57,038 research outputs found
Security Estimates for Quadratic Field Based Cryptosystems
We describe implementations for solving the discrete logarithm problem in the
class group of an imaginary quadratic field and in the infrastructure of a real
quadratic field. The algorithms used incorporate improvements over
previously-used algorithms, and extensive numerical results are presented
demonstrating their efficiency. This data is used as the basis for
extrapolations, used to provide recommendations for parameter sizes providing
approximately the same level of security as block ciphers with
and -bit symmetric keys
The Infrastructure of a Global Field of Arbitrary Unit Rank
In this paper, we show a general way to interpret the infrastructure of a
global field of arbitrary unit rank. This interpretation generalizes the prior
concepts of the giant step operation and f-representations, and makes it
possible to relate the infrastructure to the (Arakelov) divisor class group of
the global field. In the case of global function fields, we present results
that establish that effective implementation of the presented methods is indeed
possible, and we show how Shanks' baby-step giant-step method can be
generalized to this situation.Comment: Revised version. Accepted for publication in Math. Com
Magnetism and the Weiss Exchange Field - A Theoretical Analysis Inspired by Recent Experiments
The huge spin precession frequency observed in recent experiments with
spin-polarized beams of hot electrons shot through magnetized films is
interpreted as being caused by Zeeman coupling of the electron spins to the
so-called Weiss exchange field in the film. A "Stern-Gerlach experiment" for
electrons moving through an inhomogeneous exchange field is proposed. The
microscopic origin of exchange interactions and of large mean exchange fields,
leading to different types of magnetic order, is elucidated. A microscopic
derivation of the equations of motion of the Weiss exchange field is presented.
Novel proofs of the existence of phase transitions in quantum XY-models and
antiferromagnets, based on an analysis of the statistical distribution of the
exchange field, are outlined.Comment: 36 pages, 3 figure
Practical improvements to class group and regulator computation of real quadratic fields
We present improvements to the index-calculus algorithm for the computation
of the ideal class group and regulator of a real quadratic field. Our
improvements consist of applying the double large prime strategy, an improved
structured Gaussian elimination strategy, and the use of Bernstein's batch
smoothness algorithm. We achieve a significant speed-up and are able to compute
the ideal class group structure and the regulator corresponding to a number
field with a 110-decimal digit discriminant
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