Implementation of an 8-bit bit-slice AES S-box with rapid single flux quantum circuits

Rapid single flux quantum(RSFQ)circuits are a kind of superconducting digital circuits,having properties of a natural gate-level pipelining synchronous sequential circuit,which demonstrates high energy efficiency and high throughput advantage.We find that the high-throughput and high-speed performance of RSFQ circuits can take the advantage of a hardware implementation of the encryption algorithm,whereas these are rarely applied to this field.Among the available encryption algorithms,the advanced encryption standard(AES)algorithm is an advanced encryption standard algorithm.It is currently the most widely used symmetric cryptography algorithm.In this work,we aim to demonstrate the SubByte operation of an AES-128 algorithm using RSFQ circuits based on the SIMIT Nb0_(3) process.We design an AES S-box circuit in the RSFQ logic,and compare its operational frequency,power dissipation,and throughput with those of the CMOS-based circuit post-simulated in the same structure.The complete RSFQ S-box circuit costs a total of 42237 Josephson junctions with nearly 130 Gbps throughput under the maximum simulated frequency of 16.28 GHz.Our analysis shows that the frequency and throughput of the RSFQ-based S-box are about four times higher than those of the CMOS-based S-box.Further,we design and fabricate a few typical modules of the S-box.Subsequent measurements demonstrate the correct functioning of the modules in both low and high frequencies up to 28.8 GHz.

Estimating up-limits of eccentricities for the binary black holes in the LIGO-Virgo catalog GWTC-1

In the first Gravitational-Wave Transient Catalogue of LIGO and Virgo,all events are announced having zero eccentricity.In the present paper,we investigate the performance of SEOBNRE,which is a spin-aligned eccentric waveform model in time-domain.By comparing with all the eccentric waveforms in SXS library,we find that the SEOBNRE coincides perfectly with numerical relativity data.Employing the SEOBNRE,we re-estimate the eccentricities of all black hole merger events.We find that most of these events allow a possibility for existence of initial eccentricities at 10 Hz band,but are totally circularized at the observed frequency(≥20 Hz).The upcoming update of LIGO and the next generation detector like Einstein Telescope will observe the gravitational waves starting at 10 Hz or even lower.If the eccentricity exists at the lower frequency,then it may significantly support the dynamical formation mechanism taking place in globular clusters.

Analytical effective one-body formalism for extreme-mass-ratio inspirals with eccentric orbits

Extreme-mass-ratio inspirals(EMRIs)are among the most important sources for future spaceborne gravitational wave detectors.In this kind of system,compact objects usually orbit around central supermassive black holes on complicated trajectories.Usually,these trajectories are approximated as the geodesics of Kerr space-times,and orbital evolution is simulated with the help of the adiabatic approximation.However,this approach omits the influence of the compact object on its background.In this paper,using the effective one-body formalism,we analytically calculate the trajectory of a nonspinning compact object around a massive Kerr black hole in an equatorial eccentric orbit(omitting the orbital inclination)and express the fundamental orbital frequencies in explicit forms.Our formalism includes the first-order corrections for the mass ratio in the conservative orbital motion.Furthermore,we insert the mass-ratio-related terms into the first post-Newtonian energy fluxes.By calculating the gravitational waves using the Teukolsky equations,we quantitatively reveal the influence of the mass of the compact object on the data analysis.We find that the shrinking of geodesic motion by taking small objects as test particles may not be appropriate for the detection of EMRIs.