Faster sieving for shortest lattice vectors using spherical locality-sensitive hashing

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16 Citaten (Scopus)

Samenvatting

Recently, it was shown that angular locality-sensitive hashing (LSH) can be used to significantly speed up lattice sieving, leading to heuristic time and space complexities for solving the shortest vector problem (SVP) of $2^{0.3366n + o(n)}$. We study the possibility of applying other LSH methods to sieving, and show that with the recent spherical LSH method of Andoni et al.\ we can heuristically solve SVP in time and space $2^{0.2972n + o(n)}$. We further show that a practical variant of the resulting SphereSieve is very similar to Wang et al.'s two-level sieve, with the key difference that we impose an order on the outer list of centers. Keywords: lattices, shortest vector problem, sieving algorithms, (approximate) nearest neighbor problem, locality-sensitive hashing
Originele taal-2Engels
TitelProgress in Cryptology - LATINCRYPT 2015 (Fourth International Conference on Cryptology and Information Security in Latin America, Guadalajara, Mexico, August 23-26, 2015)
RedacteurenK. Lauter, F. Rodríguez-Henríquez
Plaats van productieBerlin
UitgeverijSpringer
Pagina's101-118
ISBN van geprinte versie978-3-319-22173-1
DOI's
StatusGepubliceerd - 2015

Publicatie series

NaamLecture Notes in Computer Science
Volume9230
ISSN van geprinte versie0302-9743

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  • Citeer dit

    Laarhoven, T. M. M., & Weger, de, B. M. M. (2015). Faster sieving for shortest lattice vectors using spherical locality-sensitive hashing. In K. Lauter, & F. Rodríguez-Henríquez (editors), Progress in Cryptology - LATINCRYPT 2015 (Fourth International Conference on Cryptology and Information Security in Latin America, Guadalajara, Mexico, August 23-26, 2015) (blz. 101-118). (Lecture Notes in Computer Science; Vol. 9230). Springer. https://doi.org/10.1007/978-3-319-22174-8_6