Lattice based cryptography involves constructions of crypto primitives(one which forms the basis for any cryptographic protocol/algorithms) using the mathematical structures, Lattice. This type of constructions are widely used in Quantum safe cryptographic protocols, for ex: CRYSTALS Kyber/Dilithium, Falcon, FrodoKEM(not standardized due to low performance), NTRUEncrypt & SWIFFT.
Though not all, still a lot of lattice based constructions are safe from both quantum & classical computers, unlike Diffie-Hellman Key Exchange, ECC & RSA.
Technically, Lattices are discrete subgroups of Rn, i.e. it can be thought of as a regularly spaced grid of elements/points stretching up to infinity. In cryptography, we only consider integer lattices, which are those belonging to Zn.
The basis of a lattice, L can be written as:
