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Abstract. There is a large gap between theory and practice in the complexities of sieving algorithms for solving the shortest vector problem in an arbitrary Euclidean lattice. In this paper, we work t...
The hardness of finding short vectors in ideals of cyclotomic number fields (hereafter, Ideal-SVP) can serve as a worst-case assumption for numerous efficient cryptosystems, via the average-case probl...
We describe an algorithm to solve the approximate Shortest Vector Problem for lattices corresponding to ideals of the ring of integers of an arbitrary number field KK. This algorithm has a pre-process...
In this work, we generalize the previous result to general ideals. We show an efficient way of finding a close enough principal multiple of any ideal by exploiting the classical theorem that, in our s...
In this paper, we propose a parallel implementation of LDSieve, a recently published sieving algorithm for the SVP, which achieves the best theoretical complexity to this day, on parallel shared-memor...
In 2014, the orthogonalized integer representation is presented indepently by Dan Ding etc and Fukase etc to solve SVP respectively by genetic algorithm and sampling technique, and both work have a...
In this paper, we propose a genetic algorithm for solving the shortest vector problem (SVP) based on sparse integer representations of short vectors in lattices as chromesomes, which, we prove, can ...
Lattice-based cryptography became a hot-topic in the past years because it seems to be quantum immune, i.e., resistant to attacks operated with quantum computers. The security of lattice-based cryptos...
In this paper, we propose a new phase-based enumeration algorithm based on two interesting and useful observations for y-sparse representations of short lattice vectors in lattices from SVP challeng...
In this paper, we assess the practicability of HashSieve, a recently proposed sieving algorithm for the Shortest Vector Problem (SVP) on lattices, on multi-core shared memory systems. To this end, we ...
In this paper, we report that we have solved the SVP Challenge over a 128-dimensional lattice in Ideal Lattice Challenge from TU Darmstadt, which is currently the highest dimension in the challenge th...
We present a study of the concrete complexity of solving instances of the unique shortest vector problem (uSVP). In particular, we study the complexity of solving the Learning with Errors (LWE) proble...

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