Public-key cryptosystems from the worst-case shortest vector problem

Chris Peikert
2009 Proceedings of the 41st annual ACM symposium on Symposium on theory of computing - STOC '09  
We construct public-key cryptosystems that are secure assuming the worst-case hardness of approximating the minimum distance of n-dimensional lattices to within small poly(n) factors. Prior cryptosystems with worst-case connections were based either on the shortest vector problem for a special class of lattices (Ajtai and Dwork, STOC 1997; Regev, J. ACM 2004), or on the conjectured hardness of lattice problems for quantum algorithms (Regev, STOC 2005). Our main technical innovation is a
more » ... n from variants of the shortest vector problem to corresponding versions of the "learning with errors" (LWE) problem; previously, only a quantum reduction of this kind was known. As an additional contribution, we construct a natural chosen ciphertext-secure cryptosystem having a much simpler description and tighter underlying worst-case approximation factor than prior schemes based on lattices.
doi:10.1145/1536414.1536461 dblp:conf/stoc/Peikert09 fatcat:23ygv3hvgreshdh2bwobrimb6m