The Power of XOR

by Amara Graps

It’s a simple idea.  XOR, ⊕, is a bitwise operator, that means “exclusive or.” The logical operation it performs, is: if the input bits are the same, then the output bit will be false (0) else true (1).

XOR table:

X	Y	X⊕ Y
0	0	0
0	1	1
1	0	1
1	1	0

How Quantum Key Distribution (QKD) Works 

Quantum Key Distribution (QKD) is built upon the XOR. How does that work? 

Let X = a sender: Alice, and Y = a receiver: Bob. From Alice’s and Bob’s shared key, which is a binary string, Alice’s binary message to Bob is encoded using their shared key and the XOR encryption process. On the receiving end, Bob can decode it using their shared key and an XOR decryption. This cryptography mechanism is called a ‘one-time pad’. 

‘Public key cryptography’ goes one step further than the one-time pad with two binary keys shared by Alice and Bob: one public, which they share, and one private, that each keeps individually. While the world might know their public key, Alice and Bob can still securely communicate amongst themselves, and still using the XOR.

“How long do you want these messages to remain secret? […]
I want them to remain secret for as long as men are capable of evil.”
― Neal Stephenson, Cryptonomicon

QKD goes one step further using photon polarization. The polarization of individual photons is measured relative to an axis. Since polarization is a binary process, Alice and Bob can communicate their one-time key by denoting one of the axes, say horizontal: “0”, and the other axis, say vertical: “1”. The communication is secure because of quantum mechanics. The photon is in a superposition of mutually exclusive outcomes, simultaneously. If there is an eavesdropper, the eavesdropper must intercept each photon to measure it, which collapses the quantum state of the photon. It is that collapse from a superposition to just one state, that tells Alice and Bob that an eavesdropper is present. A very nice video explanation steps you through this QKD process, including the BB84 algorithm, which we talked about here and the E91 algorithm, which you can read about with other QKD protocols here. GQI’s Quantum Safe State of Play describes these protocols in its 73-slide presentation, as well. 

The Power of XOR Makes Quantum Satellites Possible

By transmitting each bit of the key using a single photon, QKD creates extremely secure keys between parties that are far apart. Katanya Kuntz, who spoke this week  at the Quantum Security and Defence Association’s weekly QKD/QSAT lecture, is the person who alerted me to the ‘Power of XOR’ in the context of QKD and Quantum Satellites (QSATs). She is the Science Team Coordinator and Technical Support for the Canadian Space Agency’s Quantum EncrYption and Science Satellite (QEYSSat) mission, the Canadian mission to test QKD in space, and a Co-Founder, and CEO, of QUBO. She described some of the ten-year (so far) journey to validate the QSAT concept, first with a ground-to-plane, demonstration.

With that successful demonstration, the QEYSSat mission could proceed. Kuntz’ presentation and the  paper: Jennewein et al., 2014  provided the principles of the QEYSSat mission, which is an UPLINK demonstration, from ground to spacecraft. QEYSSat, a 3–5-year mission, with its current launch date projected to be late 2025, is a microsatellite (<100 kg), to be in Low-Earth Orbit (LEO), with a quantum UPLINK channel for detecting quantum entanglement. Its main payload is a 4-state Polarization Analyzer with a 780 nm-795 passband, which is one of the seven, low-loss, transmission windows for photons to pass through the Earth’s atmosphere, see Fig. 3 of Jennewein et al., 2014  paper.  

A complete quantum optical simulation of the QEYSSat QKD system was developed by modeling the beam spreading caused by diffraction and atmospheric turbulence, accounting for background counts from city lights, the Moon, and the sky, as well as single-photon detector performance. The performance of each satellite trajectory enables the computation of an average QKD key rate and the quantum bit error rate (QBER) per month. Satellite passes were simulated using expected orbit characteristics. In addition to Jennewein’s paper, the research for this mission includes papers by Bourgoin et al, 2013 (design and modeling), Bourgoin et al., 2015 (more analysis), C. Pugh et al., 2017 (airplane demonstration), Anisimova et al., 2017 (radiation damage), and DSouza et al., 2020 (radiation damage and thermal annealing). 

As QEYSSat is a space mission to demonstrate capabilities, along with science, there are additional tests for Quantum Memory, Quantum Ground Station key distribution (National and International), Entanglement in Relativistic settings, and Adaptive Optics capabilities. The Canadian government has provided significant resources for this mission’s Science team, currently at thirteen Canadian universities. QEYSSat’s international science partners are currently located at ten sites in seven countries. It’s clear from the scope of this project, that the Canadian government has significant quantum technology plans, beyond this mission, especially in quantum communication. The Power of XOR will eventually connect the country. I’ll go into some of those Canadian plans in the next article. 

Our Quantum Safe Future

Canada’s quantum communication development highlights a journey to the Quantum Internet which I described in a previous QCR article about a ‘Killer App’. The Quantum Internet follows established secure nodes, which are ‘quantum safe’. 

GQI’s vision for a quantum safe future is one that is multi-layered, that is ‘math-based’ using NIST’s PQC protocols as they evolve, with one that is ‘physics-based’ using QKD, hardware security modules (HSM) and quantum random number generators (QRNG).  See the next Figure. 

These photon based QKD devices, are one component, yet deeply embedded inside of the Quantum Technology Value Chain. See the next Figure. 

(*) GQI offers six presentation slide-decks for customers which describe the State of Play in various sectors: Quantum Technology Introduction, Quantum Hardware, Quantum Safe, Quantum Sensing, Imaging, and Times, Quantum Software, and Quantum Landscape. If you are interested to learn more, please don’t hesitate to contact info@global-qi.com. 

October 23, 2024