Tears for quantum fears

Tears for Quantum Fears
On a Quantum of Security
Mark C. (@LargeCardinal)
(Now with added kittens!)

What is a quantum, anyway?
A 'quantum is just the 'smallest finite piece of something'...
'Quantum' effects are what are used in 'quantum
technologies' - these are usually (but not limited to):
• Superposition – a particle is in multiple possible states
simultaneously
• Entanglement – two particles can become in a sense
inseparable such that the measurement of one gives you
knowledge about the other.
Although Entanglement is important, we won't deal with it
much here because this is not a lecture!

What will quantum affect?
There are 4 domains of effect...
Quantum Computing – and
how it will affect classical
cryptography...
Post-Quantum Crypto - what
is it? Why do we (or NIST) care
about it?
Quantum Algorithms – Handy
helpers or solutions in search
of valid problems?
Quantum Key Distribution –
Using quantum effects
themselves to do key exchg

Quantum Computation - Class 0
(Mark – go here... https://www.geogebra.org/m/fjb5kvf5 )
If you want to play along at home: follow this QR Code:

Quantum Computation – Class 0
So a qubit is a computing unit that can be some combination of the |0⟩
and 1 ; mathematically this is expressed as:
For 𝛼, 𝛽 ∈ ℂ , with 𝛼2
+ 𝛽2
= 1 we can express our states as:
0 =
1
0
, 1 =
0
1
, and our state 𝜓 = 𝛼 0 + 𝛽|1⟩
The sphere representation you see is called the ‘Bloch Sphere’.
Just as classical computers are made up from logic gates – AND, OR,
NAND, NOR, XOR, etc. etc.
Quantum algorithms are made up from quantum gates – which are
matrices strung together into sequences called quantum circuits.
Source: “Quantum Mechanical Computers”, R. Feynman (1985)

So what do these quantum circuits look like?

What does a quantum output look like?

Resources and Sources for QC
Qiskit – python library and full environment developed by IBM –
run `pip install qiskit` (requires python3)
Qiskit’s Documentation -
https://qiskit.org/textbook/preface.html
Quantiki – a website accessibly detailing many quantum
algorithms and their nuances - https://quantiki.org/
Quantum Algorithm Zoo – A very comprehensive resource for
information about quantum algorithms -
https://quantumalgorithmzoo.org/

Resources and Sources for QC
IBM Quantum Experience – IBM’s quantum computer in the
cloud interface. Has a web UI and an API that is built into the
qiskit libraries (just add your API token):
https://quantum-computing.ibm.com/
D-Wave LEAP – D-Wave’s online cloud offering:
https://www.dwavesys.com/take-leap
Azure Quantum – who knows? They haven’t answered any of
my emails in over 6 weeks…

So what breaks? And how?
Shor’s Algorithm
• Developed by Peter Shor in 1994
• Solves the problem:
’Given a number N, find it’s prime factors’
…and does so in sub-exponential time
• This is BAD – because we rely on factoring
being exponentially hard to secure a lot of
crypto: RSA and ECC in particular!
Grover’s Algorithm
• Published by Lov Grover in 1996
• Solves the problem:
“Search a database with N-many entries
for a specific value..”
• It does this in up to 𝑁 -many steps.
• This is BAD – because it means that the
search of a key-space goes from 2 𝑛
to 2 𝑛/2
• This takes AES128 to AES64 (aka DES) and
AES256 to AES128.

So when does the cr*p hit the koolaid??
Shor’s Algorithm
Shor’s Algo requires ~3 times as many
qubits as there are bits in the number
N to factor
So you need ~3,500 qubits for a
RSA1024 key…
~7-15 years
Grover’s Algorithm
Evers-Sweeney (2019 -
https://kryptera.ca/paper/2019-03/)
propose 6,681 qubits needed to break
AES256
MIT’s efficient Grover’s Algo attack on
AES needs 20Mil qubits
~8-18 years
These calculations use that we have ~26
qubits in a single QC currently, and that
this will double each year to log2 3500 𝑎𝑛𝑑 log2(6681)

So what is the fix?
Short-Term Fixes
• Use RSA 4096-bit as your minimum key
length…
• Shor’s algorithm requires ~3 times as
many qubits as bits in an RSA key to
crack it, so longer keys mean you need
bigger QC’s
• For ECC use P384 as much as possible
• Upgrade to AES256 as much as possible
• Use AES in GCM mode – which adds a
significant complexity to the overall
attack
Long-Term fixes
• The NIST competition for the next
USGOV standard cryptography will use
‘Post-Quantum Cryptography’
• The competition has entered its third
round – see QRCode/Link below
• This means that we are
moving towards PQC
becoming the common
type of crypto in use.
• See:https://csrc.nist.gov/News/2020/pqc-third-round-
candidate-announcement

Post Quantum Cryptography
Post-Quantum Cryptography
This simply means:
“Cryptography that does not rely on
factoring as the ‘hard problem’ to make
the cryptography secure”
Current Candidates in NIST R3:
• Lattice based crypto: Kyber, Saber,
NTRU
• Supersingular Isogeny based: SIKE
• Other: Classic McEliece
• Hash algos: CRYSTALS-DILITHIUM,
FALCON, Rainbow

LWE – A Worked Example
4 1 11 10
5 5 9 5
3 9 0 10
1 3 3 2
12 7 3 4
6 5 11 4
3 3 5 0
6
9
11
11
4
8
1
10
4
12
9
x =
NOT SECURE!
This is Easy to solve with basic Linear
Algebra (vectors and matrices!) by
means of Gaussian Elimination
(mod 13)
Random Array Secret Output
Source: https://summerschool-croatia.cs.ru.nl/2018/slides/Introduction%20to%20post-quantum%20cryptography%20and%20learning%20with%20errors.pdf

LWE – The Setup
4 1 11 10
5 5 9 5
3 9 0 10
1 3 3 2
12 7 3 4
6 5 11 4
3 3 5 0
6
9
11
11
4
7
2
11
5
12
8
x =
We add a ‘small error’ term, which is
essentially random noise, to be able to skew
slightly the output – hence the name:
Learning with Errors (LWE)
0
-1
1
1
1
1
0
-1
+ (mod 13)
Random Array Secret Small Noise Output

LWE – The Problem
4 1 11 10
5 5 9 5
3 9 0 10
1 3 3 2
12 7 3 4
6 5 11 4
3 3 5 0
x =
Given the random array
and the output, find
the secret!
+ (mod 13)
Random Array Secret Small Noise Output
4
7
2
11
5
12
8

But how is this hard?
Well, we know the following is NP-hard…
There is no
known
quantum
algorithmic
speedup for
this
problem!

So when will PQC be commonplace?
Current Candidates in NIST R3:
• Lattice based crypto: Kyber, Saber, NTRU
• Supersingular Isogeny based: SIKE
• Other: Classic McEliece
• Hash algos: CRYSTALS-DILITHIUM, FALCON, Rainbow
We are now in ‘round 3’ of the competition…
We can expect some more code and more attacks to be
launched against these ciphers before they are chosen.
But remember – we don’t know what it’ll be called!
Within 2 years we should have the results…
Expect multiple ciphers with many notes,
recommendations, requirements, and key lengths!

Math Cat with their little mew…

Quantum Key Distribution
In 1984, Charles Bennett and Gilles Brassard worked out a way of using the quantum
properties of photons to make a provably secure key exchange mechanism
This protocol, known as BB84, paved the way for further protocols such as Ekert in ‘91,
called E91, and a plethora of others.

But how does QKD Work?
Source: http://www.jetir.org/papers/JETIR1906L90.pdf

So why isn’t this everywhere?
There is something that is not often talked about with QKD…
With Classical cryptography the security is in the mathematics that underpins the
cryptography. We rely on this to secure the systems that we use that cryptography
on. But this mathematics is distinct from the system we communicate over…
With quantum cryptography, we still use mathematics to secure the system –
But the mathematics is inherently linked to the system we communicate over!!
“You can’t packet switch photons without measuring them…”
-- C. 2020
Source:
https://www.forbes.com/sites/daveywinder/2020/08/04/meet-the-scrappy-space-startup-taking-quantum-security-into-space-honeywell-loft-orbital-qkd-encryption/

So why isn’t this everywhere?
With quantum cryptography, we still use mathematics to secure the system –
But the mathematics is inherently linked to the system we communicate over!!
“You can’t packet switch photons without measuring them…”
-- C. 2020

QKD Companies…
ID Quantique are the market leaders –
https://www.idquantique.com/
MagiQ have also been around for a while –
https://www.magiqtech.com/
Toshiba are the other main player in delivering QKD solutions
https://www.toshiba.co.jp/qkd/en/
Want to scare a QKD vendor? Ask them how their tech works
with cloud-based infrastructure…

QKD Hackers…
“Hacking Single-photon Avalanche Detection in QKD via Pulse Illumination” Zhihao
Wu et al. (2020)
https://arxiv.org/abs/2002.09146
“Hacking QKD via Injection Locking” Xiao-Ling et al. (2020)
“Hacking Alice’s Box in CV-QKD” J. Pereira, S. Pirandola (2018)
“Hacking commercial quantum cryptography systems by tailored bright
illumination” Lars Lydersen et al. (2011)

But what about other Quantum Algorithms?
There is more to quantum computing
than ‘factoring big numbers for TLAs’
• Quantum Finance – is an area
concerned with finding models akin
to Black-Scholes that work on QCs
• Quantum Chemistry Simulations –
recently making the news, using QCs
to simulate quantum systems seems
very natural
• Quantum Random Number
Generation…

So how do we do that?
Quantum Random Number Generation…
We are very happy to release a proof of
concept showing how to integrate cloud
quantum computing solutions (IBM-Q
here) into regular python scripting to
achieve something.
We will follow the flow chart on the right,
and will build our system with the following
limitations:
• No optimisations!
• Non-standard CSPRNG implementation

So what quantum circuit do we use?
The QRNG Circuit
We place all of the qubits into
superposition, and then measure
them all to get quantumly
random bits!
The ibmq_16_melbourne
quantum computer has 15 qubits
available – but you can only run
for 8192 shots.
This means we can get up to
122,880 random bits per job!

Proof of Concept Release!!
Quantum Random Number Generation…
Remember, this system has the following
limitations:
• No optimisations!
• Non-standard CSPRNG implementation
As such this code is
DEFINITELY NOT FOR PROD!!
Link:
https://gist.github.com/unprovable/43756
1c660f7d85f283e510a16ef5834

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