when the box is opened for servicing (this is needed every few years to change the battery). Keys are loaded into the device afterwards in multiple components by trusted bank staff.

In this device, which dated from the late 1980's, the key values were substantially intact on power-up. The number of bits in error was of the order of 5-10%. I cannot give more accurate figures as I was not permitted to copy down either the correct master key values, nor the almost-correct values that had been `burned in' to the static RAM chips. I am also not permitted to name the bank at which these modules are installed, and it may not be prudent to name their manufacturer.

Nonetheless the crypto community should consider the consequences.

If each DES key is wrong by five bits, then the effort involved in searching for the 10 wrong bits in a double DES key might be thought to be 112-choose-10 operations. Each operation would involve (a) doing a 2-key 3DES decryption of a 64 bit PIN key whose enciphered value is widely known to the bank's programmers (b) in the 2^{-8} of cases where this result has odd parity, enciphering an account number with this as a DES key to see if the (decimalised) result is the corresponding PIN. The effort is 4 times 112-choose-10 DES operations - about 2^50. But it would probably be cheaper to do a hardware keysearch on the PIN key directly than to try to implement this more complex 2^50 search in either hardware or software.

However, the bytewise nature of the DES key redundancy reduces the effort by orders of magnitude. If no key byte has a double error, then the effort is seven tries for each even parity byte observed, or 7^10 - about 2^28, which is easy. If there is one key byte with a double error, the effort is 2^38, giving a search of 2^40 DES operations - which is still feasible for an individual.

Conclusions

I have shown that the key parity in DES enables us to slash the cost of real attacks on both old systems (banking security modules) and new ones (electronic wallet smartcards).

I had already mentioned in [5] that a common fault in the driver software for banking security modules was that `key parity error' messages were often ignored rather than copied to the bank's security manager to give warning of an attempted attack. This note shows that key parity is even more serious than that.

The nature of DES key redundancy now appears to be a design error; it would have been much better to calculate the redundancy on the whole key. The 16 bit MAC used in the Clipper and Capstone chips is preferable (although as shown in [6], 16 bits may not be enough to prevent some protocol attacks).

The lesson for bankers is that existing security modules (and other cryptographic devices) should be destroyed carefully at the end of their working life.

The lesson for security engineers is that we should add key redundancy, and the question of whether we can rely on a device's eventual destruction, to the growing list of system parameters that must be (a) explicitly considered during design and (b) examined carefully when the product is being evaluated.

Bibliography

[1] "The Next Stage of Differential Fault Analysis: How to break completely unknown cryptosystems'', Eli Biham, Adi Shamir, October 30th, 1996

[2] "Tamper Resistance - A Cautionary Note'', Ross Anderson, Markus Kuhn, to appear at Usenix Electronic Commerce 96 (19th November)

[3] "Hardwaresicherheit von Mikrochips in Chipkarten'', Osman Kocar, Datenschutz und Datensicherheit v 20 no 7 (July 96) pp 421--424

[4] "Secure Deletion of Data from Magnetic and Solid-State Memory'', Peter Gutmann, Usenix Security 96 pp 77--89

[5] "Why Cryptosystems Fail'', Ross Anderson, in Communications of the ACM v 7 no 11 (Nov 94) pp 32--40

[6] "Protocol Failure in the Escrowed Encryption Standard'', Matt Blaze, in Proceedings of the 2nd ACM Conference on Computer and Communications Security (2-4 November 1994), ACM Press, pp 59--67

Added by jya.com November 20, 1996:

See Anderson and Kuhn's "Improved DFA" and their new comprehensive paper on tampering.