Recursive Lattice Reduction

13 years 2 months ago

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Abstract. Lattice reduction is known to be a very powerful tool in modern cryptanalysis. In the literature, there are many lattice reduction algorithms that have been proposed with various time complexity (from quadratic to subexponential). These algorithms can be utilized to ﬁnd a short vector of a lattice with a small norm. Over time, shorter vector will be found by incorporating these methods. In this paper, we take a different approach by presenting a methodology that can be applied to any lattice reduction algorithms, with the implication that enables us to ﬁnd a shorter vector (i.e. a smaller solution) while requiring shorter computation time. Instead of applying a lattice reduction algorithm to a complete lattice, we work on a sublattice with a smaller dimension chosen in the function of the lattice reduction algorithm that is being used. This way, the lattice reduction algorithm will be fully utilized and hence, it will produce a better solution. Furthermore, as the dimensi...

Thomas Plantard, Willy Susilo

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