… of Table II, where a defined number of Y consecutive fixed complexity structures, resulting in
… This altered algorithm shall therefore be called fixed complexity LLL algorithm (fcLLL). Note …

… In this paper, variants of the LLL algorithm with either reduced or fixed complexity are …
Our proposed algorithm in this Section is based on the fixedcomplexity LLL algorithm given …

… algorithm. Last, we demonstrate that the proposed fcLLL exhibits better performance than the
LLL … paper, we adopt the complex-valued version for LLL and fcLLL algorithms. The rest of …

… by roughly 50% [26], a rigorous complexity analysis is yet to be … the complexity of complex
LLL and propose variants of the LLL algorithm with either lower theoretic complexity or a fixed-…

The Lenstra–Lenstra–Lovász lattice basis reduction algorithm (called LLL or ${\rm L}^3$) is
a fundamental tool in computational number theory and theoretical computer science, which …

… Thus, we compare the complexity of LLL reduction algorithms in terms of the required
number of flops rather than the number of LLL loops in this paper. The worst-case complexity of …

… a fixed complexity LLL (fcLLL) algorithm by adopting fixed column traverse strategy and limited
LLL loop … To describe LLL algorithm, we first give the definition of the LLL-reduced basis. …

… recall what is the LLL algorithm and we give … complexity of the optimal LLL algorithm in
three-dimensional case. Finally, in Section 5, we prove that in fixed dimension, the LLL algorithm …

… Performance of ELLL Variants with Fixed Complexity Firstly, we consider the fixed-complexity
cases, ie, the maximum number of the ELLL iterations is fixed in each LR algorithm. Fig. 1 …

… the complexity of the LLL algorithm in the case when the approximation parameter of the
algorithm has … Here we prove that, for any fixed dimension n, the number of iterations of the LLL …