964 research outputs found
Normal Elliptic Bases and Torus-Based Cryptography
We consider representations of algebraic tori over finite fields.
We make use of normal elliptic bases to show that, for infinitely many
squarefree integers and infinitely many values of , we can encode
torus elements, to a small fixed overhead and to -tuples of
elements, in quasi-linear time in .
This improves upon previously known algorithms, which all have a
quasi-quadratic complexity. As a result, the cost of the encoding phase is now
negligible in Diffie-Hellman cryptographic schemes
TS2PACK: A Two-Level Tabu Search for the Three-dimensional Bin Packing Problem
Three-dimensional orthogonal bin packing is a problem NP-hard in the strong sense where a set of boxes must be orthogonally packed into the minimum number of three-dimensional bins. We present a two-level tabu search for this problem. The first-level aims to reduce the number of bins. The second optimizes the packing of the bins. This latter procedure is based on the Interval Graph representation of the packing, proposed by Fekete and Schepers, which reduces the size of the search space. We also introduce a general method to increase the size of the associated neighborhoods, and thus the quality of the search, without increasing the overall complexity of the algorithm. Extensive computational results on benchmark problem instances show the effectiveness of the proposed approach, obtaining better results compared to the existing one
Algorithmic problems for free-abelian times free groups
We study direct products of free-abelian and free groups with special
emphasis on algorithmic problems. After giving natural extensions of standard
notions into that family, we find an explicit expression for an arbitrary
endomorphism of \ZZ^m \times F_n. These tools are used to solve several
algorithmic and decision problems for \ZZ^m \times F_n : the membership
problem, the isomorphism problem, the finite index problem, the subgroup and
coset intersection problems, the fixed point problem, and the Whitehead
problem.Comment: 38 page
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