23,537 research outputs found
Computing low-degree isogenies in genus 2 with the Dolgachev-Lehavi method
Let ell be a prime, and H a curve of genus 2 over a field k of characteristic
not 2 or ell. If S is a maximal Weil-isotropic subgroup of Jac(H)[ell], then
Jac(H)/S is isomorphic to the Jacobian of some (possibly reducible) curve X. We
investigate the Dolgachev--Lehavi method for constructing the curve X,
simplifying their approach and making it more explicit. The result, at least
for ell=3, is an efficient and easily programmable algorithm suitable for
number-theoretic calculations
Families of fast elliptic curves from Q-curves
We construct new families of elliptic curves over \FF_{p^2} with
efficiently computable endomorphisms, which can be used to accelerate elliptic
curve-based cryptosystems in the same way as Gallant-Lambert-Vanstone (GLV) and
Galbraith-Lin-Scott (GLS) endomorphisms. Our construction is based on reducing
\QQ-curves-curves over quadratic number fields without complex
multiplication, but with isogenies to their Galois conjugates-modulo inert
primes. As a first application of the general theory we construct, for every
, two one-parameter families of elliptic curves over \FF_{p^2}
equipped with endomorphisms that are faster than doubling. Like GLS (which
appears as a degenerate case of our construction), we offer the advantage over
GLV of selecting from a much wider range of curves, and thus finding secure
group orders when is fixed. Unlike GLS, we also offer the possibility of
constructing twist-secure curves. Among our examples are prime-order curves
equipped with fast endomorphisms, with almost-prime-order twists, over
\FF_{p^2} for and
The Q-curve construction for endomorphism-accelerated elliptic curves
We give a detailed account of the use of -curve reductions to
construct elliptic curves over with efficiently computable
endomorphisms, which can be used to accelerate elliptic curve-based
cryptosystems in the same way as Gallant--Lambert--Vanstone (GLV) and
Galbraith--Lin--Scott (GLS) endomorphisms. Like GLS (which is a degenerate case
of our construction), we offer the advantage over GLV of selecting from a much
wider range of curves, and thus finding secure group orders when is fixed
for efficient implementation. Unlike GLS, we also offer the possibility of
constructing twist-secure curves. We construct several one-parameter families
of elliptic curves over equipped with efficient
endomorphisms for every p \textgreater{} 3, and exhibit examples of
twist-secure curves over for the efficient Mersenne prime
.Comment: To appear in the Journal of Cryptology. arXiv admin note: text
overlap with arXiv:1305.540
Easy scalar decompositions for efficient scalar multiplication on elliptic curves and genus 2 Jacobians
The first step in elliptic curve scalar multiplication algorithms based on
scalar decompositions using efficient endomorphisms-including
Gallant-Lambert-Vanstone (GLV) and Galbraith-Lin-Scott (GLS) multiplication, as
well as higher-dimensional and higher-genus constructions-is to produce a short
basis of a certain integer lattice involving the eigenvalues of the
endomorphisms. The shorter the basis vectors, the shorter the decomposed scalar
coefficients, and the faster the resulting scalar multiplication. Typically,
knowledge of the eigenvalues allows us to write down a long basis, which we
then reduce using the Euclidean algorithm, Gauss reduction, LLL, or even a more
specialized algorithm. In this work, we use elementary facts about quadratic
rings to immediately write down a short basis of the lattice for the GLV, GLS,
GLV+GLS, and Q-curve constructions on elliptic curves, and for genus 2 real
multiplication constructions. We do not pretend that this represents a
significant optimization in scalar multiplication, since the lattice reduction
step is always an offline precomputation---but it does give a better insight
into the structure of scalar decompositions. In any case, it is always more
convenient to use a ready-made short basis than it is to compute a new one
Polymorphic Types in ACL2
This paper describes a tool suite for the ACL2 programming language which
incorporates certain ideas from the Hindley-Milner paradigm of functional
programming (as exemplified in popular languages like ML and Haskell),
including a "typed" style of programming with the ability to define polymorphic
types. These ideas are introduced via macros into the language of ACL2, taking
advantage of ACL2's guard-checking mechanism to perform type checking on both
function definitions and theorems. Finally, we discuss how these macros were
used to implement features of Specware, a software specification and
implementation system.Comment: In Proceedings ACL2 2014, arXiv:1406.123
Internet Radio: A New Engine for Content Diversity?
While traditional radio stations are subject to extensive government
regulations, Internet radio stations remain largely unregulated. As Internet
radio usage has increased certain stakeholders have begun to argue that these
Internet radio broadcasters are providing significant and diverse programming
to American audiences and that government regulation of spectrum-using radio
station ownership may be further relaxed.
One of the primary justifications for regulation of ownership has been to
protect diversity in broadcasting. This study hypothesizes that Internet radio
broadcasting does add diversity to the radio broadcasting industry and that it
should be considered as relevant by regulators.
This study evaluates the role of Internet radio broadcasters according to
five criteria intended to gauge the level of diversity being delivered to
listeners online. By measuring the levels of format, channel, ownership,
location and language diversity among Internet radio stations, it is possible
to draw benchmark lessons about the new medium's ability to provide Americans
with diverse broadcasting options.
The study finds that Internet radio broadcasters are in fact adding
measurable diversity to the radio broadcasting industry. Internet broadcasters
are providing audiences with access to an increasing number of stations,
owners, formats, and language choices, and it is likely that technologies
aiding in the mobility of access as well as broadband evolution will reinforce
these findings.Comment: 29th TPRC Conference, 200
Stochastic continuity equations with conservative noise
The present article is devoted to well-posedness by noise for the continuity
equation. Namely, we consider the continuity equation with non-linear and
partially degenerate stochastic perturbations in divergence form. We prove the
existence and uniqueness of entropy solutions under hypotheses on the velocity
field which are weaker than those required in the deterministic setting. This
extends related results of [Flandoli, Gubinelli, Priola; Invent. Math., 2010]
applicable for linear multiplicative noise to a non-linear setting. The
existence proof relies on a duality argument which makes use of the regularity
theory for fully non-linear parabolic equations.Comment: 42 page
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