Photo-ionization and fragmentation of Sc3N@C80 following excitation above the Sc K-edge

We have investigated the ionization and fragmentation of a metallo-endohedral fullerene, Sc3N@C80, using ultrashort (10 fs) x-ray pulses. Following selective ionization of a Sc (1s) electron (hν = 4.55 keV), an Auger cascade leads predominantly to either a vibrationally cold multiply charged parent molecule or multifragmentation of the carbon cage following a phase transition. In contrast to previous studies, no intermediate regime of C2 evaporation from the carbon cage is observed. A time-delayed, hard x-ray pulse (hν = 5.0 keV) was used to attempt to probe the electron transfer dynamics between the encapsulated Sc species and the carbon cage. A small but significant change in the intensity of Sc-containing fragment ions and coincidence counts for a delay of 100 fs compared to 0 fs, as well as an increase in the yield of small carbon fragment ions, may be indicative of incomplete charge transfer from the carbon cage on the sub-100 fs time scale

Almost All Discrete Log Bits Are Simultaneously Secure

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) = \alphax is one-way. We reduce the 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 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-ix 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 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, Naslund [HN98]. For groups of even order 2sq we show that the j least-significant bits of \lfloor x/2s\rfloor, as well as the j most-significant bits of x/q \in [0,1), are simultaneously secure iff the 2-j-fractions of exp\alpha\u27 are one-way for \alpha\u27 := \alpha2s . 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 t 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} (2j/q)1/4)

An Optimal, Stable Continued Fraction Algorithm for Arbitrary Dimension

. We analyse a continued fraction algorithm (abbreviated CFA) for arbitrary dimension n showing that it produces simultaneous diophantine approximations which are up to the factor 2 (n+2)=4 best possible. Given a real vector x =(x1 ; : : : ; xn\Gamma1 ; 1) 2R n this CFA generates a sequence of vectors (p (k) 1 ; : : : ; p (k) n\Gamma1 ; q (k) ) 2Z n ; k = 1; 2; : : : with increasing integers jq (k) j satisfying for i = 1; : : : ; n \Gamma 1 jx i \Gamma p i (k) =q (k) j 2 (n+2)=4 p 1 + x 2 i = jq (k) j 1+ 1 n\Gamma1 : By a theorem of Dirichlet this bound is best possible in that the exponent 1 + 1 n\Gamma1 can in general not be increased. 1 Introduction We analyse a CFA which computes for real vectors x 2 R n diophantine approximations to x that are up to the factor 2 (n+2)=4 best possible. Given x 2 R n this CFA constructs a sequence of lattice bases of the lattice Z n consisting of vectors that approximate the line xR: For given ffl ? 0 ; this C..

A Stable Integer Relation Algorithm

We study the following problem: given x 2 IR n either find a short integer relation m 2 ZZ n ; so that ! x; m ?= 0 holds for the inner product ! : ; : ? ; or prove that no short integer relation exists for x: Hastad, Just, Lagarias and Schnorr (1989) give a polynomial time algorithm for this problem. We present a stable variation of the HJLS--algorithm that preserves lower bounds on (x) for infinitesimal changes of x: Given x 2 IR n and ff 2 IN this algorithm finds a nearby point x 0 and a short integer relation m for x 0 : The nearby point x 0 is 'good' in the sense that no very short relation exists for points x within half the x 0 --distance from x: On the other hand if x 0 = x then m is, up to a factor 2 n=2 ; a shortest integer relation for x: Our algorithm uses, for arbitrary real input x; at most O(n 4 (n + log ff)) many arithmetical operations on real numbers. If x is rational the algorithm operates on integers having at most O(n 5 + n 3 (log ff) 2 +..