802 research outputs found
Detection of Laplace-resonant three-planet systems from transit timing variations
Transit timing variations (TTVs) are useful to constrain the existence of
perturbing planets, especially in resonant systems where the variations are
strongly enhanced. Here we focus on Laplace-resonant three-planet systems, and
assume the inner planet transits the star. A dynamical study is performed for
different masses of the three bodies, with a special attention to terrestrial
planets. We consider a maximal time-span of ~ 100 years and discuss the shape
of the inner planet TTVs curve. Using frequency analysis, we highlight the
three periods related to the evolution of the system: two periods associated
with the Laplace-resonant angle and the third one with the precession of the
pericenters. These three periods are clearly detected in the TTVs of an inner
giant planet perturbed by two terrestrial companions. Only two periods are
detected for a Jupiter-Jupiter-Earth configuration (the ones associated with
the giant interactions) or for three terrestrial planets (the Laplace periods).
However, the latter system can be constrained from the inner planet TTVs. We
finally remark that the TTVs of resonant three or two Jupiter systems mix up,
when the period of the Laplace resonant angle matches the pericenter precession
of the two-body configuration. This study highlights the importance of TTVs
long-term observational programs for the detection of multiple-planet resonant
systems.Comment: 8 pages, 8 figures, accepted in MNRA
Formation of '3D' multiplanet systems by dynamical disruption of multiple-resonance configurations
Assuming that giant planets are formed in thin protoplanetary discs, a '3D'
system can form, provided that the mutual inclination is excited by some
dynamical mechanism. Resonant interactions and close planetary encounters are
thought to be the primary inclination-excitation mechanisms, resulting in a
resonant and non-resonant system, respectively. Here we propose an alternative
formation scenario, starting from a system composed of three giant planets in a
nearly coplanar configuration. As was recently shown for the case of the Solar
system, planetary migration in the gas disc (Type II migration) can force the
planets to become trapped in a multiply resonant state. We simulate this
process, assuming different values for the planetary masses and mass ratios. We
show that such a triple resonance generally becomes unstable as the resonance
excites the eccentricities of all planets and planet-planet scattering sets in.
One of the three planets is typically ejected from the system, leaving behind a
dynamically 'hot' (but stable) two-planet configuration. The resulting
two-planet systems typically have large values of semimajor axial ratios (a1/a2
< 0.3), while the mutual inclination can be as high as 70{\deg}, with a median
of \sim30{\deg}. A small fraction of our two-planet systems (\sim5 per cent)
ends up in the stability zone of the Kozai resonance. In a few cases, the
triple resonance can remain stable for long times and a '3D' system can form by
resonant excitation of the orbital inclinations; such a three-planet system
could be stable if enough eccentricity damping is exerted on the planets.
Finally, in the single-planet resulting systems, which are formed when two
planets are ejected from the system, the inclination of the planet's orbital
plane with respect to the initial invariant plane -presumably the plane
perpendicular to the star's spin axis- can be as large as \sim40{\deg}.Comment: 9 pages, 5 figures, published in MNRA
Interesting dynamics at high mutual inclination in the framework of the Kozai problem with an eccentric perturber
We study the dynamics of the 3-D three-body problem of a small body moving
under the attractions of a star and a giant planet which orbits the star on a
much wider and elliptic orbit. In particular, we focus on the influence of an
eccentric orbit of the outer perturber on the dynamics of a small highly
inclined inner body. Our analytical study of the secular perturbations relies
on the classical octupole hamiltonian expansion (third-order theory in the
ratio of the semi-major axes), as third-order terms are needed to consider the
secular variations of the outer perturber and potential secular resonances
between the arguments of the pericenter and/or longitudes of the node of both
bodies. Short-period averaging and node reduction (Laplace plane) reduce the
problem to two degrees of freedom. The four-dimensional dynamics is analyzed
through representative planes which identify the main equilibria of the
problem. As in the circular problem (i.e. perturber on a circular orbit), the
"Kozai-bifurcated" equilibria play a major role in the dynamics of an inner
body on quasi-circular orbit: its eccentricity variations are very limited for
mutual inclination between the orbital planes smaller than ~40^{\deg}, while
they become large and chaotic for higher mutual inclination. Particular
attention is also given to a region around 35^{\deg} of mutual inclination,
detected numerically by Funk et al. (2011) and consisting of long-time stable
and particularly low eccentric orbits of the small body. Using a 12th-order
Hamiltonian expansion in eccentricities and inclinations, in particular its
action-angle formulation obtained by Lie transforms in Libert & Henrard (2008),
we show that this region presents an equality of two fundamental frequencies
and can be regarded as a secular resonance. Our results also apply to binary
star systems where a planet is revolving around one of the two stars.Comment: 12 pages, 9 figures, accepted for publication in MNRA
Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability into the light of Kolmogorov and Nekhoroshev theories
We investigate the long-time stability of the Sun-Jupiter-Saturn-Uranus
system by considering a planar secular model, that can be regarded as a major
refinement of the approach first introduced by Lagrange. Indeed, concerning the
planetary orbital revolutions, we improve the classical circular approximation
by replacing it with a solution that is invariant up to order two in the
masses; therefore, we investigate the stability of the secular system for
rather small values of the eccentricities. First, we explicitly construct a
Kolmogorov normal form, so as to find an invariant KAM torus which approximates
very well the secular orbits. Finally, we adapt the approach that is at basis
of the analytic part of the Nekhoroshev's theorem, so as to show that there is
a neighborhood of that torus for which the estimated stability time is larger
than the lifetime of the Solar System. The size of such a neighborhood,
compared with the uncertainties of the astronomical observations, is about ten
times smaller.Comment: 31 pages, 2 figures. arXiv admin note: text overlap with
arXiv:1010.260
Accountable Tracing Signatures from Lattices
Group signatures allow users of a group to sign messages anonymously in the
name of the group, while incorporating a tracing mechanism to revoke anonymity
and identify the signer of any message. Since its introduction by Chaum and van
Heyst (EUROCRYPT 1991), numerous proposals have been put forward, yielding
various improvements on security, efficiency and functionality. However, a
drawback of traditional group signatures is that the opening authority is given
too much power, i.e., he can indiscriminately revoke anonymity and there is no
mechanism to keep him accountable. To overcome this problem, Kohlweiss and
Miers (PoPET 2015) introduced the notion of accountable tracing signatures
(ATS) - an enhanced group signature variant in which the opening authority is
kept accountable for his actions. Kohlweiss and Miers demonstrated a generic
construction of ATS and put forward a concrete instantiation based on
number-theoretic assumptions. To the best of our knowledge, no other ATS scheme
has been known, and the problem of instantiating ATS under post-quantum
assumptions, e.g., lattices, remains open to date.
In this work, we provide the first lattice-based accountable tracing
signature scheme. The scheme satisfies the security requirements suggested by
Kohlweiss and Miers, assuming the hardness of the Ring Short Integer Solution
(RSIS) and the Ring Learning With Errors (RLWE) problems. At the heart of our
construction are a lattice-based key-oblivious encryption scheme and a
zero-knowledge argument system allowing to prove that a given ciphertext is a
valid RLWE encryption under some hidden yet certified key. These technical
building blocks may be of independent interest, e.g., they can be useful for
the design of other lattice-based privacy-preserving protocols.Comment: CT-RSA 201
Dynamical stability analysis of the HD202206 system and constraints to the planetary orbits
Long-term precise Doppler measurements with the CORALIE spectrograph revealed
the presence of two massive companions to the solar-type star HD202206.
Although the three-body fit of the system is unstable, it was shown that a 5:1
mean motion resonance exists close to the best fit, where the system is stable.
We present here an extensive dynamical study of the HD202206 system aiming at
constraining the inclinations of the two known companions, from which we derive
possible ranges of value for the companion masses.
We study the long term stability of the system in a small neighborhood of the
best fit using Laskar's frequency map analysis. We also introduce a numerical
method based on frequency analysis to determine the center of libration mode
inside a mean motion resonance.
We find that acceptable coplanar configurations are limited to inclinations
to the line of sight between 30 and 90 degrees. This limits the masses of both
companions to roughly twice the minimum. Non coplanar configurations are
possible for a wide range of mutual inclinations from 0 to 90 degrees, although
configurations seem to be favored. We also confirm the
5:1 mean motion resonance to be most likely. In the coplanar edge-on case, we
provide a very good stable solution in the resonance, whose does not
differ significantly from the best fit. Using our method to determine the
center of libration, we further refine this solution to obtain an orbit with a
very low amplitude of libration, as we expect dissipative effects to have
dampened the libration.Comment: 14 pages, 18 figure
On the influence of the Kozai mechanism in habitable zones of extrasolar planetary systems
Aims. We investigate the long-term evolution of inclined test particles representing a small Earth-like body with negligible gravitational effects (hereafter called massless test-planets) in the restricted three-body problem, and consisting of a star, a gas giant, and a massless test-planet. The test-planet is initially on a circular orbit and moves around the star at distances closer than the gas giant. The aim is to show the influences of the eccentricity and the mass of the gas giant on the dynamics, for various inclinations of the test-planet, and to investigate in more detail the Kozai mechanism in the elliptic problem.
Methods. We performed a parametric study, integrating the orbital evolution of test particles whose initial conditions were distributed on the semi-major axis â inclination plane. The gas giantâs initial eccentricity was varied. For the calculations, we used the Lie integration method and in some cases the Bulirsch-Stoer algorithm. To analyze the results, the maximum eccentricity and the Lyapunov characteristic indicator were used. All integrations were performed for 105 periods of the gas giant.
Results. Our calculations show that inclined massless test-planets can be in stable configurations with gas giants on either circular or elliptic orbits. The higher the eccentricity of the gas giant, the smaller the possible range in semi-major axis for the test-planet. For gas giants on circular orbits, our results illustrate the well-known results associated with the Kozai mechanism, which do not allow stable orbits above a critical inclination of approximately 40°. For gas giants on eccentric orbits, the dynamics is quite similar, and the massless companion exhibits limited variations in eccentricity. In addition, we identify a region around 35° consisting of long-time stable, low eccentric orbits. We show that these results are also valid for Earth-mass companions, therefore they can be applied to extrasolar systems: for instance, the extrasolar planetary system HD 154345 can possess a 35° degree inclined, nearly circular, Earth-mass companion in the habitable zone
Zero-Knowledge Arguments for Matrix-Vector Relations and Lattice-Based Group Encryption
International audienceGroup encryption (GE) is the natural encryption analogue of group signatures in that it allows verifiably encrypting messages for some anonymous member of a group while providing evidence that the receiver is a properly certified group member. Should the need arise, an opening authority is capable of identifying the receiver of any ciphertext. As introduced by Kiayias, Tsiounis and Yung (Asiacrypt'07), GE is motivated by applications in the context of oblivious retriever storage systems, anonymous third parties and hierarchical group signatures. This paper provides the first realization of group encryption under lattice assumptions. Our construction is proved secure in the standard model (assuming interaction in the proving phase) under the Learning-With-Errors (LWE) and Short-Integer-Solution (SIS) assumptions. As a crucial component of our system, we describe a new zero-knowledge argument system allowing to demonstrate that a given ciphertext is a valid encryption under some hidden but certified public key, which incurs to prove quadratic statements about LWE relations. Specifically, our protocol allows arguing knowledge of witnesses consisting of X â Z mĂn q , s â Z n q and a small-norm e â Z m which underlie a public vector b = X · s + e â Z m q while simultaneously proving that the matrix X â Z mĂn q has been correctly certified. We believe our proof system to be useful in other applications involving zero-knowledge proofs in the lattice setting
UC Updatable Databases and Applications
We define an ideal functionality \Functionality_{\UD} and a construction \mathrm{\Pi_{\UD}} for an updatable database (\UD). \UD is a two-party protocol between an updater and a reader. The updater sets the database and updates it at any time throughout the protocol execution. The reader computes zero-knowledge (ZK) proofs of knowledge of database entries. These proofs prove that a value is stored at a certain position in the database, without revealing the position or the value.
(Non-)updatable databases are implicitly used as building block in priced oblivious transfer, privacy-preserving billing and other privacy-preserving protocols. Typically, in those protocols the updater signs each database entry, and the reader proves knowledge of a signature on a database entry. Updating the database requires a revocation mechanism to revoke signatures on outdated database entries.
Our construction \mathrm{\Pi_{\UD}} uses a non-hiding vector commitment (NHVC) scheme. The updater maps the database to a vector and commits to the database. This commitment can be updated efficiently at any time without needing a revocation mechanism. ZK proofs for reading a database entry have communication and amortized computation cost independent of the database size. Therefore, \mathrm{\Pi_{\UD}} is suitable for large databases. We implement \mathrm{\Pi_{\UD}} and our timings show that it is practical.
In existing privacy-preserving protocols, a ZK proof of a database entry is intertwined with other tasks, e.g., proving further statements about the value read from the database or the position where it is stored. \Functionality_{\UD} allows us to improve modularity in protocol design by separating those tasks. We show how to use \Functionality_{\UD} as building block of a hybrid protocol along with other functionalities
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