TY - BOOK
T1 - Efficient (ideal) lattice sieving using cross-polytope LSH
AU - Becker, Anja
AU - Laarhoven, T.M.M.
PY - 2015
Y1 - 2015
N2 - Combining the efficient cross-polytope locality-sensitive hash family of Terasawa and Tanaka with the heuristic lattice sieve algorithm of Micciancio and Voulgaris, we show how to obtain heuristic and practical speedups for solving the shortest vector problem (SVP) on both arbitrary and ideal lattices. In both cases, the asymptotic time complexity for solving SVP in dimension n is 2^(0.298n).
For any lattice, hashes can be computed in polynomial time, which makes our CPSieve algorithm much more practical than the SphereSieve of Laarhoven and De Weger, while the better asymptotic complexities imply that this algorithm will outperform the GaussSieve of Micciancio and Voulgaris and the HashSieve of Laarhoven in moderate dimensions as well. We performed tests to show this improvement in practice.
For ideal lattices, by observing that the hash of a shifted vector is a shift of the hash value of the original vector and constructing rerandomization matrices which preserve this property, we obtain not only a linear decrease in the space complexity, but also a linear speedup of the overall algorithm. We demonstrate the practicability of our cross-polytope ideal lattice sieve IdealCPSieve by applying the algorithm to cyclotomic ideal lattices from the ideal SVP challenge and to lattices which appear in the cryptanalysis of NTRU.
Keywords: (ideal) lattices, shortest vector problem, sieving algorithms, locality-sensitive hashing
AB - Combining the efficient cross-polytope locality-sensitive hash family of Terasawa and Tanaka with the heuristic lattice sieve algorithm of Micciancio and Voulgaris, we show how to obtain heuristic and practical speedups for solving the shortest vector problem (SVP) on both arbitrary and ideal lattices. In both cases, the asymptotic time complexity for solving SVP in dimension n is 2^(0.298n).
For any lattice, hashes can be computed in polynomial time, which makes our CPSieve algorithm much more practical than the SphereSieve of Laarhoven and De Weger, while the better asymptotic complexities imply that this algorithm will outperform the GaussSieve of Micciancio and Voulgaris and the HashSieve of Laarhoven in moderate dimensions as well. We performed tests to show this improvement in practice.
For ideal lattices, by observing that the hash of a shifted vector is a shift of the hash value of the original vector and constructing rerandomization matrices which preserve this property, we obtain not only a linear decrease in the space complexity, but also a linear speedup of the overall algorithm. We demonstrate the practicability of our cross-polytope ideal lattice sieve IdealCPSieve by applying the algorithm to cyclotomic ideal lattices from the ideal SVP challenge and to lattices which appear in the cryptanalysis of NTRU.
Keywords: (ideal) lattices, shortest vector problem, sieving algorithms, locality-sensitive hashing
M3 - Report
T3 - Cryptology ePrint Archive
BT - Efficient (ideal) lattice sieving using cross-polytope LSH
PB - IACR
ER -