Complexity of an extended lattice reduction algorithm
نویسنده
چکیده
We consider the complexity of a Lenstra Lenstra Lovász lattice reduction algorithm ([LLL]) in which the vectors are allowed to be linearly dependent and in which one also asks for the matrix of the transformation from the given generators to the reduced basis. The main problem will be to show that the entries of the transformation matrix remain bounded through the algorithm, with a reasonable bound. Here the difficulty is of course that due to the dependence of the generators the transformation is not determined by the basis. To remedy this we work with two inner products and apply the LLL methods to both.
منابع مشابه
TREE AUTOMATA BASED ON COMPLETE RESIDUATED LATTICE-VALUED LOGIC: REDUCTION ALGORITHM AND DECISION PROBLEMS
In this paper, at first we define the concepts of response function and accessible states of a complete residuated lattice-valued (for simplicity we write $mathcal{L}$-valued) tree automaton with a threshold $c.$ Then, related to these concepts, we prove some lemmas and theorems that are applied in considering some decision problems such as finiteness-value and emptiness-value of recognizable t...
متن کاملTime and Space Complexity Reduction of a Cryptanalysis Algorithm
Binary Decision Diagram (in short BDD) is an efficient data structure which has been used widely in computer science and engineering. BDD-based attack in key stream cryptanalysis is one of the best forms of attack in its category. In this paper, we propose a new key stream attack which is based on ZDD(Zero-suppressed BDD). We show how a ZDD-based key stream attack is more efficient in time and ...
متن کاملNew Factorization Algorithms for Channel-Factorization Aided MMSE Receiver in MIMO Systems
Channel-factorization aided detector (CFAD) is one of the important low-complexity detectors used in multiple input, multiple output (MIMO) receivers. Through channel factorization, this method transforms the original MIMO system into an equivalent system with a betterconditioned channel where detection is performed with a low-complexity detector; the estimate is then transferred back to the or...
متن کاملLow - Dimensional Lattice Basis Reduction Revisited ( Extended Abstract )
Most of the interesting algorithmic problems in the geometry of numbers are NP-hard as the lattice dimension increases. This article deals with the low-dimensional case. We study a greedy lattice basis reduction algorithm for the Euclidean norm, which is arguably the most natural lattice basis reduction algorithm, because it is a straightforward generalization of the well-known two-dimensional ...
متن کاملTime and Space Complexity Reduction of a Cryptanalysis Algorithm
Binary Decision Diagram (in short BDD) is an efficient data structure which has been used widely in computer science and engineering. BDD-based attack in key stream cryptanalysis is one of the best forms of attack in its category. In this paper, we propose a new key stream attack which is based on ZDD(Zero-suppressed BDD). We show how a ZDD-based key stream attack is more efficient in time and ...
متن کامل