8,110 research outputs found
A Discrete Logarithm-based Approach to Compute Low-Weight Multiples of Binary Polynomials
Being able to compute efficiently a low-weight multiple of a given binary
polynomial is often a key ingredient of correlation attacks to LFSR-based
stream ciphers. The best known general purpose algorithm is based on the
generalized birthday problem. We describe an alternative approach which is
based on discrete logarithms and has much lower memory complexity requirements
with a comparable time complexity.Comment: 12 page
Burgess's Bounds for Character Sums
We prove that Burgess's bound gives an estimate not just for a single
character sum, but for a mean value of many such sums.Comment: Minor changes and addition of reference to Gallagher & Montgomer
Heat kernel expansions on the integers and the Toda lattice hierarchy
We consider the heat equation where is a second-order difference
operator in a discrete variable . The fundamental solution has an expansion
in terms of the Bessel functions of imaginary argument. The coefficients
in this expansion are analogs of Hadamard's coefficients for
the (continuous) Schrodinger operator.
We derive an explicit formula for in terms of the wave and the
adjoint wave functions of the Toda lattice hierarchy. As a first application of
this result, we prove that the values of these coefficients on the diagonals
and define a hierarchy of differential-difference equations which
is equivalent to the Toda lattice hierarchy. Using this fact and the
correspondence between commutative rings of difference operators and algebraic
curves we show that the fundamental solution can be summed up, giving a finite
formula involving only two Bessel functions with polynomial coefficients in the
time variable , if and only if the operator belongs to the family of
bispectral operators constructed in [18].Comment: corrected typo
Extremal Transitions in Heterotic String Theory
In this paper we study extremal transitions between heterotic string
compactifications, i.e., transitions between pairs (M,V) where M is a
Calabi-Yau manifold and V a gauge bundle. Bundle transitions are described
using language recently espoused by Friedman, Morgan, Witten. In addition,
partly as a check on our methods, we also study how small instantons are
described in the same language, and also describe the sheaves corresponding to
small instantons.Comment: 26 pages, LaTex, 3 figures, references adde
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