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Computer-stored encryption keys are not safe from side-channel attacks

Approximately December 24, perhaps it was 1996, I published an idea on a USENET area (maybe it was SCI.CRYPT) that proposed an idea that clock oscillators used in computers could be frequency-modulated with a long-period pseudo-random (linear feedback shift register) value to smear the output of the signal (and everything that depends on it) over a range of frequencies.Curiously, in early 2007 (When I was at United States Penitentiary, Florence Colorado) I received a letter from a law firm offering me $5,000 for ownership of this idea.  (They had apparently figured out who I was, and had traced me down at my then-current address.)  I presumed that around that time, there was probably a lawsuit challenging a patent on this matter, and the law firm was doing 'due diligence' looking for ammunition.  I counter-offered that if they pay me 1/3 of the value of this idea, I would settle for that.  Never heard back from them.         Jim Bell 

     On Friday, March 13, 2015 3:56 AM, Eugen Leitl <[email protected]> wrote:


Computer-stored encryption keys are not safe from side-channel attacks

By Michael Kassner March 11, 2015, 1:25 PM PST

Using side-channel technology, researchers at Tel Aviv University can extract
decryption keys from RSA and ElGamal implementations without altering or
having control of a computer. 

Figure A: Tel Aviv University researchers built this self-contained PITA
receiver.  Image courtesy of Daniel Genkin, Lev Pachmanov, Itamar Pipman,
Eran Tromer, and Tel Aviv University

Not that long ago, grabbing information from air-gapped computers required
sophisticated equipment. In my TechRepublic column Air-gapped computers are
no longer secure, researchers at Georgia Institute of Technology explain how
simple it is to capture keystrokes from a computer just using spurious
electromagnetic side-channel emissions emanating from the computer under

Daniel Genkin, Lev Pachmanov, Itamar Pipman, and Eran Tromer, researchers at
Tel Aviv University, agree the process is simple. However, the scientists
have upped the ante, figuring out how to ex-filtrate complex encryption data
using side-channel technology.

The process In the paper Stealing Keys from PCs using a Radio: Cheap
Electromagnetic Attacks on Windowed Exponentiation (PDF), the researchers
explain how they determine decryption keys for mathematically-secure
cryptographic schemes by capturing information about secret values inside the
computation taking place in the computer.

"We present new side-channel attacks on RSA and ElGamal implementations that
use the popular sliding-window or fixed-window (m-ary) modular exponentiation
algorithms," the team writes. "The attacks can extract decryption keys using
a low measurement bandwidth (a frequency band of less than 100 kHz around a
carrier under 2 MHz) even when attacking multi-GHz CPUs."

If that doesn't mean much, this might help: The researchers can extract keys
from GnuPG in just a few seconds by measuring side-channel emissions from
computers. "The measurement equipment is cheap, compact, and uses
readily-available components," add the researchers. Using that philosophy the
university team developed the following attacks.

Software Defined Radio (SDR) attack: This comprises of a shielded loop
antenna to capture the side-channel signal, which is then recorded by an SDR
program installed on a notebook.

Portable Instrument for Trace Acquisition (PITA) attack: The researchers,
using available electronics and food items (who says academics don't have a
sense of humor?), built the self-contained receiver shown in Figure A. The
PITA receiver has two modes: online and autonomous.

Online: PITA connects to a nearby observation station via Wi-Fi, providing
real-time streaming of the digitized signal.  Autonomous: Similar to online
mode, PITA first measures the digitized signal, then records it on an
internal microSD card for later retrieval by physical access or via Wi-Fi.

Consumer radio attack: To make an even cheaper version, the team leveraged
knowing that side-channel signals modulate at a carrier frequency near 1.7
MHz, which is within the AM radio frequency band. "We used a plain
consumer-grade radio receiver to acquire the desired signal, replacing the
magnetic probe and SDR receiver," the authors explain. "We then recorded the
signal by connecting it to the microphone input of an HTC EVO 4G smartphone."

Cryptanalytic approach

This is where the magic occurs. I must confess that paraphrasing what the
researchers accomplished would be a disservice; I felt it best to include
their cryptanalysis description verbatim:

"Our attack utilizes the fact that, in the sliding-window or fixed window
exponentiation routine, the values inside the table of ciphertext powers can
be partially predicted. By crafting a suitable ciphertext, the attacker can
cause the value at a specific table entry to have a specific structure.

"This structure, coupled with a subtle control flow difference deep inside
GnuPG's basic multiplication routine, will cause a noticeable difference in
the leakage whenever a multiplication by this structured value has occurred.
This allows the attacker to learn all the locations inside the secret
exponent where the specific table entry is selected by the bit pattern in the
sliding window. Repeating this process across all table indices reveals the

Figure B is a spectrogram displaying measured power as a function of time and
frequency for a recording of GnuPG decrypting the same ciphertext using
different randomly generated RSA keys. The research team's explanation:

"It is easy to see where each decryption starts and ends (yellow arrow).
Notice the change in the middle of each decryption operation, spanning
several frequency bands. This is because, internally, each GnuPG RSA
decryption first exponentiates modulo the secret prime p and then modulo the
secret prime q, and we can see the difference between these stages.

"Each of these pairs looks different because each decryption uses a different
key. So in this example, by observing electromagnetic emanations during
decryption operations, using the setup from this figure, we can distinguish
between different secret keys."

Figure B: A spectrogram Image courtesy of Daniel Genkin, Lev Pachmanov,
Itamar Pipman, Eran Tromer, and Tel Aviv University

Any way to prevent the leakage?

One solution, albeit unwieldy, is operating the computer in a Faraday cage,
which prevents any spurious emissions from escaping. "The cryptographic
software can be changed, and algorithmic techniques used to render the
emanations less useful to the attacker," mentions the paper. "These
techniques ensure the behavior of the algorithm is independent of the inputs
it receives."

Interestingly, the research paper tackles a question about side-channel
attacks that TechRepublic readers commented on in my earlier article, "It's a
hardware problem, so why not fix the equipment?"

Basically the researchers mention that the emissions are at such a low level,
prevention is impractical because:

Any leakage remnants can often be amplified by suitable manipulation as we do
in our chosen-ciphertext attack; and Leakage is often an inevitable side
effect of essential performance-enhancing mechanisms.

Something else of interest: the National Institute of Standards and
Technology (NIST) considers resistance to side-channel attacks an important
evaluation consideration in its SHA-3 competition.

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