4,152 research outputs found
Fast Exponentiation in Extension Field with Frobenius Mappings
This paper proposes an exponentiation method with Frobenius mappings. Our method is closely related to so-called interleaving exponentiation. Different from the interleaving exponentiation methods, our method can carry out several exponentiations using same base at the same time. The efficiency to use Frobenius mappings for an exponentiation in extension field is well introduced by Avanzi and Mihailescu. This exponentiation method is based on so-called simultaneous exponentiation and uses many Frobenius mappings. Their method more decreased the number of multiplications; however, the number of Frobenius mappings inversely increased. Compared to their method , the number of multiplications needed for the proposed method becomes about 20% larger; however, that of Frobenius mappings becomes small enough
Higher order pair corrections to electron-positron annihilation
Radiative corrections due to pair production in process of electron-positron
annihilation are considered. The main attention is paid to the corrections of
the third order. Simultaneous emission of photons and pairs is taken into
account. The leading log approximation and convolution procedure are used.
Exponentiation is discussed. Theoretical uncertainty in description of higher
order secondary pairs is estimated.Comment: 14 pages, extended version prepared for JHE
Thermonuclear supernova simulations with stochastic ignition
We apply an ad hoc model for dynamical ignition in three-dimensional
numerical simulations of thermonuclear supernovae assuming pure deflagrations.
The model makes use of the statistical description of temperature fluctuations
in the pre-supernova core proposed by Wunsch & Woosley (2004). Randomness in
time is implemented by means of a Poisson process. We are able to vary the
explosion energy and nucleosynthesis depending on the free parameter of the
model which controls the rapidity of the ignition process. However, beyond a
certain threshold, the strength of the explosion saturates and the outcome
appears to be robust with respect to number of ignitions. In the most energetic
explosions, we find about 0.75 solar masses of iron group elements. Other than
in simulations with simultaneous multi-spot ignition, the amount of unburned
carbon and oxygen at radial velocities of a few 1000 km/s tends to be reduced
for an ever increasing number of ignition events and, accordingly, more
pronounced layering results.Comment: 7 pages, 6 figures, accepted for publication in Astron. Astrophys.;
PDF version with full resolution figures available from
http://www.astro.uni-wuerzburg.de/~schmidt/Paper/StochIgnt_AA.pd
Security of almost ALL discrete log bits
Let G be a finite cyclic group with generator \alpha and with an encoding so that multiplication is computable in polynomial time. We study the security of bits of the discrete log x when given \exp_{\alpha}(x), assuming that the exponentiation function \exp_{\alpha}(x) = \alpha^x is one-way. We reduce he general problem to the case that G has odd order q. If G has odd order q the security of the least-significant bits of x and of the most significant bits of the rational number \frac{x}{q} \in [0,1) follows from the work of Peralta [P85] and Long and Wigderson [LW88]. We generalize these bits and study the security of consecutive shift bits lsb(2^{-i}x mod q) for i=k+1,...,k+j. When we restrict \exp_{\alpha} to arguments x such that some sequence of j consecutive shift bits of x is constant (i.e., not depending on x) we call it a 2^{-j}-fraction of \exp_{\alpha}. For groups of odd group order q we show that every two 2^{-j}-fractions of \exp_{\alpha} are equally one-way by a polynomial time transformation: Either they are all one-way or none of them. Our key theorem shows that arbitrary j consecutive shift bits of x are simultaneously secure when given \exp_{\alpha}(x) iff the 2^{-j}-fractions of \exp_{\alpha} are one-way. In particular this applies to the j least-significant bits of x and to the j most-significant bits of \frac{x}{q} \in [0,1). For one-way \exp_{\alpha} the individual bits of x are secure when given \exp_{\alpha}(x) by the method of Hastad, N\"aslund [HN98]. For groups of even order 2^{s}q we show that the j least-significant bits of \lfloor x/2^s\rfloor, as well as the j most-significant bits of \frac{x}{q} \in [0,1), are simultaneously secure iff the 2^{-j}-fractions of \exp_{\alpha'} are one-way for \alpha' := \alpha^{2^s}. We use and extend the models of generic algorithms of Nechaev (1994) and Shoup (1997). We determine the generic complexity of inverting fractions of \exp_{\alpha} for the case that \alpha has prime order q. As a consequence, arbitrary segments of (1-\varepsilon)\lg q consecutive shift bits of random x are for constant \varepsilon >0 simultaneously secure against generic attacks. Every generic algorithm using generic steps (group operations) for distinguishing bit strings of j consecutive shift bits of x from random bit strings has at most advantage O((\lg q) j\sqrt{t} (2^j/q)^{\frac14})
New Applications of Resummation in Non-Abelian Gauge Theories: QED X QCD Exponentiation for LHC Physics, IR-Improved DGLAP Theory and Resummed Quantum Gravity
We present the elements of three applications of resummation methods in
non-Abelian gauge theories: (1), QED X QCD exponentiation and shower/ME
matching for LHC physics; (2), IR improvement of DGLAP theory; (3), resummed
quantum gravity and the final state of Hawking radiation. In all cases, the
extension of the YFS approach, originally introduced for Abelian gauge theory,
to non-Abelian gauge theories, QCD and quantum general relativity, leads to new
results and solutions which we briefly summarize.Comment: 6 pages, 2 figures, presented at RADCOR05, Kanagawa, Japan, Oct.,
200
Axioms and Decidability for Type Isomorphism in the Presence of Sums
We consider the problem of characterizing isomorphisms of types, or,
equivalently, constructive cardinality of sets, in the simultaneous presence of
disjoint unions, Cartesian products, and exponentials. Mostly relying on
results about polynomials with exponentiation that have not been used in our
context, we derive: that the usual finite axiomatization known as High-School
Identities (HSI) is complete for a significant subclass of types; that it is
decidable for that subclass when two types are isomorphic; that, for the whole
of the set of types, a recursive extension of the axioms of HSI exists that is
complete; and that, for the whole of the set of types, the question as to
whether two types are isomorphic is decidable when base types are to be
interpreted as finite sets. We also point out certain related open problems
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