Abstract
Quantum random number generators find applications in both quantum and classical communications schemes, particularly in security protocols where they can be used as a source of random seed or key material. In this work, we describe the implementation of a quantum random number generator onboard a nanosatellite deployed in low Earth orbit. Our generator samples shot noise from an entangled photonpair source based on spontaneous parametric downconversion, linking the entropy of the output to the quantization of the downconverted beam. We present analyzed data from the orbiting instrument alongside data taken from a groundbased engineering model where the statistical test suites indicate a good match to the output from a uniform distribution. Finally, we use the source to implement a prototype for an offgrid randomness beacon. This work paves the way to future low Earth orbit based public quantum randomness beacons.
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Introduction
Quantum random number generators (QRNGs) access the inherent randomness of quantum processes as a source of entropy in order to produce an unbiased and unpredictable output. These devices have been shown to have many prospective use cases, notably in cryptography^{1}, simulation^{2}, telecommunications^{3}, and financial systems^{4}.
In contrast to other physical random number generators, the unpredictability, which is a natural consequence of quantum mechanics, provides an abundant and uncomplicated source of randomness. Despite this relative availability, it is nontrivial to extract randomness from a quantum source due to the presence of technical noise arising from the imperfect nature of the measurement devices^{5}.
In recent years, there have been many successful demonstrations of quantum random number generators in laboratories^{6,7,8}, and several commercial products have entered the marketplace^{9}. Besides this, there has been theoretical progress in more advanced QRNG schemes that allow public verification^{10}, selftesting^{11} and even deviceindependent quantum random number generation^{12,13}.
Of the many schemes to extract entropy from a photonic quantum system, we highlight: measuring the photon number statistics of a suitably attenuated source^{14}, projective measurements of photon polarization orthogonal to the preparation basis^{15}, and the measurement of interference between laser pulses with random phase^{16}. Where entanglement is present, there are also opportunities to exploit the corresponding superclassical correlations to produce randomness which contains a degree of device independence^{12,13,17}, or to generate socalled certified randomness^{17,18}.
In this work, we describe the implementation of a quantum random number generator on an orbiting nanosatellite, SpooQy1^{19}. While we are able to repurpose the satellite’s primary quantum optics payload for QRNG operation, constraints imposed by the resourcescarce platform restrict us to a simple scheme based on photon number statistics. In addition to the applications noted previously, orbiting random number generators enable the implementation of a resource known as a randomness beacon^{20}. While a number of randomness beacons are currently accessible via the internet^{20,21}, an orbiting beacon would be available to remote infrastructures with only sporadic, highlatency internet access, for example, monitoring stations connected via storeandforward satellite services^{22,23}. These installations could then make use of beacon pulses in applications such as timestamping algorithms to increase the integrity of recordkeeping, or for auditable input to a sampling process^{24}. We describe here a proofofconcept implementation of a public randomness beacon, and demonstrate the retrieval of beacon data via two distant ground stations, located in Switzerland and Singapore. Preliminary data from this publication was previously presented^{25}, lacking detailed analysis and the demonstration of a prototype randomness beacon.
Results and discussion
The quantum optics payload onboard SpooQy1 performs tomography on pairs of polarizationentangled photons generated from a spontaneous parametric downconversion process. This paves the way to future implementation of entanglementbased quantum key distribution protocols such as Ekert91^{26} and BBM92^{27} in satellitetoground and satellitetosatellite settings. For full details of the instrument, we refer readers to references^{19,28}. Certified randomness can in principle be extracted from the correlation measurements of entangled photon pairs. However, the detection scheme on SpooQy1 enables only the counting of coincident detections, and does not permit the timestamping of individual events. Due to this design constraint, it is not feasible to utilize entanglement as a source of entropy for our QRNG. Instead, we take as our entropy source fluctuations in the discrete event rates captured during payload operation.
In the context of our QRNG implementation, it is sufficient to consider the production and detection of correlated photon pairs, with random detection times inherited from the statistical properties of the pump beam (see Fig. 1). The observation of shot noise in the measured event rate can be traced directly to the quantum description of the laser source, i.e., a coherent state [^{29}, Chapter 8]. (see Supplementary note 1 for a discussion on shot noise as a randomness source).
Photon pairs produced in the instrument are separated using a dichroic mirror and directed to two avalanche photodiodes. The digitized electronic signal from these detectors is routed to an AND gate and coincident detection events are recorded by a microcontroller.
Prior to detection, photons undergo polarization projection, implemented using a pair of liquid crystal polarization rotators and polarizers. This projection is used to select a measurement basis for each photon. When the same measurement bases are selected for both photons, the majority of coincident events are attributed to photon pairs. This approach allows accidental coincidences attributed to other sources (e.g., detector dark counts, stray light) to be rendered negligible by the use of a sufficiently short timing window. For example, in this implementation, they account for ~2% of the signal^{28,30}, and this could be further reduced with more precise timing electronics.
As a direct consequence of the polarization entanglement generated by the optical system, any polarization basis measured simultaneously on both of the photons produce equivalent correlations. During QRNG operation, we select the diagonal basis to measure both of the photons. This detection scheme based on coincident events can be used to minimize the contribution from other entropy sources, significantly reducing the classical effect that would otherwise dominate the single detection channels. In the absence of any external noise source, random variations in the detected event rates can be traced to the quantization of the spontaneous parametric downconversion field, which can be considered a uniform sampling of the photons in the pump beam. We use this as our raw entropy source.
Our approach resembles the work described by ref. ^{5}, where random numbers are generated by sampling a coherent illuminating beam with a mobile phone camera. Due to the random interarrival times of the photons, the number of detected coincident events per unit of time may be expected to follow a Poisson distribution^{31}. Care is taken to operate the instrument in a regime where the detectors are not saturated, preserving the Poissonian distribution of the source (see Supplementary note 2 for a discussion of how these statistics might be affected by detector recovery times). To extract uniform bits from this distribution we employ a Toeplitz hashbased extractor, as outlined in the Methods section.
To validate the uniformity of our QRNG’s output, a 35.6 kB sequence of random data generated in the laboratory is evaluated using the “Dieharder” test suite, and the result is visualized using the KS test (summarized in Fig. 2), alongside output generated using the C language RNG implementation^{32}. In this analysis, the expectation for a random source is that the p value for each test should be distributed in the interval [0.01, 0.99]. Our data appears to conform to this expectation showing the empirically obtained p values remain close to the theoretical ideal line. This test also illustrates the limitations of such statistical analysis in assessing a random generator, specifically that such tests are restricted to the assessment of uniformity. The reader will note the similar performance obtained using the C RNG, which is pseudorandom and therefore entirely predictable with the knowledge of the seed.
Experiment performance in orbit
The experiment is repeated onboard SpooQy1, after deployment in low Earth orbit. Due to the limited duty cycle of satellite operations and communication bandwidth, we are restricted to retrieve at most 256 random bits per trial. It is nontrivial to test the quality of randomness of such small datasets. For example, the “Dieharder” test is not suitable for these datasets^{33}. However, one may estimate the quality of randomness of such short sequences of bits by observing the frequencies of occurrences of substrings of a particular length (namely the Borel normality condition)^{34}, with a perfectly random sequence expected to produce a uniform distribution for each length. Figure 3 shows an analysis of 16896 random bits (i.e., the result of 66 trials in orbit), with the relative frequencies matching this expectation. For example, asymptotically the relative frequencies of occurrences of both 0 and 1 should be 50%, and occurrences of each of the strings 00, 01, 10, and 11 should be 25%. In our analysis of 66 trials, the occurrences of 0 and 1 are 49.8(3)% and 50.5(3)% respectively. The sequences 00, 01, 10, and 11 are observed with occurrences 24.5(4)%, 26.0(4)%, 24.3(4)%, and 25.0(4)% respectively.
Implementing a prototype randomness beacon
A randomness beacon^{20} is a public, periodically updated source of randomness provided as a resource for a variety of tasks which require a random input. The beacon publishes “pulses” of random bits on a predefined schedule, which are typically broadcast over the internet.
We implement a prototype randomness beacon with a 24hour refresh interval onboard the nanosatellite SpooQy1, with the goal of demonstrating the feasibility of distributing such a beacon to offgrid infrastructures. There are a few established functionality principles that a randomness beacon must satisfy in order to be useful^{20}. These include the signing of each “pulse” using a public key traceable to the beacon originator, in order that the provenance of the beacon pulse can be confirmed. Pulses must also bear references to their parent in order to facilitate verification of the beacon’s integrity. While these features should be straightforward to implement on a dedicated satellite, SpooQy1’s primary mission objectives laid stringent resource constraints on the QRNG subsystem. However, we were able to reinforce several standard elements of the satellite’s onboard radio to meet these requirements.
The onboard radio (Nanocom AX100, GOMspace) broadcasts a beacon signal at 30second intervals, and is able to contain a simple data structure consisting of up to 256 generated random bits. The radio implements a hashbased message authentication code (HMAC), linking beacons to the satellite’s private key^{35}. Alongside a timestamp, our data structure includes the current randomness beacon data in the form of 256 bits of fullentropy randomness. As computing a hash of the previous beacon data would be too computationally expensive for our highly constrained platform, we opt instead to include the full 256 random bits from the previous beacon, satisfying the requirement for linking to previous pulses.
The satellite beacon is encoded using a proprietary data format, which can be decoded by the GOMspace GS100 ground station receiver^{36}. Beacons were recorded at two ground stations, located at Windisch (Switzerland) and on the National University of Singapore’s Kent Ridge campus (Singapore). As our satellite was deployed from the ISS (International Space Station) orbit (inclination 51.6^{∘}, period ~90 minutes), we typically observe six passes per day over the Switzerland site, and up to four passes over the Singapore site. Since the two ground stations are in different time zones, it yields a possibility for us to receive the same beacon at two different stations approximately 10 times in 24 hours. Ground track, locations of our ground stations, and a randomness beacon received by the ground stations on 12 January, 2020 are shown in Fig. 4.
As microsatellitebased broadband internet proliferates^{37}, there may be an increased demand for satellitebased cryptographic infrastructures such as randomness beacons. To be truly useful, an orbital randomness beacon would require a higher refresh rate than demonstrated in this work (for example, the NIST beacon^{20} updates every 60 s), robust cryptographic authentication, and rigorous linking of sequential pulses^{38}. While it was not possible to implement all of these on SpooQy1, we believe that our proofofconcept demonstration shows that such beacons can be hosted onboard lowresource satellites using existing technologies.
Conclusion
We have implemented a quantum random number generator on board an orbiting nanosatellite where the entropy is derived from the shot noise of photon correlations. QRNG output is tested using randomness testing suites, suggesting that the results are strongly indicative of highly uniform distribution. More comprehensive tests on the random bit string generated can be carried out once sufficient data is available. However, this work clearly shows the feasibility and practicality of this QRNG approach. We also implement a prototype randomness beacon, broadcasting randomness generated from a known and characterized quantum process.
Our results demonstrate the feasibility of implementing a sophisticated, photonicsbased solution despite the challenges imposed by these small, resourcelimited platforms. We hope that these results can pave the way towards more powerful QRNG implementations in orbit, including selftesting^{39} or even deviceindependent designs^{12}.
Methods
In order to construct a randomness extractor, we must first estimate the available entropy of the sampled random signal. For a coincidence rate λ, with X a random variable corresponding to the number of events observed in one second, the probability of observing a particular outcome n is given by
The accessible entropy from this source is estimated using the min entropy of this distribution, given by
We extract uniform random numbers from this signal using a Toeplitz hashing extractor^{40} with extraction ratio g. With k bits encoding each event X, g must be less than \({H}_{\min }(X)/k\), with this value calculated following Equation (2). The result is uniformly distributed random bits^{5} with probability
Here m is the number of input low entropy bits and l is the number of extracted high entropy bits. The security parameter, ϵ > 0, is the probability of failure for the randomness extraction.
In our experiment, coincidence data is encoded in k = 16bit registers. From analysis of 47, 422 seconds of data generated using a groundbased identical copy of the source, we estimate the quantum randomness per bit as g ≥ 1/4. We employ a Toeplitz matrix with dimensions l = 256 and m = 3072, yielding 256 bits of extracted randomness per 192 16bit registers and achieving a generation rate of 80 bits/minute (see, Fig. 5). From equation (3), we expect the generated random bits to deviate from perfect randomness with probability at most 2^{−256}. This means that one must collect and process 2^{256} random bits before being able to predict the next bit, assuming full control over, or knowledge of, the classical noise of the original source.
Figure 6a depicts detector coincident counts collected for 125 minutes in a laboratory setting using a source identical to that on the satellite. The raw data collected exhibits a slowmoving trend (orange curve). After removing the lowfrequency components using fast Fourier transform (FFT) (cutoff frequency used 0.01 (Hz)), we obtain data which conforms well to a Poisson distribution (mean 1785 and Fano factor^{41} of 1 ± 0.013, Fig. 6c). This suggests that the remaining data consists of shot noise^{5}. While resource constraints on the satellite do not permit the use of FFT algorithms, the use of only shortduration data blocks (192 samples of the coincident event rate) enables us to disregard these lowfrequency contributions. This is confirmed by Fig. 6b, in which Fano factors of 192point data blocks are shown to be within the range from 0.8 to 1.2, a signature of Poisson statistics reinforcing the absence of significant lowfrequency effects.
Data availability
The data that support the results of this work are available from the corresponding author on reasonable request.
Code availability
The code developed to analyze the data is available from the corresponding author on reasonable request.
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Acknowledgements
This research was carried out at the Centre for Quantum Technologies, National University of Singapore, and supported by the National Research Foundation, Prime Minister’s Office, Singapore under the grant NRFCRP12201302.
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A.R., T.I., X.B., C.W., A.L., and J.G. contributed equally to the work.
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The authors declare that there are no competing interests. James A. Grieve is a Guest Editor for Communications Physics, but was not involved in the editorial review of, or the decision to publish this article.
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Reezwana, A., Islam, T., Bai, X. et al. A quantum random number generator on a nanosatellite in low Earth orbit. Commun Phys 5, 314 (2022). https://doi.org/10.1038/s42005022010967
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DOI: https://doi.org/10.1038/s42005022010967
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