figure table

# A prototype for pulsar observations at low radio frequencies using log
periodic dipole antennas

Kshitij S. Bane  Indian Institute of Astrophysics, 2nd Block, Koramangala,
Bangalore 560034, India  Indrajit V. Barve  Radio Astronomy Field Station,
Indian Institute of Astrophysics, Gauribidanur 561210, India  G. V. S. Gireesh
Radio Astronomy Field Station, Indian Institute of Astrophysics, Gauribidanur
561210, India  C. Kathiravan  Indian Institute of Astrophysics, 2nd Block,
Koramangala, Bangalore 560034, India  R. Ramesh  Indian Institute of
Astrophysics, 2nd Block, Koramangala, Bangalore 560034, India

###### Abstract

A prototype for dedicated observations of pulsars and other astrophysical
transients in the frequency range 50 - 80 MHz has been recently commissioned
at the Gauribidanur radio observatory near Bangalore in India. The antenna
set-up, analog & digital receiver systems, and the initial observations are
presented.

###### keywords:

pulsars, radio observations, low frequencies, instrumentation

<EMAIL_ADDRESS>
##  1 Introduction

A pulsar is a neutron star, i.e. the ultra-dense core that remains after a
massive star undergoes a supernova explosion. It spins at very rapid rates
ranging from once in a few seconds to as much as ${\sim}$700 times per second.
The strong magnetic fields (${\sim}10^{8}{-}10^{14}$ G) created when the
neutron star was formed and the star’s rapid rotation results in a
magnetosphere. Due to misalignment of the magnetic and rotation axes of the
pulsar, the radio emission comes out in two beams, one from each pole of the
magnetosphere. The observed emission is coherent, but the mechanism behind the
coherence is still being debated. These rotating beams of radiation could be
noticed whenever they intersect our line of sight to the pulsar, much like a
lighthouse on the sea-shore. Each rotation of the pulsar thus produces a
narrow pulse of radiation. The first pulsar was observed at a low frequency of
${\approx}$ 81.5 MHz[1]. But, much of our present knowledge about pulsars have
come primarily from radio observations at frequencies $>$300 MHz. The primary
reason for this is that the emission from the pulsars at low frequencies are
more affected by dispersion and scattering during their propagation through
the interstellar medium (ISM) as compared to higher frequencies. While the
delay in the arrival time of the pulses due to the dispersive properties of
the ISM varies as $\nu^{-2}$ (where $\nu$ is the frequency of observation),
the interstellar scattering changes as ${\sim}\nu^{-4}$ (see e.g. 2). The
latter leads to broadening of the pulses as a result of which they overlap[3,
4]. It then becomes difficult to distinguish the maxima and minima in a pulse.
The periodic nature of the signal is either subdued or nearly lost when the
pulse broadening time becomes nearly comparable to the spin period of the
pulsar (see e.g. 5). The other reasons for the limited observations of pulsars
at frequencies $\lesssim$100 MHz are the comparatively intense synchrotron
emission from the Galactic background, and the radio frequency interference
(RFI).

Pulsar observations at frequencies $\lesssim$100 MHz are necessary to
understand the emission mechanism and the characteristics of the pulse profile
as a function of frequency which are still being examined. For e.g., the
radius-to-frequency mapping (RFM) effect in pulsars are most prominent at
lower frequencies[6, 7]. Many pulsars exhibit a turn-over in the spectrum
close to ${\approx}$100 MHz[8, 9]. Therefore the extension of their spectra
towards lower radio frequencies is naturally of great interest. This is
especially so for those pulsars whose intensity is increasing with decreasing
frequency in the known part of their spectra. An understanding of the
propagation of the low frequency radio waves in the ISM is also important. The
$\nu^{-4}$ dependence of scattering in the ISM makes the dispersion effects
more stronger at lower frequencies and hence it is easier to carry out better
measurements of the dispersion measure (DM). Observations of pulsars at
frequencies $\lesssim$100 MHz are currently carried out with LOFAR[10, 11],
UTR-2 telescope[12], MWA[13], LWA[2], and EDA[14, 15] in the time sharing
mode. Exploration of transient phenomena in the Universe is an exciting and
rapidly growing area of radio astronomy. Considering these, we have set-up a
radio telescope in the Gauribidanur observatory[16, 17] (Longitude:
$77.4^{\circ}$ E; Latitude: $13.6^{\circ}$ N) for dedicated observations of
pulsars in the frequency range 50 - 80 MHz. RFI in Gauribidanur is also
minimal[18, 19, 20]. We propose to observe and understand the characteristics
of the known pulsars and the periodic Fast Radio Bursts (FRBs)[21, 22, 23, 24]
at low frequencies. The observing facility described in the work is a
dedicated instrument with wide sky coverage, large bandwidth, and high time
resolution (see Sections 2 and 3) all of which are important for observations
of fast transients (see e.g. 5). In the rapidly developing field of study of
the transient sky, FRBs are perhaps the most exciting objects of scrutiny at
present. So there is potential for new observations[25].

##  2 The Antenna and Front-end Analog Receiver System

The basic signal reception element used in the present case is a Log Periodic
Dipole Antenna (LPDA). It is a type of broadband directional antenna whose
characteristics are nearly constant over its entire operating frequency
range[26]. We have set-up an array of 16 LPDAs on a north-south baseline with
a spacing of 5 m between the adjacent antennas. They are combined as two
groups with 8 LPDAs in each group (see Figure 1). The LPDAs used in the array
are designed according to the formulations reported in the literature[27]. The
characteristic impedance of the LPDA is ${\approx}$50 ${\Omega}$. Its half-
power beam widths (HPBW) as per calculations are ${\approx}80^{\circ}$
(E-plane) and ${\approx}110^{\circ}$(H-plane). All the 16 LPDAs have been
mounted with their H-plane in the east-west direction. The effective
collecting area and gain of each LPDA is ${\approx}$0.4${\lambda}^{2}$ (where
${\lambda}$ is the wavelength corresponding to the observing frequency) and
${\approx}$6.5 dBi (with respect to an isotropic radiator), respectively. The
Voltage Standing Wave Ratio (VSWR) is $<$2 over the frequency range
${\approx}$40 - 440 MHz[28]. The aforementioned effective collecting area and
the HPBW of the LPDA are larger compared to that of the other similar
frequency independent receiving elements like the inverted V-shaped dipoles
and bowtie antennas, respectively, used elsewhere. Since the LPDAs are
arranged on a north-south baseline, the combined response pattern of the array
(16 LPDAs) is ${\approx}110^{\circ}$ in the east-west (hour angle) direction
and ${\approx}3^{\circ}$ in the north-south (declination) direction for
observations near the zenith at a typical frequency like 65 MHz. It is a fan-
beam with the above resolution in declination. The width of the east-west
response pattern is nearly independent of frequency. Being very wide, it helps
to observe a radio source continuously for $\gtrsim$7 h. A RG58U coaxial cable
connected to the feedpoint near the top of the LPDA is used to transmit the
radio frequency (RF) signal incident on the LPDA to the input of a low-pass
filter with 3 dB cut-off at ${\approx}$85 MHz, followed by a high-pass filter
with 3 dB cut-off at ${\approx}$35 MHz and a wideband amplifier with an
uniform gain ${\approx}$30 dB in the frequency range 35-85 MHz. The two
filters and the amplifier are kept near the base of the LPDA to minimize the
length of the RG58U cable and hence the transmission loss. The high- and low-
pass filters help to attenuate the unwanted signal at frequencies
${\lesssim}$30 MHz and ${\gtrsim}$85 MHz. The filtered and amplified signal
from each LPDA is then passed via a cable delay unit (see the following
paragraph). Subsequently, they are combined using two sets of 8-way power
combiner followed by again a high-pass filter, low-pass filter and wideband
amplifier as mentioned above.

---
Figure 1:  The array configuration and the front-end signal path.

As the array is oriented in the north-south direction, RF signal coming from
an astronomical source whose declination is different from the local zenith
(${\approx}14^{\circ}$ N) will be incident on each LPDA in the array at
different instances of time. So, in order to coherently combine the signal
from the different LPDAs, there is provision to include cable of appropriate
length in the signal path from each LPDA in the array to compensate the
aforesaid time delay. This allows the response pattern (‘beam’) of the each
group of eight LPDAs to be ‘phased’ towards any desired declination in the
range ${\approx}{-26^{\circ}}$ S to ${\approx}{+54^{\circ}}$ N. The limits are
due to the HPBW of the LPDA along its E-plane and the local latitude mentioned
earlier. The step interval in the cable delay unit corresponds to an angle of
${\approx}3^{\circ}$, and the maximum angle to which the ‘beam’ of the group
of eight LPDAs could be ‘phased’ in the north-south direction is
${\approx}45^{\circ}$. Note that the aforementioned minimum step interval in
the delay unit results in a phasing error of ${\pm}1.5^{\circ}$ (same as that
for the ‘beam’ of the array in declination mentioned in the previous
paragraph). It corresponds to a delay error of ${\pm}$3 nsec for the total
length of 35 m for the group of eight LPDAs (see Figure 1). We neglect this
since it is small in general and also lesser than the minimum delay of
${\approx}$11 nsec that could be applied digitally in the present case (see
Section 3). The combined output from each group of antennas are then
transmitted to the receiver building (located ${\approx}$300 m away) via low-
loss coaxial cables buried ${\approx}$1 m below the ground level to minimize
possible diurnal variations in the characteristics of the cable. In order to
compensate for the transmission losses during propagation, the RF signal from
the two antenna groups are amplified in the receiver building. The output of
the amplifiers are passed through 50 - 80 MHz bandpass filters to attenuate
any spurious pick-up outside the band. Then the signal is fed to the input of
the digital receiver.

---
Figure 2:  Schematic of the digital receiver system.

##  3 The Back-end Digital Receiver System

We have used a Field Programmable Gate Array
(FPGA)111https://www.xilinx.com/products/silicon-devices/fpga/what-is-an-
fpga.html based digital spectrometer which converts the input voltage signal
to its power spectrum using the Fast Fourier Transformation (FFT) technique.
The spectrometer is implemented on Reconfigurable Open Architecture Computing
Hardware (ROACH) from the Collaboration for Astronomy Signal Processing and
Electronics Research (CASPER). The ROACH board hardware has Xilinx Virtex-5
FPGA222https://casper.astro.berkeley.edu/wiki/ROACH. Figure 2 shows the
schematic of the digital receiver system used in the present case.

The RF signals corresponding to the two antenna groups in Figure 1 are
connected to the input of an analog-to-digital converter (ADC). It is a quad-
ADC containing four AD9480
ICs333https://www.analog.com/en/products/ad9480.html. We use two channels of
the ADC for the present work. The ADC converts the input voltage to a 8-bit
Fixed point number (Fix 8.7) between -1 and +1. Note that a linear relation
between the input and output of the ADC for a large range of the input signal
is important for any digital system. To check this in the present case, a
broadband noise signal with provision to vary the input power level was
connected to the input of the ADC. The output from the ADC were recorded for
different levels of the input signal, and then processed offline to get the
power spectrum using Fast Fourier Transformation (FFT). Figure 3 shows the
results of the above test. The spectral power is linear for the input signal
amplitude in the range ${\approx}$ -42 dBm to ${\approx}$ -4 dBm. This implies
that the measured dynamic range (MDR) of the ADC is ${\approx}$ 38 dB. The
effective number of bits (ENOB) = MDR/6.02 = 6.3
bits444https://www.allaboutcircuits.com/technical-articles/understanding-the-
dynamic-range-specification-of-an-ADC/. Note that for a 8-bit ADC, the
expected dynamic range (EDR) and ENOB are ${\approx}$ 6.02${\times}$8 = 48 dB,
and ${\approx}$ 7.3 bits555https://www.analog.com/media/en/technical-
documentation/data-sheets/AD9480.pdf, respectively. But these numbers are
valid primarily for continuous wave (CW) signals at specific spot frequencies
only.

---
Figure 3:  Results of the ADC linearity test.

We use a 90 MHz clock to sample the bandlimited RF signal of 50-80 MHz in the
present case since the latter is in the 2nd Nyquist zone (45 - 90 MHz) of the
aforementioned sampling
frequency666https://www.mikrocontroller.net/attachment/341426/Understanding{_}digital{_}signal{_}processing.pdf.
Depending upon the declination of the source, appropriate delays are applied
to the RF signal from either of the two groups in steps of 11.11 nsec to
coherently combine the signals later. The corresponding delay error (i.e.
${\pm}$5.5 nsec) limits the phasing of the north-south ‘beam’ of the array to
${\pm}2.3^{\circ}$ with respect to the source declination. To obtain the power
spectra of the RF voltage signals, the outputs from the delay units are
processed using a combination of a finite impulse response (FIR) filter and
FFT, together called a ‘Polyphase filterbank’ (PFB). Since the FFT is computed
over finite number of samples, its response suffers from spectral leakage. But
when a FIR filter with windowing function is used before the FFT, leakage into
the adjacent spectral channels is considerably reduced[29]. In our design, a
4-tap FIR filter with Hamming window of 18-bit coefficients followed by
2048-points FFT is used. The latter has 1024 ‘positive’ frequency bins. The
total bandwidth sampled in the present case is 45 MHz as mentioned earlier.
So, the frequency resolution is 43.945 kHz. To test the spectral leakage, CW
signal at different frequencies (64.9 - 65.1 MHz in steps of 1 kHz) was fed to
the input of the digital receiver in succession. An inspection of the test
results (Figure 4) indicate that the isolation between adjacent frequency bins
is ${\approx}$ -49 dB. The full-width at half-maximum (FWHM) of each frequency
bin is ${\approx}$ 36 kHz. Note that the latter should have been ${\approx}$
43.945 kHz as mentioned above. But due to the frequency response of the 4-tap
PFB, the FWHM of each bin is reduced to ${\approx}$ 36 kHz. The isolation
offered by a 4-Tap PFB (${\approx}$ 50 dB, see Figure 5) is sufficient for
isolating spectral leakage. Note that increasing the number of taps in the PFB
will improve the isolation. The main lobe response will be more flatter (see
Figure 5 for a comparision between 4-tap and 8-tap PFBs). These are useful to
carry out high precision timing studies of pulsars. But the possibilities of
timing studies at low frequencies as in the present case are restricted since
the pulse profiles are scatter broadened. Further, folded / average pulse
profiles are only generated on most occassions. So a 4-tap PFB with Hamming
window was used.

---
Figure 4:  Spectral leakage test.

Note that the pulsar signal gets dispersed during its propogation through the
ISM. The higher frequency components in the signal reach the observer earlier
compared to the lower frequency components. Therefore the received signal
needs to be de-dispersed to reconstruct the pulse. There are two types of de-
dispersion methods: coherent and incoherent[30]. We use the incoherent de-
dispersion technique as it is computationally
easier777http://www.ncra.tifr.res.in/ncra/gmrt/gmrt-users/low-frequency-radio-
astronomy/ch17.pdf. The frequency resolution mentioned above allows finer
correction for the dispersion, and also limits the possible leakage of the
narrowband RFI to adjacent spectral channels. The PFB block output is 36-bit
wide with 18-bit each for real and imaginary parts. The outputs corresponding
to the two antenna groups are combined and squared to get the power spectrum
(see Figure 6). The spectral data are then integrated for the desired
duration. The output at this stage is 39-bit wide. The 10Gb Ethernet interface
(see Figure 2) allows 64-bit data to be transmitted888https://casper-
toolflow.readthedocs.io/projects/tutorials/en/latest/tutorials/roach/tut{_}ten{_}gbe.html.
To facilitate the transfer, the aforementioned output is truncated to a 32
bits by leaving 7 bits from the LSB (Least significant bit) and thereby making
it easier to packetize the data in such a way that two data points are muxed
together. Any degradation of the signal due to this truncation is expected to
be minimal since the information content in the LSBs correspond primarily to
noise fluctuations in the data only. The integrated output, which is now
quantized to a 32-bit unsigned number, is packetized with headers and sent to
the data acquisition computer over 10 Gb Ethernet (see Figure 2). Each packet
contains a standard UDP header, and custom header. The latter has observation
details, 1 PPS (pulse per second) count, and a packet count. The 1 PPS signal
is derived from a GPS clock (Trimble Thunderbolt E-GPS Disciplined
clock)999https://timing.trimble.com/wp-content/uploads/thunderbolt-e-gps-
disciplined-clock-datasheet.pdf and given to the FPGA via the ADC card to
generate the 1 PPS count. Packet count is a unique packet number assigned to
each packet.

---
Figure 5:  Spectral response of 4-tap and 8-tap PFB.

##  4 Data Processing Pipeline

---
Figure 6:  A sample power spectrum obtained from observations of the sky
background. The amplitude variation (${\approx}$ 5 dB) across the 50 - 80 MHz
range is due to a combination of the differential attenuation (as a function
of frequency) in the coaxial cables used for the RF signal transmission, and
the non-thermal spectral nature of the radio emission from the sky background.
One could notice that RFI is very minimal as mentioned in Section 1.

The data acquired are first processed through a MATLAB based quick-look code
for a quality check of the observation. The spectral response (see e.g. Figure
6) is plotted and inspected to ensure that the system performance was in order
during the observation. The aforesaid code checks for any ‘packet loss’ that
might have happened while writing the data to the hard disk of the acquisition
computer. The ‘packet loss’ would give rise to gaps in the data stream which
in turn affect the arrival times of the pulses leading to a lower signal-to-
noise (S/N) for the observed pulsar. In extreme cases, it may not be possible
to detect the pulsar when the data are folded. An unique number is assigned to
each packet and the same is mentioned in the file header while writing the
data. The packet number is used to assess ‘packet loss’. If there are any, a
new file is created by inserting zeros in the place of the lost packets to
maintain continuity in the data stream. After the above processes, the data
are converted to SIGPROC ‘filterbank’
format101010http://sigproc.sourceforge.net/sigproc.pdf for further analysis
using the Pulsar Search and Exploration Toolkit (PRESTO)[31]. The file is read
using the ‘readfile’ tool and the meta-data are examined. RFI mitigation is
performed using the ‘rfifind’ tool which searches for prominent RFI in the
time-series as well as in the frequency domain, and creates ‘mask’ files. It
also generates diagnostic files containing data statistics, identifies the
time-domain statistical issues and marks them as RFI. The RFI ‘masks’ are used
in the subsequent stages of data processing. Subsequently, the ‘prepfold’ tool
is used to carry out folding and de-dispersion. It searches over a range of
pulse periods and DM values to obtain the best fit for the corresponding
parameters, i.e. the period and DM of the pulsar present in the observed data.
Finally, the integrated pulse profile with the highest S/N is generated.

##  5 Trial Observations

We carried out observations of the sky background in the meridian transit mode
to understand the characteristics of the antenna array and the receiver
system. Figure 7 shows the observations carried out on 2021 June 30 at a
typical frequency like 65 MHz. The bandwidth and integration time used were
${\approx}$ 30 MHz and ${\approx}$ 1 sec, respectively. The maximum in the
observed emission was around $\rm{\approx}\,18^{h}$ Local Sidereal Time (LST)
as expected (see e.g. 32, 33). The duration of the observed profile (at the
half maximum level) derived from the least squares fit is ${\approx}$ 9 h.
This corresponds to an angular extent of ${\approx}\,135^{\circ}$. Compared to
this, the HPBW of the array pattern (in the east-west direction) is
${\approx}\,110^{\circ}$ (see Section 2). Note that the observed deflection in
Figure 7 is primarily due to the intense patch of emission extending over the
LST range ${\approx}$ 16 h - 21 h in any low frequency all-sky map (see e.g.
32, 34). A convolution of the aforementioned region (angular extent
${\approx}\,75^{\circ}$) with the array pattern (HPBW
${\approx}\,110^{\circ}$) could give rise to ${\approx}\,135^{\circ}$ width
for the observed profile (see e.g. 35, 36).

---
Figure 7:  Observations of the sky background radiation with the pulsar array
at 65 MHz with an integration time of ${\approx}$ 1 sec and bandwidth of
${\approx}$ 30 MHz. RFI was very minimal during the observing period.

Moving on to pulsar observations, we targeted the historical B1919+21
(J1921+2153) for our trial run. It is also located closer to the local zenith
(${\approx}\,14^{\circ}$ N) in Gauribidanur. Some of the characteristics of
this pulsar are[37]: mean flux at 65 MHz ${\approx}$ 1.6 Jy, period = 1.337
sec, pulse width ${\approx}$ 0.104 sec, and DM ${\approx}$ 12.437 $\rm
pc\,cm^{-3}$. Note that the dispersive nature of the ISM causes smearing of
the pulsar signal over a time $\rm t_{smear}$ which depends on the DM of the
pulsar, frequency and bandwidth of observation[38]. For the FWHM of the
frequency bins mentioned earlier (${\approx}$ 36 kHz) and the frequency band
of observation in the present case (i.e. 80 - 50 MHz), $\rm t_{smear}$ for
B1919+21 will be in the range ${\approx}$ 5 - 34 msec. These values are well
within the pulse period of B1919+21 (i.e. 1.337 sec). We observed the pulsar
for a total duration of ${\approx}$ 2 h with an integration time of
${\approx}$ 4 msec. The north-south ‘beam’ of the array was ‘phased’ to the
declination of the pulsar ($21^{\circ}$ N) for the observations (see Section
2). Figure 8 shows the results of our observations. The pulsar was detected
with S/N ${\approx}$ 23\. Comparing this with the mean flux of the pulsar, we
find that the noise fluctuations should be ${\approx}$ 0.07 Jy. This is
reasonably consistent with the estimated $\rm{\Delta}S_{min}$ (${\approx}$
0.12 Jy) taking into consideration the above S/N and duty cycle (i.e. ratio of
the width W of the pulse profile to its period P) of the pulsar to be
${\approx}$ 0.078[37]. The other parameters used in the calculations are:
total observing period ${\approx}$ 2 hr, $\rm T_{sys}\,{\approx}\,8500$ K at
65 MHz[37], bandwidth ${\approx}$ 30 MHz, and number of polarizations = 1. The
above observational results from Figures 7 & 8 indicate that our observing
system is well characterized. Note that for a total effective collecting area
of $\rm{\approx}136\,m^{2}$ and an observing/integration period of
${\approx}$1 msec, the minimum detectable flux density of the system is
${\approx}$1 kJy. This is lower than the peak flux density (${\sim}$100 kJy)
of the FRBs reported recently in the frequency range 400 - 800 MHz[39].
Assuming that the flux densities of the FRBs are expected to increase towards
the lower frequencies[40], similar detections as well as observations of giant
pulses from the Crab nebula pulsar[41] are possible with our system. We would
like to add here that subsequent to the detection of B1919+21, the pulsars
B0950+08, B0834+06, and B1133+16 were also successfully observed with our
system. The related results will be reported separately.

---
Figure 8:  Observations of B1919+21 at 65 MHz with the pulsar array in the
Gauribidanur observatory. The data were analysed using PRESTO. RFI was very
minimal during the observing period. They were mitigated using the ‘rfifind’
tool in PRESTO (see Section 4).

##  6 Ongoing Work

Further development is in progress to: (i) digitize the RF signal from
individual antennas in the array. By applying different sets of delays while
combining the signals, multiple beams can be formed to simultaneously observe
different regions of the sky in declination. The array beam is already wide
along RA (${\approx}110^{\circ}$). By having several beams in declination
(each ${\approx}3^{\circ}$ wide), a larger area of the sky can be monitored at
the same time. This can be useful for observations of FRBs; (ii) use Cross-
polarized Log Periodic Dipoles (CLPD[42]) and carry out polarization
observations (see e.g. 43); (iii) use phase-coherent de-dispersion scheme with
the DSPSR software package[44]; (iv) increase the sampling frequency and
thereby minimize the delay error relative to the source position (see Section
3); (v) use calibrated noise sources that can be switched into the signal path
and/or routine observations of B1919+21 for calibration purposes. For
polarization data, it is planned to use observations of radio transients from
the Sun since some of them like type I bursts exhibit 100% circular
polarization[45].

##  7 Summary

We have presented the characteristics of the low frequency (50 - 80 MHz)
observing system set up recently at the Gauribidanur observatory near
Bangalore in India, and the initial observations that were carried out. Its
large bandwidth (${\approx}$ 30 MHz), wide sky coverage
(${\approx}\,110^{\circ}{\times}80^{\circ}$), high spectral and temporal
resolutions ($\rm{\approx}\,36\,kHz$ and 1 msec, respectively), geographical
location (${\approx}14^{\circ}$ N), and the fact that the array is dedicated
for time domain astronomy, are expected to be very useful to observe pulsars,
radio bursts from the Sun[46, 47], and other high time resolution
astrophysical phenomena like the FRBs.

### Disclosures

The authors declare that there are no conflicts of interest.

### Acknowledgments

We express our gratitude to the staff of the Gauribidanur observatory for
their help in setting up the antenna/receiver systems, and carrying out the
observations. We thank A. A. Deshpande for his encouragement and suggestions.
We acknowledge the referees for their kind comments which helped us to present
the results more clearly.

### Data, Materials, and Code Availability

Data used in the study are available at
https://www.iiap.res.in/gauribidanur/home.html.

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###### List of Figures

  1. 1  The array configuration and the front-end signal path.
  2. 2  Schematic of the digital receiver system.
  3. 3  Results of the ADC linearity test.
  4. 4  Spectral leakage test.
  5. 5  Spectral response of 4-tap and 8-tap PFB.
  6. 6  A sample power spectrum obtained from observations of the sky background. The amplitude variation (${\approx}$ 5 dB) across the 50 - 80 MHz range is due to a combination of the differential attenuation (as a function of frequency) in the coaxial cables used for the RF signal transmission, and the non-thermal spectral nature of the radio emission from the sky background. One could notice that RFI is very minimal as mentioned in Section 1.
  7. 7  Observations of the sky background radiation with the pulsar array at 65 MHz with an integration time of ${\approx}$ 1 sec and bandwidth of ${\approx}$ 30 MHz. RFI was very minimal during the observing period.
  8. 8  Observations of B1919+21 at 65 MHz with the pulsar array in the Gauribidanur observatory. The data were analysed using PRESTO. RFI was very minimal during the observing period. They were mitigated using the ‘rfifind’ tool in PRESTO (see Section 4).


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##  Appendix A Secure Database Queries using TEEs

In this section, we review the TEE-based secure computation for handling
encrypted database queries. Unlike general-purpose secure computation, secure
database query protocols aim to implement data query tasks with optimal
performance. Over the past two decades, the notion of encrypted databases
(Popa et al., 2011) has been proposed to enhance data availability while
keeping data confidential. It not only provides a hardware and software
infrastructure for securely storing sensitive data, such as personal records,
financial documents, and government data, but also offers data query services
to authorized users. As before, we divide secure database queries into three
categories: secure outsourced queries, secure distributed queries, and secure
multiparty queries.

###  A.1. Secure Outsourced Queries

####  A.1.1. Problem Statement

Generally, a Secure Outsourced Queries (SOQ) protocol consists of three
entities: a data owner, a client, and a cloud server. First, the data owner
encrypts the original database $\bm{d}$ and then uploads its encrypted form
$(\llbracket{\bm{d}}\rrbracket,\llbracket{\bm{\Lambda}}\rrbracket)$ to the
cloud server, in which $\llbracket{\bm{d}}\rrbracket$ is the encryption of
original data and $\llbracket{\bm{\Lambda}}\rrbracket$ is an encrypted index
allowing server to provide query services efficiently. Once the database is
uploaded, any authorized client can submit an encrypted query
$\llbracket{q}\rrbracket$ to the cloud server. The server performs the query
services in encrypted form and obtains
$(\llbracket{y}\rrbracket,\Gamma)=\Phi\left((\llbracket{\bm{d}}\rrbracket,\llbracket{\bm{\Lambda}}\rrbracket),\llbracket{q}\rrbracket\right)$,
where $\Phi$ is a well-designed secure outsourced analytics protocol and $y$
is the query result. Obliviously, it is a special case of secure outsourced
computation. The correctness means that the accurate query results are
returned to the client, and the completeness means that all correct results
should be returned. The privacy means that the cloud server cannot learn
anything sensitive information about $q$ (query privacy),
$(\bm{d},\bm{\Lambda})$ (database privacy), and $y$ (output privacy). The
integrity forces the cloud server to run the program $\Phi$ honestly, where
$\Gamma$ is the proof for proving the integrity of execution.

The early SOQ protocols (Popa et al., 2011; Arasu et al., 2015) are based on
various cryptographic primitives, for example, searchable encryption,
homomorphic encryption, structured encryption, order-preserving encryption for
comparison-based queries, accumulator, and Merkle-hash proof for providing
integrity guarantee. However, they just support some simple queries and fail
to answer complex queries efficiently, such as queries involving join
operations. Since the emergence of trusted hardware, TEE-based SOQ has
provided a promising way to achieve a practical encrypted database while
providing privacy protection and integrity guarantee. Besides, TEE is also a
natural choice for implementing complex access-control policies in the
encrypted database.

As shown in Fig. 10, we provide the basic SOQ workflow to explain the
interactions between a data owner, a client, and a TEE-equipped server. (1)
The data owner outsources database $(\bm{d},\bm{\Lambda})$ to the cloud
server. Note that the encrypted database is stored on the untrusted domain.
(2) The data owner initializes the TEE and then proves the exact program
$\Phi$ for providing SOQ services has been loaded into server’s enclave
successfully. (3) The client also builds a secure channel with TEE via remote
attestation and then sends a query $q$ to the cloud. (4) The cloud server
employs TEE to execute the SOQ protocol honestly, which is run between the EPC
and unprotected memory by ecall / ocall invocations. (5) Finally, the enclave
returns the final results $(y,\Gamma)$, in which
$y=\Phi((\bm{d},\bm{\Lambda}),q)$ and $\Gamma$ proves the program is executed
honestly. Note that all messages communicated with the enclave are sent over
the secure channel.

Figure 10. Secure Outsourced Queries

Assessment

####  A.1.2. Research Status

Relational Database. In (Priebe et al., 2018), EnclaveDB ensures the data and
the query are confidential, intact, and fresh, even if the host is malicious.
The database logs are verified for achieving integrity and freshness.
EnclaveDB presents a solution to implement minimal thread synchronization
required for concurrent, asynchronous appending and truncation. By
experiments, EnclaveDB introduces about 40% overhead compared to the
traditional database systems. However, EnclaveDB only works on the encryption
mode, and the access pattern may leak sensitive information to the attackers.

To mitigate the side channel attacks, ObliDB was presented to provide
efficient and secure SQL queries via multiple access methods (Eskandarian and
Zaharia, 2019). For example, four oblivious SELECT algorithms are embedded in
the database system, obliDB takes advantage of knowledge about the query to
choose an optimal algorithm to finish the SELECT operation. Therefore the
methods apply to different settings. However, the structure of the queries is
leaked to the adversary. In (Dang et al., 2017), Dang et al. presented an
optimal computational model called Scramble-then-Compute (STC). STC introduced
a new component (called Scrambler) to prevent leakage from access patterns,
and the main idea is to permute the input data randomly before the original
algorithm is invoked. In such a way, the access pattern does not leak any
sensitive information while the TCB is kept lean. With STC, one can improve
the efficiency of an extensive body of oblivious algorithms (e. g. sort,
compaction, selection, aggregation, join). In (Vinayagamurthy et al., 2019), a
scalable encrypted database (StealthDB) was presented to support full SQL
queries, which include query services as well as database creation and
transaction processing. While ObliDB achieves the strongest protection by
making the user data completely inaccessible, StealthDB offers add-on features
but only achieves weaker protection. In (Sun et al., 2021), Sun et al.
explored the trade-offs in security, performance, and functionality. They
proposed the Enclage, which leverages B+ tree to design a three-tier index
(record level, buffer level, and page level). With the three-tier index, they
studied the optimal node size, buffer size, and page size. Extensive
experiments showed that Enclage achieves 5-9x improvements than previous
schemes.

Besides, VeriDB (Zhou et al., 2021) studies the verifiable general queries
technologies on the relational databases via SGX. VeriDB ensures the
correctness, completeness, and freshness of the query results. Note that
VeriDB focuses on the verifiability of queries and is built on top of an
unencrypted database. Thus it fails to provide the privacy proetction of the
database. To achieve verifiability, VeriDB only incurs only about 1-2 ms on
read/write operations and 9%-39% overhead for the complex analytical workload.

Key-Value Store. To ensure confidentiality and integrity of key-value store
management, a basic strategy is to load the entire key-value store to the
enclave. Then a client can read or write the data via the enclave interfaces.
However, the performance is very low when a large store is maintained because
of the limited EPC and the page switches. ShieldStore (Kim et al., 2019)
manages the key-value stores by the hash table, and it overcomes the EPC
limits by maintaining an encrypted hash table in untrusted memory associated
with Merkle trees for integrity protection. ShieldStore only stores the header
pointer of the hash table and Merkle tree root nodes in the enclave. With the
protection of enclaves, ShieldStore outperforms 8-11 times than baseline SGX
key-value stores. In order to ensure freshness against rewind attacks,
SPEICHER (Bailleu et al., 2019) borrows the idea from RocksDB by embedding an
asynchronous trusted counter to an authenticated and confidentiality-
preserving LSM data structure, which is maintained in the untrusted storage
medium. Compared with the RocksDB, SPEICHER only incurs reasonable overheads
for ensuring confidentiality, integrity, and freshness.

Labeled Documents. Labeled documents consist of many documents, and each is
associated with one or several keyword(s). Inverted index design is very
popular in labeled document retrieval systems. An inverted index contains a
set of keywords, and a document posting list of each keyword represents
documents that contain the keyword. Shao et al. (Shao et al., 2020) proposed
the masked inverted index (MII), which supports efficient query processing
with the help of SGX.

In (Ferreira et al., 2020), Ferreira et al. designed the BISEN, a new Boolean
Symmetric Searchable Encryption (SSE) scheme based on trusted hardware and the
traditional SSE. BISEN supports multiple clients with access control features,
provides verifiability against fully malicious adversaries, supports dynamic
updates with forward and backward privacy, and supports arbitrarily complex
boolean queries with filters. Note that BISEN only reveals which encrypted
index entries are accessed. By leveraging TEEs as remote trust anchors, BISEN
is able to move most client-side computations to the server, reducing
computation, storage, and communication overheads. In fact, BISEN builds the
index on cloud server. Besides, (Fuhry et al., 2017) and (Kim et al., 2019)
showed how to build B+ tree and TF-IDF securely using Intel SGX in remote
servers.

###  A.2. Secure Distributed Queries

####  A.2.1. Problem Statement

Secure distributed queries (SDQ) is run between a master node and multiple
slave nodes, similar as SDC described in Sec. 3.2. The data owner outsources
the encrypted database to the master node and authorities the query services
to the master node. The master node splits the large-scale database into
small-scale databases and then distributes them to the slave nodes. When
receiving a query $q$ from a client, each slave node computes an intermediate
result based on its inputs. Then the master node aggregates all intermediates
into the final results. Precisely, an SDQ protocol consists of two sub-
protocols $\Psi$ and $\Pi$, where $\Psi$ is run in slave nodes for obtaining
the intermediate results, and $\Pi$ is run between the master node and the
slave nodes for getting the final results. Specifically,

(3)
$\Phi\left((\bm{d},\bm{\Lambda)},q\right)=\Pi\left(\Psi((\bm{d_{1}},\bm{\Lambda_{1}}),q),\Psi((\bm{d_{2}},\bm{\Lambda_{2}}),q),\cdots,\Psi((\bm{d_{N}},\bm{\Lambda_{N}}),q)\right)$

Where
$(\bm{d},\bm{\Lambda})\triangleq(\bm{d}_{1},\bm{\Lambda}_{1})\circ\cdots\circ(\bm{d}_{N},\bm{\Lambda}_{N})$
222$\circ$ denotes the joint operation between the databases.. Similar to SDC,
the privacy and integrity also should be achieved in an SDQ protocol.

While many primitives to design SDQ protocols are similar to those for SOQ in
an outsourced framework, SDQ protocols focus more on the compatibility with
some popular distributed platforms such as MapReduce and Spark. Therefore,
besides methods for achieving secure queries, we also care about whether a
protocol is compatible with existing distributed platforms. As shown in Fig.
11, we provide the basic SDQ workflow to explain the interactions among a data
owner, a client and the TEE-equipped nodes. (1) The data owner outsources
database $(\bm{d},\bm{\Lambda})$ to master node. Note that the encrypted
database is stored on the untrusted domain. (2) The data owner initializes the
TEE and then proves the exact program $\Pi$ for providing aggregation SDQ
services has been loaded into master’s enclave successfully. (3) The master
node splits the database $(\bm{d},\bm{\Lambda})$ into small-scale databases
$(\bm{d}_{i},\bm{\Lambda}_{i})$, $i=1,2,\cdots,N$. (4) The master node also
builds secure channel via remote (or local) attestation with the slaves and
then ensures the distributed program $\Psi$ is loaded into slaves’ TEE
successfully. (5) The client also builds a secure channel with TEE via remote
attestation and then sends a query $q$ to master node. (6) Then The master
node sends $q$ to all slave nodes, and each slave node obtains an intermediate
result $(\Psi\left((\bm{d}_{i},\bm{\Lambda}_{i}),q\right),\Gamma_{i})$, which
is run between the enclave and untrusted host by ecall/ocall invocations. Note
that $\Gamma_{i}$ is employed to prove the program is run honestly in each
slave node. (7) After that, $\Pi$ is called to aggregate all intermediate
results into the final results. (8) Finally, the master node returns the final
results $(y,\Gamma)$, in which $y=\Phi((\bm{d},\bm{\Lambda}),q)$ and $\Gamma$
proves the program is executed honestly. Noted all messages communicated with
enclave are sent over the secure channel.

Figure 11. Secure Distributed Queries

Assessment

####  A.2.2. Research Status

In (Zheng et al., 2017), Zheng et al. proposed the distributed analytics
platform Opaque. Opaque promises obliviousness of SQL operations and thus
achieves a strong privacy guarantee. To ensure obliviousness, Opaque
introduces the Intra-machine oblivious sorting algorithm and the Inter-machine
oblivious sorting algorithm, which serve as the basic building blocks for the
oblivious filter, oblivious aggregation, and oblivious join. Furthermore, they
also designed novel query planning techniques that improve efficiency by
reducing the number of sort invocations and introducing mixed sensitive
attributes. The experimental results showed that obliviousness by fully-
padding mechanism comes with a 1.6-46x overhead. The fully-padding mechanism
prevents information leakage from the size of intermediate results. To further
improve the efficiency, Hermetic (Xu et al., 2019) applied the differential
private (DP) padding mechanism to the distributed data analytics. The DP-
padding method achieves 1.6-43x improvement than the fully-padding mechanism.
When Hermetic only applies DP to pad the intermediate results, DPSpark (Wu et
al., 2021) also applies it to the algorithms and thus introduces the notion of
($\epsilon,\delta$)-differentially private obliviousness
(($\epsilon,\delta$)-DPO), which relaxes full obliviousness to enable
efficiency improvements. They first presented the perturbation-shuffle-
analysis framework and then designed several differentially oblivious
operators (such as sort and join). The DPSpark system is optimized by reducing
the number of oblivious shuffles and is benchmarked in different parameters.
In (Allen et al., 2019), several classical algorithms were implemented with
differential obliviousness.

For Key-value stores, Bailleu et al. proposed Avocado (Bailleu et al., 2021),
which overcomes the physical memory limitation and thus achieves high-
performance and fault-tolerance in a malicious environment. By experiments,
Avocado provides a fast lookup speed of about 1.5x-9x faster than ShieldStore.
For stream data, Part et al. presented the StreamBox-TZ (Park et al., 2019),
which processes large stream data in an IoT environment. StreamBox-TZ solves
two major challenges: minimizes the TCB in edge devices and verifies the
execution of stream analytics on edge. Moreover, on the octa-core ARMv8
platform, StreamBox-TZ exhibits performance with sub-second delay.

###  A.3. Secure Multiparty Queries

####  A.3.1. Problem Statement

Like SMC, a secure multiparty queries (SMQ) protocol also targets answering a
joint database query securely among several distinct yet connected parties.
SMQ is usually designed to handle complex queries. Specifically, each
participant has a local database $(\bm{d}_{i},\bm{\Lambda}_{i})$ and the goal
is to design a protocol to answer a query $q$ on the joint database
$(\bm{d},\bm{\Lambda})\triangleq(\bm{d}_{1},\bm{\Lambda}_{1})\circ\cdots\circ(\bm{d}_{N},\bm{\Lambda}_{N})$.
The correctness means that the SMQ protocol completes the analytical tasks and
obtains the final result correctly, and privacy means that the execution of
the protocol only reveals the final result to the intended parties. Integrity
ensures that all parties follow the protocol steps honestly. Finally, fairness
is also defined in SMQ, which means malicious parties receive the outputs if
and only if other honest parties also receive their outputs.

Many cryptographic SMC protocols can be leveraged to design SMQ protocols
(Bater et al., 2017; Volgushev et al., 2019); however, they are still
impractical because of either the huge communication cost or the extensive
computational cost. In this survey, we focus on the hardware-assisted
approaches, which improve efficiency significantly. Fig. 12 shows the workflow
of a secure two-party SMQ protocol. The two parties each has a database,
denoted as $(\bm{d}_{1},\bm{\Lambda}_{1})$ and
$(\bm{d}_{2},\bm{\Lambda}_{2})$, respectively. Then the local program $\Phi$
is loaded into the enclave. When receiving a query $q$, the two parties finish
the computation in an interactive manner, which consists of multiple rounds of
communication. In each round, a message-proof tuple $(m_{i},\Gamma_{i})$ is
derived from its private inputs, and then the tuple is sent to another party.
$\Gamma_{i}$ is employed to prove the message $m_{i}$ is computed honestly.
Finally, the two parties may run a fair protocol to distribute the final
result $\Phi((\bm{d},\bm{\Lambda}),q)$, where
$(\bm{d},\bm{\Lambda})\triangleq(\bm{d}_{1},\bm{\Lambda}_{1})\circ(\bm{d}_{2},\bm{\Lambda}_{2})$
is the joint database. Noted that all messages between the two parties are
sent over the secure channel.

Figure 12. Secure Multiparty Queries

Assessment

####  A.3.2. Research Status

While protocols (such as SFA (RishabhPoddar and Hellerstein, 2014), Shrinkwrap
(Bater et al., 2018), ObliJoin (Krastnikov et al., 2021; Chang et al., 2022))
are based on differential privacy or cryptographic methods, OCQ proposed in
(Dave et al., 2020) leveraged hardware enclaves to build a general framework
for secure multiparty analytics. Since SMQ is executed among different parties
and thus it always results in high communication costs. In OCQ, parties
involved in the protocol should share a schema in advance, then execute the
well-designed protocols obliviously for some allowed queries in the wide-area
network. They also presented an optimized query planner with sensitive
cardinalities, which executes the queries based on relational operators in
order to prevent data leakage caused by side channels such as memory access
patterns, network traffic, and other factors such as cardinality and
statistics. Compared to the Opaque, OCQ is up to 9.9x faster in the wide-area
network. However, the improvement is only applicable for selection and
aggregation queries, and for the join queries, the cost is still not
practical. The works discussed in Sec. 3.3 are workable for data analytics.
However, they only work for very small-scale data sets. Although some SDQ
protocols can be extended to SMQ protocols, designing practical SMQ protocols
is still very challenging. Generally, it remains an open problem to design
practical SMQ protocols with high throughput.

###  A.4. Comparisons

We present a comprehensive comparison of secure database queries protocols
based on their setting, methodology, security features, and performance. Table
3 demonstrates that many of current hardware-supported encrypted database
systems focus on the SQL queries over relation databases, and some of them
focus on set/get operations over key-value stores or keyword queries over
labeled documents set. However, there are very few studies on analyzing the
steam data, except for (Park et al., 2019). From the security perspective,
keeping input/output privacy is the basic security requirement of TEE-based
protocols. Employing oblivious primitives provides stronger privacy
protection, for example some SOQ protocols (e.g. ObliDB (Eskandarian and
Zaharia, 2019), Enclage (Eskandarian and Zaharia, 2019)) can avoid access
pattern leakage in the memory level, whereas some SDQ (e.g. Hermetic (Xu et
al., 2019), DPSpark (Xu et al., 2019)) and SMQ (e.g. OCQ (Dave et al., 2020))
protocols prevent pattern leakage from both memory and network level. While
most of the existing protocols achieve integrity of IO and execution,
EnclaveDB (Priebe et al., 2018) and VeriDB (Zhou et al., 2021) also achieve
the query integrity. From performance aspects, we summarize the protocol costs
with regards to different configurations and different functions. If a
protocol is compared to the baseline “fully in enclave”, we employ a positive
number to represent their improvements. For example, Enclage (Eskandarian and
Zaharia, 2019) improves the baseline about 5-13 times. If a protocol is
compared to the baseline “plaintext model”, we employ a negative number to
represent their overhead. For example, Opaque (Priebe et al., 2018) introduces
about -160% – -460% overhead compared to the baseline on join operations.

Table 3. Comparisons of Secure Data Queries

Schemes | Settings | Methodology | Security | Performance
---|---|---|---|---
Security Goals |  Adversarial Models |  Formal proof
Framework | Function | Technologies | Primitives | Privacy | Integrity | Freshness | Configurations | Costs
[Opaque (Zheng et al., 2017), NSDI, 2017] | SDA, n | SQL | Stateful TEE + OP | AE, oSort |  IO, mPattern, nPattern, IR | IO, exe | ✓ | Malicious Server | ✗ |  DataSet: Relational Database Platform: Spark Number of nodes: 5 Baseline: Plaintext Model |  Join: 1.6-4.6x slowdown PageRank: 3.8x slowdown
[0.1pt/0.6pt] [STC (Dang et al., 2017), PETS, 2017] | SOA | SQL | Stateful TEE + OP | MS, PRP | IO, mPattern | IO, exe | ✗ |  Semi-honest, Adaptive Server | SIM |  DataSet: Relational Database Platform: Spark Baseline: Plaintext Model |  Sort: -79% Compaction: 3.9x slowdown Select: 2.4x slowdown Aggregation: 1.2x slowdown Join: 3.8x slowdown
[0.1pt/0.6pt] [EnclaveDB (Priebe et al., 2018), S&P, 2018] | SOA | SQL | Stateful TEE | AEAD | IO, Query |  IO, exe, Log, Query | ✓ | Malicious Server | ✗ |  DataSet: Relational Database Platform: Hekaton Baseline: Plaintext Model | TATP: 0.2x slowdown
[0.1pt/0.6pt] [ObliDB1 (Eskandarian and Zaharia, 2019), VLDB, 2019] | SOA | SQL | Stateful TEE + OP | AE, oSort |  IO, IR, mPattern | IO, exe | ✗ | Malicious Server | ✗ |  DataSet: Relational Database Platform: Spark Baseline: Opaque | Join: 1.4-2.7x speedup
[0.1pt/0.6pt] [ShieldStore2 (Kim et al., 2019), EuroSys, 2019] | SOA | Set/Get | Stateful TEE | AE, MAC, MHT | IO | IO, exe | ✗ | Malicious Server | ✗ |  DataSet: Key-value store Platform: Ubuntu Server Number of Entries: 10M Baseline: Fully in Enclave |  RD50_Z: 1.2x speedup RD95_Z: 1.6x speedup RD100_Z: 1.7x speedu
[0.1pt/0.6pt] [SPEICHER (Bailleu et al., 2019), FAST, 2019] | SOA | Set/Get | Stateful TEE | Skiplist, LSM | IO, State | IO, exe | ✓ | Malicious Server | ✗ |  DataSet: RocksDB Platform: Ubuntu Server Baseline: Plaintext Model |  RD90_U: 14.8x slowdown RD80_U: 15.2x slowdown RD100_U: 32x slowdown
[0.1pt/0.6pt] [StealthDB (Vinayagamurthy et al., 2019), PETS, 2019] | SOA | SQL | Stateful TEE | AE | IO | exe | ✗ | Semi-honest Server | SIM |  DataSet: Relational Database Baseline: Plaintext Model | 0.18-1.2x slowdown
[0.1pt/0.6pt] [Hermetic (Xu et al., 2019) , Tech. Report, 2019] | SDA, n | SQL | Stateful TEE + DOP | DP |  IO, mPattern, nPattern, IR | IO, exe | ✗ |  Semi-honest, Adaptive Server | DP Analysis |  DataSet: Relational Database Platform: Spark $$(\epsilon,\delta)$: (5e-3, 1e-5) Baseline: Fully-Padding in Enclave |  Select: 2.1-3.2x speedup Groupby: 1.8—2.7x speedup Join: 4.1—8.3x speedup
[0.1pt/0.6pt] [SBT3 (Park et al., 2019), USENIX ATC, 2019] | SDA, n | Stream Algorithms | Stateless TEE | AE | IO | IO,exe | ✗ |  Malicious Edge Devices | ✗ |  DataSet: Taxi IDs Platform: octa core ARMv8 p Baseline: Plaintext Model |  Top-k: 0.04-0.12x slowdown WinSum: 0.5-0.8x slowdown Filter: 0.5-0.9x slowdown
[0.1pt/0.6pt] [BISEN4 (Ferreira et al., 2020), TDSC, 2020] | SOA | Boolean Queries | Stateful TEE | AE + PRF | IO, Query | IO, exe | ✗ | Malicious Server | ✗ |  DataSet: Labeled Document Platform: Ubuntu Server Number of documents: 5.5M Baseline: No baseline |  Search: 50s Update: 2.7h
[0.1pt/0.6pt] [OCQ (Dave et al., 2020), EuroSys, 2020] | SMA | SQL | Stateful TEE + OP | AE, oSort |  IO, mPattern, nPattern, IR | IO, exe | ✗ | Malicious Server | SIM |  DataSet: Relational Database Platform: Spark Number of nodes: 5. Baseline:Opaque |  Aggregation: 6.7—9.9x speedup Join: 1.0—2.3x speedup
[0.1pt/0.6pt] [DPSpark (Wu et al., 2021), TDSC, 2021] | SDA, n | SQL | Stateful TEE + DOP | DP |  IO, mPattern, nPattern, IR | IO, exe | ✗ |  Semi-honest, Adaptive Server | DP Analysis |  DataSet: Relational Database Platform: Spark Baseline: Plaintext model |  WordCount: 0.1-0.2x slowdown PageRank: 0.35-0.54x slowdown Log Query: 0.25-0.4x slowdown K-Means: 0.2-0.5x slowdown GroupBy: 0.45-0.85x slowdown
[0.1pt/0.6pt] [MII (Shao et al., 2020), CIKM, 2020] | SOA | Top-k | Stateful TEE | oShuffle | IO, Query | IO, exe | ✗ | Semi-honest Server |  Oblivious Analysis |  DataSet: Relational Database Number of documents: 1.3M Baseline: (Ding and Suel, 2011) | Top-k: 0.29-1.5x speedup
[0.1pt/0.6pt] [Enclage (Sun et al., 2021), VLDB, 2021] | SOA | Set/Get | Stateful TEE + OP | DE, B+ tree |  IO, IR, mPattern | IO, exe | ✗ | Malicious Server | ✗ |  DataSet: Key-value store Platform: Ubuntu Server Number of Items: 10M Baseline: Fully in Enclave | YSCB: 5-13x speedup
[0.1pt/0.6pt] [VeriDB (Zhou et al., 2021), SIGMOD, 2021] | SOA | SQL | Stateful TEE | MHT | ✗ | IO, exe, query | ✓ | Malicious Server | ✗ |  DataSet: Relational Database Platform: Ubuntu Server Number of Items: 10M Baseline: No baseline |  Select: 20-30s Join: 80-90s
[0.1pt/0.6pt] [Avocado5 (Bailleu et al., 2021), USENIX ATC, 2021] | SDA, n | Set/Get | Stateful TEE | BFT |  IO, IR, mPattern | IO, exe | ✓ | Malicious Server | ✗ |  DataSet: Key-value store Platform: Ubuntu Server Number of Items: 10M Baseline: ShieldStore | YSCB: 6-24x speedup

  * •

AE: Authenticated Encryption, MS: Melbourne Shuffle, PRP: Pseudo-Random
Permutation, IR: Intermediate Results, SIM: Simulate-based Proof, TATP: The
workload that consists of 40000 transactions, MAC: Message Authentication
Code, MHT: Merkle Hash Tree, LSM: Log-Structured Merge Tree, PRF: Pseudo-
Random Functions, OP: Oblivious Primitives, DOP: Differential Oblivious
Primitives, DE: Delta Encryption , oSort: Oblivious Sort, oShuffle: Oblivious
Shuffle, BFT: Byzantine Fault Tolerance;

  * 1

https://github.com/SabaEskandarian/ObliDB.git,

  * 2

https://github.com/cocoppang/ShieldStore.git,

  * 3

http://xsel.rocks/p/streambox,

  * 4

https://github.com/bernymac/BISEN.git,

  * 5

https://github.com/mbailleu/avocado.git;