On a problem in lattice based Cryptography: the learning with errors problem

Lattice based Cryptography allows for homomorphic encryption so that computations can be
carried out on ciphertext. The learning with errors problem which hardness relates to various
well-known problems in lattice based Cryptography is used in many cryptosystems. In this talk,
we will discuss weak instances of this problem for classes of number fields studied by Eisentraeger,
Hallgren and Lauter, and present joint work with Lauter, Ozman, and Stange where we extend these
attacks to a larger class of number fields.