Tuning in to random numbers

Tomorrow at Cryptographic Hardware and Embedded Systems 2009 I’m going to be presenting a frequency injection attack on random number generators formed from ring oscillators.

Random numbers are a vital part of cryptography — if predictable numbers are being used an attacker may be able to read secret messages, impersonate either party, or replay transactions. In addition, many countermeasures to attacks such as Differential Power Analysis involve adding randomness to operations — without the randomness algorithms such as RSA become susceptible.

To create unpredictable random numbers in a predictable computer involves measuring some kind of physical process. Examples include circuit noise, radioactive decay and timing variations. One method commonly used in low-cost circuits such as smartcards is measuring the jitter from free-running ring oscillators. The ring oscillators’ frequencies depend on environmental factors such as voltage and temperature, and by having many independent ring oscillators we can harvest small timing differences between them (jitter).

But what happens if they aren’t independent? In particular, what happens if the circuit is faced with an attacker who can manipulate the outside of the system?

The attack turns out to be fairly straightforward. An effect called injection locking, known since 1665, considers what happens if you have two oscillators very lightly connected. For example, two pendulum clocks mounted on a wall tend to synchronise the swing of their pendula through small vibrations transmitted through the wall.

In an electronic circuit, the attacker can inject a signal to force the ring oscillators to injection-lock. The simplest way involves forcing a frequency onto the power supply from which the ring oscillators are powered. If there are any imbalances in the circuit we suggest that this causes the circuit to ring to be more susceptible at that point to injection locking. So we examined the effects of power supply injection, and can envisage a similar attack by irradiation with electromagnetic fields.

And it works surprisingly well. We tried an old version of a secure microcontroller that has been used in banking ATMs (and is still recommended for new ones). For the 32 random bits that are used in an ATM transaction, we managed to reduce the number of possibilities from 4 billion to about 225.

So if an attacker can have access to your card and PIN, in a modified shop terminal for example, he can record some ATM transactions. Then he needs to take a fake card to the ATM containing this microcontroller. On average he’ll need to record 15 transactions (the square root of 225) on the card and try 15 transactions at the ATM before he can steal the money. This number may be small enough not to set off alarms at the bank. The customer’s card and PIN were used for the transaction, but at a time when he was nowhere near an ATM.

While we looked at power supply injection, the ATM could also be attacked electromagnetically. Park a car next to the ATM emitting a 10 GHz signal amplitude modulated by the ATM’s vulnerable frequency (1.8 MHz in our example). The 10 GHz will penetrate the ventilation slots but then be filtered away, leaving 1.8 MHz in the power supply. When the car drives away there’s no evidence that the random numbers were bad – and bad random numbers are very difficult to detect anyway.

We also tried the same attack on an EMV (‘Chip and PIN’) bank card. Before injection, the card failed only one of the 188 tests in the standard NIST suite for random number testing. With injection it failed 160 of 188. While we can’t completely predict the random number generator, there are some sequences that can be seen.

So, as ever, designing good random number generators turns out to be a hard problem not least because the attacker can tamper with your system in more ways than you might expect.

You can find the paper and slides on my website.