RSA Key Extraction via Low-Bandwidth
| Daniel Genkin
| Adi Shamir
|Technion and Tel Aviv
||Weizmann Institute of Science
||Tel Aviv University
| assisted by Lev Pachmanov and numerous
Many computers emit a high-pitched noise during operation, due to vibration
in some of their electronic components. These acoustic emanations are more
than a nuisance: they can convey information about the software running on
the computer and, in particular, leak sensitive information about
security-related computations. In a preliminary
presentation, we have shown that different RSA keys induce different
sound patterns, but it was not clear how to extract individual key bits. The
main problem was the very low bandwidth of the acoustic side channel (under
20 kHz using common microphones, and a few hundred kHz using ultrasound
microphones), many orders of magnitude below the GHz-scale clock rates of
the attacked computers.
Here, we describe a new acoustic cryptanalysis key extraction
attack, applicable to GnuPG's current implementation of RSA. The attack can
extract full 4096-bit RSA decryption keys from laptop computers (of various
models), within an hour, using the sound generated by the computer during
the decryption of some chosen ciphertexts. We experimentally demonstrate
that such attacks can be carried out, using either a plain mobile phone
placed next to the computer, or a more sensitive microphone placed 4 meters
Beyond acoustics, we demonstrate that a similar low-bandwidth attack can be
performed by measuring the electric potential of a computer chassis. A
suitably-equipped attacker need merely touch the target computer with his
bare hand, or get the required leakage information from the ground wires at
the remote end of VGA, USB or Ethernet cables.
- A detailed account of the results and their context is given in the full
version of our paper (8MB PDF). It is archived as IACR ePrint
- This work was presented at the CRYPTO
2014 conference in August 2014. A short version
appeared in the conference proceedings. A video
of the CRYPTO 2014 talk is available, including a live
demonstration of acoustic key extraction (though the on-stage setup is
not visible in the video).
- These results, were first published on 18 December 2013. Preliminary
results were announced in the Eurocrypt 2004 rump session
presentation, "Acoustic cryptanalysis: on nosy people and noisy
machines", and are now archived.
Progress since publication of the preliminary results is summarized in
- This research won the Black Hat 2014 Pwnie
Award for Most Innovative Research.
- In August 2014 we published a follow-up paper, Get
Your Hands Off My Laptop: Physical Side-Channel Key-Extraction
Attacks On PCs, which extends the attack to additional physical
channels and (in some settings) reduces key extraction time to a few
- In February 2015 we published another
follow-up paper, "Stealing Keys from PCs using a
Radio: Cheap Electromagnetic Attacks on Windowed Exponentiation",
which shows how to extract RSA and ElGamal keys from modern
implementations (that use windowed exponentiation), in a few seconds,
using cheap radio receivers.
Q1: What information is leaked?
This depends on the specific
computer hardware. We have tested numerous laptops, and several desktops.
- In almost all machines, it is possible to distinguish an idle CPU
(x86 "HLT") from a busy CPU.
- On many machines, it is moreover possible to distinguish different
patterns of CPU operations and different programs.
- Using GnuPG as our study case, we
can, on some machines:
- distinguish between the acoustic signature of different RSA secret
keys (signing or decryption), and
- fully extract decryption keys, by measuring the sound the machine
makes during decryption of chosen ciphertexts.
Q2: What is making the noise?
The acoustic signal of interest is generated by vibration of electronic
components (capacitors and coils) in the computer's voltage regulation
circuit, as it struggles to supply constant voltage to the CPU.
When different secret keys are used for decryption, they cause different
patterns of CPU operations, which draw different amounts of power. The
voltage regulator changes its behavior to maintain a stable voltage to the
CPU despite the changes in power draw, and this alters the electric currents
and voltages inside the voltage regulator itself. Those electric
fluctuations cause mechanical vibrations in the electronic component, and
the vibrations are transmitted into the air as sound waves.
The relevant signal is not caused by mechanical components such as
the fan or hard disk, nor by the laptop's internal speaker.
Q3: Does the attack require special equipment?
It sure helps, and in the paper
we describe an expensive hardware setup for getting the best sensitivity and
frequency response. But in some cases, a regular mobile phone is good
enough. We have used a mobile phone to acoustically extract keys from a
laptop at a distance of 30cm, as in the following picture.
Q4: What is the acoustic attack range?
depends on many factors. Using a sensitive parabolic microphone, we
surpassed 4 meters. In the following example, a parabolic microphone,
attached to a padded case of equipment (power supply, amplifier, filters,
and a laptop running the attack code) is extracting an RSA key from a target
laptop (on the far side of the room).
Without the ungainly parabolic dish, we achieved a range of 1 meter. In the
following, the target (A) is on the right, and the attacker is on the left.
Only the capsule of the microphone, marked (B), is sensitive to position and
orientation; the rest of the attacker's equipment can be hidden away.
Q5: What are some examples of attack
We discuss some prospective attacks in our paper. In a
- Install an attack app on your phone. Set up a meeting with the victim
and place the phone on the desk next to his laptop (see Q2).
- Break into the victim's phone, install the attack app, and wait until
the victim inadvertently places his phone next to the target laptop.
- Construct a web page use the microphone of the computer running the
browser (using Flash or HTML Media Capture, under some excuse such as
VoIP chat). When the user permits the microphone access, use it to steal
the user's secret key.
- Put your stash of eavesdropping bugs and laser microphones to a new
- Send your server to a colocation facility, with a good microphone
inside the box, and then acoustically extract keys from all nearby
- Get near a TEMPEST/1-92 protected machine, such as the one
pictured to the right, place a microphone next to its ventilation holes,
and extract its supposedly-protected secrets.
Q6: What if I don't have any microphone, or the environment is too
Another low-bandwidth channel is the electric potential of the laptop's
chassis. We've shown that in many computers, this "ground" potential
fluctuates (even when connected to a grounded power supply) and leaks the
requisite signal. This can be measured in several ways, including human
touch and far end of cable attacks, which are detailed in our
follow-up paper titled "Get Your Hands Off My Laptop:
Physical Side-Channel Key-Extraction Attacks On PCs".
Q7: Can an attacker use power analysis instead?
Yes, power analysis (by measuring the current drawn from the laptop's DC
power supply) is another way to perform our low-bandwidth attack. This too
is detailed in our follow-up paper, "Get Your Hands
Off My Laptop: Physical Side-Channel Key-Extraction Attacks On PCs".
If the attacker can measure clockrate-scale (GHz) power leakage, then
traditional power analysis may also be very effective, and far faster.
However, this is foiled by the common practice of filtering out high
frequencies on the power supply.
Q8: How can low-frequency (kHz) acoustic leakage
provide useful information about a much faster (GHz)?
Individual CPU operations are too fast for a microphone to pick up, but long
operations (e.g., modular exponentiation in RSA) can create a characteristic
(and detectable) acoustic spectral signature over many milliseconds. In the
chosen-ciphertext key extraction attack, we carefully craft the inputs to
RSA decryption in order to maximize the dependence of the spectral signature
on the secret key bits. See also Q18.
For the acoustic channel, we can't just increase the measurement bandwidth:
the bandwidth of acoustic signals is very low: up to 20 kHz for audible
signals and commodity microphones, and up to a few hundred kHz using
ultrasound microphones. Above a few hundred kHz, sound propagation in the
air has a very short range: essentially, when you try to vibrate air
molecules so fast they just heat up, instead of moving in unison as a sound
Q9: How vulnerable is GnuPG now?
We have disclosed our attack to GnuPG developers under CVE-2013-4576,
suggested suitable countermeasures, and worked with the developers to test
them. New versions of GnuPG 1.x and of libgcrypt (which underlies GnuPG
2.x), containing these countermeasures and resistant to our current
key-extraction attack, were released concurrently with the first public
posting of these results. Some of the effects we found (including RSA key
distinguishability) remain present.
Q10: How vulnerable are other algorithms and cryptographic
This is an open research question. Our attack requires careful cryptographic
analysis of the implementation, which so far has been conducted only for the
GnuPG 1.x implementation of RSA. Implementations using ciphertext blinding
(a common side channel countermeasure) appear less vulnerable. We have,
however, observed that GnuPG's implementation of ElGamal encryption also
allows acoustically distinguishing keys.
Q11: Is there a realistic way to perform a chosen-ciphertext attack on
To apply the attack to GnuPG, we found a way to cause GnuPG to
automatically decrypt ciphertexts chosen by the attacker. The idea is to
use encrypted e-mail messages following the OpenPGP
and PGP/MIME protocols.
For example, Enigmail (a popular
plugin to the Thunderbird e-mail client) automatically decrypts incoming
e-mail (for notification purposes) using GnuPG. An attacker can e-mail
suitably-crafted messages to the victims, wait until they reach the target
computer, and observe the acoustic signature of their decryption (as shown
above), thereby closing the adaptive attack loop.
Q12: Won't the attack be foiled by loud fan noise, or by multitasking,
or by several computers in the same room?
Usually not. The interesting
acoustic signals are mostly above 10KHz, whereas typical computer fan noise
and normal room noise are concentrated at lower frequencies and can thus be
filtered out. In task-switching systems, different tasks can be
distinguished by their different acoustic spectral signatures. Using
multiple cores turns out to help the attack (by shifting down the signal
frequencies). When several computers are present, they can be told apart by
spatial localization, or by their different acoustic signatures (which vary
with the hardware, the component temperatures, and other environmental
Q13: What countermeasures are available?
obvious countermeasure is to use sound dampening equipment, such as
"sound-proof" boxes, designed to sufficiently attenuate all relevant
frequencies. Conversely, a sufficiently strong wide-band noise source can
mask the informative signals, though ergonomic concerns may render this
unattractive. Careful circuit design and high-quality electronic components
can probably reduce the emanations.
Alternatively, the cryptographic software can be changed, and algorithmic
techniques employed to render the emanations less useful to the attacker.
These techniques ensure that the rough-scale behavior of the algorithm is
independent of the inputs it receives; they usually carry some performance
penalty, but are often used in any case to thwart other side-channel
attacks. This is what we helped implement in GnuPG (see Q9).
Q14: Why software countermeasures? Isn't it the hardware's
responsibility to avoid physical leakage?
It is tempting to enforce proper layering, and decree that preventing
physical leakage is the responsibility of the physical hardware.
Unfortunately, such low-level leakage prevention is often impractical due
to the very bad cost vs. security tradeoff: (1) any leakage remnants can
often be amplified by suitable manipulation at the higher levels, as we
indeed do in our chosen-ciphertext attack; (2) low-level mechanisms try to
protect all computation, even though most of it is insensitive or does not
induce easily-exploitable leakage; and (3) leakage is often an inevitable
side effect of essential performance-enhancing mechanisms (e.g., consider
Application-layer, algorithm-specific mitigation, in contrast, prevent the
(inevitably) leaked signal from bearing any useful information. It is
often cheap and effective, and most cryptographic software (including
GnuPG and libgcrypt) already includes various sorts of mitigation, both
through explicit code and through choice of algorithms. In fact, the
side-channel resistance of software implementations is nowadays a major
concern in the choice of cryptographic primitives, and was an explicit
evaluation criterion in NIST's AES and SHA-3 competitions.
Q15: What about other acoustic attacks?
See the discussion and references
in our paper, and the Wikipedia page on Acoustic
Cryptanalysis. In a nutshell:
Eavesdropping on keyboard keystrokes has been well discussed; keys can be
distinguished by timing, or by their different sounds. While this attack is
applicable to data that is entered manually (e.g., passwords), it is not
applicable to larger secret data such as RSA keys. Another acoustic source
is hard disk head seeks; this source does not appear very useful in the
presence of caching, delayed writes and multitasking. Preceding modern
computers is MI5's "ENGULF" technique (recounted in Peter Wright's book Spycatcher), whereby a phone tap was
used to eavesdrop on the operation of an Egyptian embassy's Hagelin cipher
machine, thereby recovering its secret key.
Declassified US government publications describe "TEMPEST" acoustic
leakage from mechanical and electromechanical devices, but do make no
mention of modern electronic computers.
- Full key extraction attack, exploiting deep internal details of GnuP's
implementation of RSA
- Dramatic improvement in range and applicability (increased from 20cm
with open chassis to 4m in normal operation)
- Much better hardware (some self-built), allowing longer range and
better signal characterization
- Signal processing and error correction, making it possible to perform
the attack using a mobile phone despite the low-quality microphone
- Many more targets tested
- Non-acoustic low-bandwidth attacks, including chassis potential
- Countermeasures implemented and tested in GnuPG (see Q9)
- Detailed writeup.
Q17: What does this acoustic leakage sound like?
To human ears, the acoustic leakage typically sounds like a faint,
high-pitched whining or buzzing noise (if it is at all within audible
range). However, if we could hear ultrasound, it might sound like this
processed audio recording of
GnuPG decrypting several ciphertexts [mp3]. (To make it audible, we
selected the interesting frequencies using a bandpass filter, and then
downshifted them to within human hearing range.) In this recording, we can
discern several pairs of tones. Each such pair is the sound made by a single
RSA decryption. There are two tones per decryption because, internally, each
GnuPG RSA decryption first exponentiates modulo the secret prime p
and then modulo the secret prime q ? and we can
actually hear the difference between these stages. Moreover, each of these
pairs of tones sounds different ? because each decryption uses a
different key. So in this example, by simply listening to the processed
signal, we can distinguish between different secret keys,
A better way to understand the signal is to visualize it as a spectrogram,
which plots the acoustic power as a function of time and frequency. For
example, here is another recording of GnuPG decrypting several RSA
In this spectrogram, the horizontal axis (frequency) spans 40 kHz, and the
vertical axis (time) spans 1.4 seconds. Each yellow arrow points to the
middle of a GnuPG RSA decryption. It is easy to see where each decryption
starts and ends. We also observe that the sound changes halfway through each
decryption: this is the aforementioned switch from the secret prime p
to the secret prime q. Most interestingly, we can see the subtle
differences between these decryptions (especially near the yellow arrows)
? and thus distinguish between different secret keys.
Q18: How do you extract the secret key bits?
The key extraction attacks finds the secret key bits one by one,
sequentially. For each bit, the attacker crafts a ciphertext of a special
form, that makes the acoustic leakage depend specifically on the value of
that bit. The attacker then triggers decryption of that chosen
ciphertext, records the resulting sound, and analyzes it. The following
demonstrates a typical stage of this attack, focusing on a single secret key
bit. If this bit is 0, then decryption of the chosen ciphertext will sound
like the left-side spectrogram (with a strong component at 35.2 kHz). If the
secret bit is 1, the decryption will sound like the right-side spectrogram
(where the strong component is at 38.1 kHz).
Using automated signal classification, the attack tells apart these cases,
and deduces the secret key bit.
Q19: Aren't sensitive devices protected by
Interestingly, many of the physical side-channel countermeasures used in
highly sensitive applications, such as air gaps, Faraday cages, and power
supply filters, provide no protection against acoustic leakage. In
particular, Faraday cages containing computers require ventilation, which
is typically provided by means of vents covered with perforated sheet
metal or metal honeycomb (see Q1 above). These
are very effective at attenuating compromising electromagnetic radiation
(``TEMPEST''), but are nearly transparent to sound.
For example, the following depicts recording the acoustic emanations
through a double-honeycomb metal ventilation mesh designed for blocking
electromagnetic radiation. (Covering this mesh with cardboard eliminates
Q20: What is the purpose of your research?
People entrust their most private information to computers, under the
assumption that their computers will keep their secrets. Our goal is to
discover when this assumption is dangerously false: to understand how
information may be leaking in unexpected ways that can be used
nefariously. We then seek ways to build software and hardware that will
better protect the users. In this case, for example, we worked with the
developers of the vulnerable software to change the mathematical
operations so that the emitted sound will not reveal the secret key.
Moreover, at a philosophical level, we are intrigued by the tension
between computation and computers. Most of computer
science deals with computation, the abstract mathematical
manipulation of numbers, with formally-designated inputs and outputs. But
this computation is eventually embodied in physical computers,
with myriad unexpected outputs (physical leakage) and inputs (via sensors
and faults). The abstractions underlying computer science and programming,
productive as they are, blind us to those phenomena. By challenging and
excavating through the convenient abstractions, we gain a deeper
understanding of those evanescent ensembles of energy and electrons to
which we entrust our daily lives.
Lev Pachmanov wrote much of the software setup
used in our experiments, including custom signal acquisition programs. Avi Shtibel
and Oded Smikt
assisted in constructing and configuring the experimental setup. Assa
assisted in various experiments, and offered valuable
suggestions. Sharon Kessler
provided copious editorial advice. We thank Werner
, lead developer of GnuPG, for the prompt response to our
disclosure and the productive collaboration in adding suitable
countermeasures. We are indebted to Pankaj
for inspiring the origin of this research, and to
for use of the Nir
and for valuable advice on audio recording. National
generously donated a National Instruments
PCI-6052E DAQ card and a MyDAQ device. Erik
analysis software was used for some of the analysis. We thank numerous
volunteers for access to test-target machines.
This work was sponsored by the Check
Point Institute for Information Security
; by the Israeli
Ministry of Science and Technology
; by the Israeli
Centers of Research Excellence I-CORE program
(center 4/11); and
by NATO's Public Diplomacy
in the Framework of "Science for Peace".