3,535 research outputs found
Fast Arithmetics in Artin-Schreier Towers over Finite Fields
An Artin-Schreier tower over the finite field F_p is a tower of field
extensions generated by polynomials of the form X^p - X - a. Following Cantor
and Couveignes, we give algorithms with quasi-linear time complexity for
arithmetic operations in such towers. As an application, we present an
implementation of Couveignes' algorithm for computing isogenies between
elliptic curves using the p-torsion.Comment: 28 pages, 4 figures, 3 tables, uses mathdots.sty, yjsco.sty Submitted
to J. Symb. Compu
Separating Bounded Arithmetics by Herbrand Consistency
The problem of separating the hierarchy of bounded arithmetic has
been studied in the paper. It is shown that the notion of Herbrand Consistency,
in its full generality, cannot separate the theory from ; though it can
separate from . This extends a
result of L. A. Ko{\l}odziejczyk (2006), by showing the unprovability of the
Herbrand Consistency of in the theory .Comment: Published by Oxford University Press. arXiv admin note: text overlap
with arXiv:1005.265
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