1. A lattice-based cryptography method comprising: obtaining, from a memory of a computer system, a first parameter for a lattice-based cryptography system, wherein the first parameter is a first global system parameter of the lattice-based cryptography system, the first parameter comprising a first set of values; obtaining pseudorandom data from a pseudorandom generator; obtaining a mask, generating, by operation of one or more processors of the computer system, a lattice basis parameter for the lattice-based cryptography system based on the first parameter and the pseudorandom data, the lattice basis parameter comprising a second set of values, the second set of values comprising: a first subset selected from the first set of values based on the mask; and a second subset based on the pseudorandom data, independent of the first parameter, wherein the lattice basis parameter comprises a first matrix having m columns, and the mask comprises a second matrix having a weight ω, where ω≥m; and establishing communication with another computer system using the lattice basis parameter in an execution of a lattice-based cryptography protocol in a communication system.