Sieving for shortest vectors in ideal lattices: a practical perspective
| Autor: | Joppe W. Bos, Michael Naehrig, Joop van de Pol |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Computer Networks and Communications
Computer science Computation Cryptography 010103 numerical & computational mathematics 02 engineering and technology Topology 01 natural sciences law.invention symbols.namesake Sieve law Lattice (order) 0202 electrical engineering electronic engineering information engineering Short vector 0101 mathematics business.industry Applied Mathematics Gauss 020206 networking & telecommunications New variant Computational Mathematics Fourier transform Computational Theory and Mathematics symbols 020201 artificial intelligence & image processing business |
| Zdroj: | International Journal of Applied Cryptography |
| ISSN: | 1753-0563 |
| DOI: | 10.1504/ijact.2017.10010312 |
| Popis: | The security of many lattice-based cryptographic schemes relies on the hardness of finding short vectors in integral lattices. We propose a new variant of the parallel Gauss sieve algorithm to compute such short vectors. It combines favourable properties of previous approaches resulting in reduced run time and memory requirement per node. Our publicly available implementation outperforms all previous Gauss sieve approaches for dimensions 80, 88, and 96. When computing short vectors in ideal lattices, we show how to reduce the number of multiplications and comparisons by using a symbolic Fourier transform. We computed a short vector in a negacyclic ideal lattice of dimension 128 in less than nine days on 1,024 cores, more than twice as fast as the recent record computation for the same lattice on the same computer hardware. |
| Databáze: | OpenAIRE |
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